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Princ of Microeconomics ECON 2106
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A SHORT COURSE IN ECONOMICS CLASS NOTES TO ACCOMPANY ECON 2106 JAMES H MURPHY PhD Richards College of Business University of West Georgia Copyright 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 TOPIC 1 CONSUMER THEORY 10 INTRODUCTION Given the bewilderingly vast array of goods and services to choose quotom as well as individuals39 limited incomes how do economists explain individuals39 choices Economists have developed the theory of consumer choice to answer this question According to this theory a given individual or household allocates his or her income among the available consumption goods to maximize his overall utility or satisfaction subject to his income level or budget This process involves two key components 1 the budget constraint determined by the prices of goods and the individual39s income 2 the individual39s relative preference for the various goods as represented by his indifference map 11 THE BUDGET CONSTRAINT The budget constraint represents the set of bundles of goods various combinations of different amounts of each of the available goods which when purchased exhaust the individual39s income Say there are only two goods X and Y Let px and py be the prices of good X and good Y respectively I is the individual39s income in the time period Then in our two good case we can represent the budget constraint as follows pxXpyYI 111 The Intercepts of the Budget Line If the individual is unable to affect prices by his purchasing decisions then prices for the purposes of deriving the budget constraint are fixed This makes the budget constraint a line we can graph in XY space Let the amount of good Y be graphed on the Y vertical axis and the amount of good X be graphed on the X horizontal axis The Y intercept is calculated by assuming all income is spent on good Y Dividing income I by the price of good Y py gives us the maximum affordable amount of good Y To determine the X intercept of the budget line we divide income I by the price of good X px 112 The Slope of the Budget Line The slope of the budget line also called the budget constraint is determined by the negative of the ratio of the price of the good on the horizontal axis in this case good X to the price of the good on the vertical axis in this case good Y Pricegaod an x axis Price good on y axis Slope of budget constraint PxPy gives the relative price of the good on the horizontal axis good X in terms of the good on the vertical axis good Y 113 What happens if Changes in prices or income level can change the intercepts and slopes of the budget constraint See your class notes for graphic examples of the effects of the following changes 1131 Price decrease for good on horizontal axis A decrease in the price of the good on the horizontal axis will cause the horizontal intercept to move farther to the right you can buy more of good X The economic interpretation of this is that as the price of the good has decreased if you spend all your income on the good who39s price has decreased you would be able to buy more of the good This also causes the budget line to become atter e g numeric value of slope decreasing from 2 to 1 1132 Price increase for good on horizontal axis An increase in the price of the good on the horizontal axis will cause the horizontal intercept to move to the left you are able to buy less of good X The economic interpretation of this is that as the price of the good has increased if you spend all your income on the good who39s price has increased you will be able to afford less of the good This causes the budget line to become steeper eg slope goes from 2 to 4 1133 Increase in the income level An increase in the income level does not change relative prices recall the slope of budget line is the negative of the relative price of good X in terms of good Y so the slope of the budget line does not change however as the intercepts are the ratios of income to the respective prices an increase in income will increase the amount of each of the goods an individual could afford if he purchased only one good 1134 An interesting read this as possible test question 114 What happens if income the price of good X and the price of good Y all double Can I afford this You can expect questions of the following variety Let px 200 py 400 I 10000 Is the bundle of goods consisting of 25 units of X and 20 units of Y on the budget line below the budget line I39ve got money to spare after buying it not affordable Can39t tell from information given 909quot You answer this by applying the formula for the budget constraint pxXpyYI You39d apply this by plugging in the prices and number of units of the goods and seeing if it added up to more less or just equal to the income level If the money required to purchase the bundle is more than income you can39t afford the bundle of goods You39d answer If the cash required to purchase the bundle just equaled your Income you39d answer quota quot If the money needed to purchase the bundle were less than your income you39d answer quotbquot Answer quotdquot would only apply if I had not given you Income the prices of all goods purchased and the amounts of all u u C goods to be purchased in that case 115 What you need to know about Budget Lines 1 2 It39s de nition see text How to nd the intercept for both axes How to plot the budget line draw a straight line connecting the intercepts How to determine the slope of the budget line What is the interpretation of the ratio of the prices What happens to the budget line if the price of x price of y or income changes How to determine if a bundle of goods say 12 Xs and 3 Ys is either a b 0 on the budget line just affordable inside the budget line we have income to spare after buying the bundle not affordable given our income you cannot tell om the given information Exercise 1 1 Let income 300month the price of a pair of shoes 60pair the price of baseball tickets 20ticket 1 How many pairs of shoes could you afford per month if you bought only shoes 2 If pairs of shoes are graphed on the xaxis What would the xintercept be 3 How many baseball tickets could you afford per month if you bought only baseball tickets 4 If baseball tickets are graphed on the y axis What would the yintercept be 5 What is the relative price of a pair of shoes in terms of baseball tickets 6 What is the slope of the budget line representing the price income scenario listed above 7 Is the bundle of three pairs of shoes and six baseball tickets a Affordable with some income left over b Not affordable c Just affordable d Unable to determine from information given Exercise 11 continued 8 Graph below the budget line implied by our scenario Also plot the point representing the goods bundle consisting of three pairs of shoes and six baseball tickets TOPIC 1 CONSUMER THEORY 12 CONSUMER PREFERENCES Our model of consumer choice stresses allocating income among the available goods to maximize satisfaction Often the terms satisfaction and utility are used interchangably Definition 121 Utility happiness or satisfaction from consumption of goods Two related concepts are marginal utility and indifference curves Definition 122 Marginal utility of a good the change in satisfaction or happiness from consuming one additional unit of the good De nition 123 Indifference curve a graphical representation of the set of all bundles of goods with which a consumer considers himself equally satisfied We will represent individual preferences with indifference maps These are sets of indifference curves There are an infinite number of indifference curves in any given indifference map 122 A few assumptions We39ll assume a few properties for our consumer Assumption 1 he always prefers more of a good to less of the good Assumption 2 he will always be able to and will determine whether he prefers some bundle of goods A to another bundle B prefers bundle B to bundle A is indifferent between bundle A and bundle B Assumption 3 If he prefers A to B and B to C then he prefers A to C A quick example may be in order Say Wimpy prefers a hamburger to a slice of pizza Wimpy also prefers a slice of pizza to a piece of sushi We39re assuming that Wimpy prefers a hamburger to a piece of sushi Assumption 4 Our consumer prefers diversity in his consumption bundle Rather than choosing a bundle consisting of either 10 slices of pizza and no hamburgers or another bundle consisting of no slices of pizza and 10 hamburger our consumer probably not Wimpy prefers a bundle consisting of some pizza and some hamburgers 123 Properties of the indifference curves we ll assume in this course 1 Every possible combination of goods is on some indifference curve This follows from assumption 2 Indifference curves are negatively sloped because you must get more of one good to maintain your level of satisfaction when you give up some of the other good Note This assumes the consumer is choosing between two GOODStwo things he would like more of The indifference curves would be shaped differently for a choice between a GOOD and a BAD for example between chocolate and air pollution Don39t worry too much about this now In this course we39ll always be dealing with two GOODS unless I explicitly say otherwise Indifference curves that are lrther from the origin are preferable because they represent bundles containing more of each good This follows from assumption 1 more is better Indifference curves never intersect The slope of an indifference curve re ects the tradeoff k between goods an individual is willing to make and remain equally satisfied based on his preferences or tastes Let MUx and MUy represent the marginal utility of goods X and Y respectively We can represent the tradeoff at any point on an indifference curve as lIUxMUy or the quotrelative subjective benefits marginal utilities of the goods Byms and Stone This tradeoff is often measured by the marginal rate of substitution or MRS which is defined as quotthe negative of the slope of an indifference curve at a given point on a particular indifference curvequot Hence change of good Y along an indifference curve MRS change of good X along an indij rence curve xy Indifference curves are convex bowed in toward the origin This is a consequence of the Law of Diminishing Marginal Rate of Substitution As the consumer consumes more of good X he becomes willing to sacrifice increasingly smaller quantities of good Y to gain more of X and still remain equally satisfied ie meaning on the same indifference curve This comes from assumption 4 124 What do I need to know about indifference curves 1 That every possible consumption bundle combination of good X and good Y is on some indifference curve For our purposes in this course they39re negatively sloped Compared to a given bundle any bundle with more of either or more of both goods Will be preferred to the initial bundle of goods This means the second bundle is on an indifference curve containing preferred bundles This curve will be found to the right above or both to the right and above the initial indifference curve as long as more is better Indifference curves do not intersect The slope of an indifference curve can be measured by the change in good Y consumption necessary to keep a consumer quotindifferen quot in response to a one unit increase in the consumption of good X The negative of this slope is referred to as the Marginal Rate of Substitution MRS Indifference curves obeying the Law of Diminishing Marginal Rate of Substitution are convex This means they39re shaped like a smile not a frown TOPIC 1 CONSUMER THEORY 13 THE CONSUIVIER S CHOICE UTILITY MAXIMIZATION Now let39s put the budget constraint together with indifference maps to see why we buy what we do Recall that the Budget Constraint tells us what we can afford to buy The indifference map tells us how we subjectively value each bundle The consumer seeks to consume a bundle of goods that is on the indifference curve that contains the most preferred bundles that he can afford This means that the consumption bundle must be both on the indifference curve and the budget line If the consumer chooses positive amounts of both goods and indifference curves are smiling then this equilibrium bundle is found where an indifference curve is tangent to the budget line By tangent we mean the bundle is both on the indifference curve and on the budget line Also at the point of tangency the combination of the two goods where the budget line is tangent to the indifference curve the slope of the budget line which is pxpy is equal to the slope of the indifference curve which is equal to MUxMUy Thus we can equate the two slope expressions pxpy MUxMUy We can further rearrange this to get MUxpx MUpy This is the quotPrinciple of equ al marginal utilities per dollar A consumer maximizes utility when the last dollar spent on any good generates the same satisfaction as the last dollar spent on every other goodquot Bymes and Stone p 471 We can also look at the equal slope condition in another way The MRS which is the negative of the slope of the indifference curve is equal to AyAX the A is shorthand for quotchange inquot The MRS represents the amount of good Y an individual is willing to give up to gain an additional unit of good X The slope of the budget line represents the opportunity cost of an additional unit of good X in terms of good Y We would expect the individual to quottrade with the marketquot until his subjective tradeoff as measured by the slope of his indifference curve is equal to the market tradeoff between the two goods as represented by the slope of the budget line 131 132 Conditions for Equilibrium A bundle which consists of positive amounts of both goods is an equilibrium if it meets the following two conditions 1 The Slope Condition The slope of the budget line and the slope of the indifference curve are equal This can be described many ways Either MRS pxpy pxpy MUxMUy AyAX pxpy where AyAX refers to the slope of the indifference curve The Budget Condition The bundle is on not inside the budget line All income is used to purchase the bundle so no purchasing power is wasted What do I need to know about Consumer Equilibrium 1 2 The conditions for equilibrium They39re listed in 131 If I give you the slope of an indifference curve or any expression that would allow you to find it such as MRS or MUx and lVIUy the price for the two goods income and a two or three prospective good bundles which of the bundles wouldbe an equilibrium You39d answer this by seeing which of the bundles meets the two Equilibrium conditions listed in 131 You39ll see plenty of examples before the first exam You should also be able to identify an equilibrium quotom a graph Exercise 13Part A Consumer Equilibrium Sample Question 1 Is the bundle 4 units of Good X and 10 units of Good Y Where the MU 8 and the MUy 4 and px 10 and py 5 an equilibrium for this consumer when I 100 Consumer Equilibrium Sample Question 2 What about the bundle 20 units of Good X and 10 Units of Good Y Where AyAX on the indifference curve at the bundle is 12 Here px 2 py 6 I 100 Consumer Equilibrium Sample Question 3 What about I 100 px 20 py 4 X 3 Y 10 MRS 5 at the point GoodX 3 Good Y 10 Exercise 13Part B Joe s income is 300month the price ofa pair of shoes is 50 and the price ofa baseball ticket is 25 Plot Joe s budget line on the graph below Put pairs of shoes on the x axis and baseball tickets on the y axis Exercise 13Part B continued 2 What is the market tradeoff Joe faces for shoes in terms of baseball tickets implied by the price of a pair of shoes and the price of baseball tickets given above If the MRsshoesim of Joe s indifference curve through the bundle 4 pairs of shoes and 4 baseball tickets is l at the point 44 how many baseball tickets is Joe Willing to give up to get another pair of shoes Is the bundle 4 pairs of shoes and 4 baseball tickets an equilibrium consumption bundle for Joe The MRSmeSLlckets of Barbara s indi erence curve through the bundle 4 pairs of shoes and 4 baseball tickets is 2 How many baseball tickets is Barbara Willing to give up to obtain one additional pair of shoes Suppose Barbara also had an income of 300 and faced the same prices Is the consumption bundle 4 pairs of shoes and 4 baseball tickets an equilibrium consumption bundle for her given that the MRSmeS mm for her indifference curve passing through the point 44 is 2 On the graph above draw a wellbehaved indifference curve that represents Barbara s preferences at the point representing 4 pairs of shoes and 4 baseball tickets TOPIC 1 CONSUMER THEORY 14 UTILITY MAXIMIZATION AND INCOME CHANGES Before we move on we need to introduce a common notion in economics ceteris paribus This is Latin for quotall other things being equalquot When we want to determine the effects of a change in income on consumption of good X we invoke the ceteris paribus assumption to emphasize that we are interested in the effects of changing only income holding constant all other variables that could affect consumption of good X This allows us to separate out the effects on good X consumption directly attributable to a change of income Now on to income changes ceteris paribus We know that two conditions must be met for a consumption bundle containing some of both goods to be an equilibrium 1 the Budget Condition 2 the Equal Slope Condition We can use these two conditions to determine the effects of a change in income on consumption To do so we39ll use these same two conditions to determine which of many possible combinations of goods represent our new equilibrium 141 Determining the new equilibrium The new income level affects the budget line The changed budget line will in turn affect the set of bundles that meet the budget conditionequilibrium must be among the set of bundles where we spend all of our income The Budget Condition says our new equilibrium must be on the appropriate budget line The steps to determine a new equilibrium in response to an income change are 1 Recompute the Budget Line using the new level of income in the equation pxX pyY I where I represents the new income level As the ratio of the prices hasn39t change the slope of the budget line is unaffected by the change in income If income increases the budget line shifts to the right parallel to the initial budget line representing an increase in purchasing power the individual is able to consume larger quantities of goods Remember that bundles to the right or above our initial bundle represent bundles of goods offering more satisfaction Why Because larger amounts of goods are represented by bundles to the right and aboveand more is better This means we can now purchase bundles preferred to our original choice However if income decreases the parallel shift is to the left representing a decrease in purchasing power Note that increases in income make previously unaffordable bundles of goods now affordable Similarly an income decrease causes previously affordable bundles of goods to now become unaffordable 2 Use the Budget Condition and the Slope Condition to find the new equilibrium Using these two conditions is equivalent to nding the point of tangency between the highest possible indifference curve and the new budget line 142 Normal and Inferior Goods If the equilibrium consumption of a good increases in response to an increase in income ceteris paribus then we say the good is a normal good Most goods fit into this category If the equilibrium consumption of a good decreases in response to an increase in income ceterisparibus then we say the good is an inferior good The classic example of an inferior good is potatoes in Ireland If you were a poor Irishman a large proportion of your diet would consist of potatoes However if you suddenly struck it rich say your English uncle left you a large inheritance then you39d consume fewer potatoes in favor of other foods such as kidney pie Exercise 14 If Joe s income goes from 10000 to 15000 per year his consumption of steak increases from 20 steaks per year to 25 steaks per year Assuming all other factors that could in uence Joe s steak consumption do not change we would conclude steaks are a an good for Joe If Barbara s income changes from 25000 to 50000 per year her consumption of steak changes from 10 steaks per year to 8 steaks per year Assuming all other factors that could in uence Barbara s steak consumption do not change we would conclude steaks are a an good for Barbara Mike s income changes from 10000 to 5000 per year causing his consumption of Slim J ims to change from 100 to 75 per year If all the other factors that could affect Mike s consumption of Slim Jims do not change then we conclude that Slim Jims are a an good for Mike Dan s income changes from 125000 to 75000 per year causing his consumption of Slim Jims to change from 15 to 25 per year If all the other factors that could affect Dan s consumption of Slim Jims do not change then we conclude that Slim Jims are a an good for Dan TOPIC 1 CONSUMER THEORY 15 UTILITY MAXIMIZATION AND PRICE CHANGES What happens if the price of one of the two goods changes How does the equilibrium quantity of goods consumed change in response to a change in the price of a good 151 The New Equilibrium Recall from our discussion in Section 11 what happens to the budget line in the case of a decrease in the price of the good on the horizontal axis The horizontal intercept moves rightward and the budget line becomes atter To find the new equilibrium we again apply our equilibrium conditions 1 the budget condition we must use all our income now taking into account the effects of a lower price for good X 2 the slope condition the slope of the budget line must be equal to the slope of the indifference curve where we exhaust all our income now taking into account the new price of good X To find the consumer39s new equilibrium we apply the same equilibrium conditions as before However now there39s a new price for good X let39s call it pxl We again find the point where the highest attainable indifference curve39s slope is equal to the slope of the budget line Now the relevant price for good X is pxl This causes the slope of the budget line to change to pxlpy note that the price of good Y has not changed The new equilibrium will be on a point on an indifference curve where the indifference curve39s slope is equal to the negative of this new price ratio The new equilibrium will also have to meet the budget condition Since the price of good X has changed the new equilibrium will have to just exhaust available income using the new price of good X in the budget constraint In most cases the quantity consumed of good X will increase in response to this price change There are really two factors at work when px decreases First for any bundle of goods containing at least some of good X there is a change in the amount of the good who39s price has changed that is due to a change in the effective purchasing power of a given level of income Economists refer to this as the income effect For normal goods the income effect causes more of the good to be consumed Secondly even if there was no increase in effective purchasing power the relative price of good X in terms of good Y has changed For the case of a price decrease of good X the relative price of good X has decreased This also causes consumption of good X to change Economists refer to the effect on quantity consumed that is caused only by relative price changes as the substitution effect 152 The Substitution Effect The substitution effect is the change in the consumption bundle chosen that is attributable only to the change in relative prices An easy way to look at the substitution effect is to use the first of our two conditions for the consumer39s equilibrium the equal slope condition The equal slope condition states that p py the slope of the indifference curve If px decreases then the slope of the budget line pxpy increases meaning the budget line becomes atter eg the slope increases quotom 12 to 13 a less negative number If our indifference curves have the six properties then the equal slope condition can only be met by moving to a bundle of goods that contains more of good X The substitution effect of a price decrease increase will increase decrease the consumption of the good who39s price has decreased increased as long as our indifference curves possess the six properties Graphically we represent the substitution effect on the good who39s price has changed as the change in the quantity chosen of the good as we change the slope of the initial budget line to re ect the new price ratio While we change the slope of the budget line we continue to maintain the tangency of the budget line and the initial indifference curve until we meet the slope condition using the new relative price ratio and the old indifference curve The process is similar to swivelling the budget line along the initial indifference curve until we reach the new budget line slope as determined by the new price of good X and the old price of good Y When we talk about the quotsubstitution effectquot in general we are referring to this movement along the initial indifference curve from the initial consumption bundle to the point of tangency between the initial indifference curve and the quotpseudobudgetquot line resulting from changing relative prices but keeping effective purchasing power and hence satisfaction constant 153 The Income Effect The income effect represents the change in the consumption bundle from the initial equilibrium to the final equilibrium that is attributable only to an increase decrease in purchasing power that resulted from a decrease increase in the price of a good in this case good X For a normal good the income effect of a price decrease is positive For an inferior good the income effect of a price decrease is negative Once we39ve swivelled the budget line to re ect the new price ratio for the purposes of determining the substitution effect the income effect is the change in the consumption bundle represented by the movement from the point of tangency between the quotpseudobudget line and the old indifference curve to the new equilibrium represented by the point of tangency between the new budget line and the new indifference curve 154 What you need to know about the effects of income and price changes 1 If I draw you an indifference map with budget lines and a set of equilibria you should be able to tell me if the resulting equilibria are the result of an income or price change If I show you an indifference map with budget lines re ecting two different income levels and the corresponding equilibria you should be able to tell me if the goods are normal or inferior goods If I show you an indifference map with budget lines that re ect a price change you should be able to identify the substitution and income effects You should also be able to tell me whether the goods are normal or inferior You should understand the concept of ceteris paribus You should know the definition of a normal good a good for which an individual consumes increasing quantities as his income increases and an inferior good a good for which the consumer decreases the quantity consumed as his income increases Ticks Exercise 15 Depicted to the left is Bob s indifference map and budget line under two price scenarios Bob s initial equilibrium is at point A on indifference curve 10 Then the price of shoes decreases This results in Bob choosing bundle C Answer the following questions below concerning the effects of this price change on Bob s consumption patterns ts 1 The effect is the part of the total change in Bob s consumption bundle that is due only to the change in the relative D Shoes price of shoes The effect is the part of the total change in Bob s consumption bundle that is due only to the increase in effective purchasing power meaning the part that allows Bob to reach higher indifference curves The total effect of the price change on Bob s consumption is represented by the movement from point to point The substitution effect is the change in Bob s consumption bundle that is represented by movement from point to point The income effect is the change in Bob s consumption bundle that is represented by movement from point to point The substitution effect on shoes is represented by the movement from point point The income effect on shoes is represented by the movement from point point Shoes are normal inferior goods for Bob Tickets are normal inferior goods for Bob TOPIC 1 CONSUMER THEORY 16 THE INDIVIDUAL39S DEMAND RELATIONSHIP What would happen if we systematically changed the price of a good so that we could see how the quantity of a good an individual purchases is related to the price of the same good ceteris paribus This is the notion behind individual demand Individual demand is the relationship between the amount of a given good a particular consumer is willing and able to purchase per time period and the price of the given good holding all other factors that could affect this amount constant We will represent these individual demand relationships in a number of wayseither as a graph as a table or as an equation 161 Determining the individual39s demand relationship How do we determine the individual39s demand curve We vary the price of a good say good X Then we determine the individual39s equilibrium based on the tangency between the highest attainable affordable indifference curve and the budget line Varying the price of good X gives us a number of equilibrium combinations of px and the amount of good X purchased The relationship between the quantity of good X an individual consumes usually graphed on the horizontal axis and the price of good X usually graphed on the vertical axis is the individual39s demand curve ceteris paribus Recall all the factors that went into the consumer39s equilibrium decision his preferences his indifference map the price of good Y his income as well as the price of good X In deriving the individual39s demand curve we hold all these other factors besides the price of the good of interest in this case good X constant 162 Changes in Demand versus Changes in Quantity Demanded Changing these other factors can shift the individual39s demand curve a demand relationship represented graphically If a change in one of these other variables causes the individual to purchase more of a good good X in our example at the same price then we say that demand for good X has increased Graphically this is represented as a rightward shift of the individual39s demand curve If in response to a change in one of these other variables the individual purchases less at the same price then we say that demand has decreased This is represented by a leftward shift of the demand curve When we say quotdemand changesquot we are referring to the entire curve shifting Economists contrast quotdemand changesquot with quotchanges in the quantity demandedquot A quotchange in the quantity demandedquot is a movement along a given demand curve in response to a change in the price of the same good If the price of chalk declined and consequently the quantity of chalk consumed increases we refer to this as an increase in the quantity demanded of chalk The Law of Demand There is an inverse relationship between quantity demanded and price of 22 a good ceteris paribus 163 Individual Demand Shift Variables Recall that individual demand is the relationship between the price of a certain good for example good X and the quantity of good X an individual is able and willing to purchase at each price ceteris paribus Underlying that relationship there are a number of variables that can change the quantity an individual is willing and able to consume at a given price We refer to these variables as shift variables Shift variables do exactly thatthey cause the demand curve demand depicted graphically to shift either to the right indicating a greater quantity the individual is willing and able to purchase at each price or to the left indicating a decrease in the quantity of the good an individual is willing and able to purchase at each price Alternatively recall that the ceteris paribus assumption quotall else being equalquot is invoked in defining individual demand Demand curve shifts are the result of changing an all else being equal variable In this class we39re going to concern ourselves with four variables that can shift individual demand income I the price of substitutes PS the price of complements PC and preferences PR First we39ll often use symbols for shorthand Below I39ve listed some of these symbols and their interpretation T means increase 1 means decrease a means shift to the right as an increase in demand is a rightward shift 6 means shift to the left means implies 1631 Income Normal goods If good X is a normal good then IT D a If good X is a normal good then Ii Dx 6 Inferior goods If goodX is an inferior good then IT Dx 9 If good X is an inferior good then Ii D a 1632 Preferences Anything that changes the indifference map to increase the attractiveness of a good such as more advertising positive government reports etc causes an increase in demand An example would be if advertising for hotdogs increases causing consumers to find hotdogs more enticing then Dhotdogs Anything that changes the indifference map to decrease the attractiveness of a good causes a decrease in demand For example a government report saying hotdogs cause cancer would decrease the demand for hotdogs Dhotdogs 9 1633 Price of Substitutes Substitute goods are goods which serve the same purpose in providing consumer satisfaction For example hamburgers and hotdogs both roughly fulfill the same needquick greasy food that clogs your arteries The consumption of substitutes is usually characterized by an quoteitherorquot choice For example at a baseball game you may want either a hamburger or a hotdog If the price of hamburgers a substitute good for hotdogs increases then the demand for hotdogs increases More generically if we39re concerned with good X and good X and good B are substitutes then TPB Dxe Conversely if the price of a substitute good decreases then the demand for the initial good decreases Once again using goods X and B this relationship can be represented as iPB Dxe 1634 Price of Complements Complement goods are goods we tend to consume together For example I might nd the prospect of a eating only mustard revolting however if I can get mustard on my hotdog then I39m rather happy about consuming mustard If the price of hotdogs increases then due to the Law of Demand my quantity demanded of hotdogs will decrease That in turn will tend to cause my consumption of mustard to decrease as I can39t stand mustard unless it s consumed with on a hotdog So a price increase of a complementary good tends to decrease the demand of the other good Let39s let good C be a complement to good X If PC increases then the demand for good X decreases More generally in notational shorthand T P DX 6 complementto good x Conversely applying the same logic 1 P DX a complementto good x j 1635 Other Shift Variables Textbooks frequently list the number of buyers expectations and govt policy as other shift variables We39ll concentrate on the four variables mentioned above as shift variables for individual demand curves Exercise 16 D1 D2 and D3 represent three of Kramer s demand curves for pizza Starting from point E indicate which is the most likely movement in response to the speci ed change Price of 5173 4 D x G P5 P3 n E 1 C F 1 D1 D2 D3 1 2 3 Slicex of pizza per day Useful information 1 Kramer considers pizza a normal good 2 Kramer considers pizza and hamburgers substitute goods 3 Kramer considers pizza and coke complement goods 4 Start each scenario at point E on demand curve D2 at a price level of 300 per slice of pizza Scenarios l Kramer s income increases 2 The price of a slice of pizza decreases to 100 3 The price of a can of coke increases to 100 4 The price of a slice of pizza increases to 500 5 Kramer s income decreases 6 The price of a hamburger declines to 200 7 The price of a coke decreases to 050 8 The price of a hamburger increases to 375 9 Kramer expects the price of pizza to increase tomorrow assume he can store pizza in his freezer 10 Kramer expects the price of pizza to decrease tomorrow TOPIC 2 DEMAND SUPPLY AND MARKET EQUILIBRIUM 21 MARKET DEMAND FOR A PURELY PRIVATE GOOD 21 H De nition market demand the relationship between the price of a good and the amount of the same good that all potential consumers are both able and willing to purchase per time period holding everything else that could affect this amount constant Note we sum horizontally for purely private goods For public goods we do something different as we ll see later in the course 212 Shift Variables To find the market demand curve for a private good we horizontally sum the individual demand curves at each price level This makes the market demand curve potentially sensitive to all the variables that could shift individual demand depending on the effect a change in the shift variables have on the various individual demands remember a good could be normal for one individual but inferior for another However when we are only dealing with market demand and supply curves unless I directly specify an individual demand or rm supply curve we39ll be referring to a market curve we39ll assume that the component individual or rm curves shift in the same direction so we can speak of an increase in income increasing market demand Therefore the shift variables for market demand mctions are Income Preferences Price of Complements Price of Substitutes plus one i shift variable we ll add for market demand the number of consumers Exercise 2 1 Consumer A and Consumer B s demand functions for cappuccino are given below If Consumer A and Consumer B are the only two potential buyers of cappuccino and cappuccino is a pure private good use the information given to derive the market demand table for cappuccino Consumer A s Consumer B s Market Demand Demand Demand Price Quantity Price Quantity Price Quantity per Demanded Demanded Demanded cup cupsday 300 0 300 l 300 250 l 250 2 250 200 2 200 3 200 150 3 150 4 150 100 4 100 5 100 75 5 75 6 75 TOPIC 2 DEMAND SUPPLY AND MARKET EQUILIBRIUM 22 FIRM S SUPPLY 221 De nition Firm39s Supply the relationship between the price of a good and the amount of the same good that a given rm is willing and able to offer for sale during a given period ceteris paribus Firm s supply can be depicted as a TABLE GRAPH or EQUATION 222 The Law of Supply All else being equal higher prices induce a rm to offer to sell more output for sale during a given period 223 Change in the Quanity Supplied versus Change in Supply As with the demand curve we ll make the distinction between a change in the quantity supplied and a change in supply A change in the quantity supplied refers to a change in the quantity a rm produces and offers to the market that is caused only by a change in the price of the good itself and hence is represented by movement along the same supply curve A change in supply refers to a change in the relationship between the price of the good and the quantity the rm is able and willing to supply at each price This is represented graphically as a shift of the rm s supply curve the rm s supply relationship depicted graphically The causes of rm supply shifts are given below in Section 224 224 SHIFT VARIABLES FOR THE FIRM SUPPLY CURVE Below are listed the four shift variables we ll concern ourselves with in this course These variables are l the technology the rm uses to produce the good 2 the prices of inputs into the production process 3 the prices of joint products and 4 the prices of substitutes in production Note that 3 the prices of j oint products and 4 the prices of substitutes in production imply the rm can produce more than one product 2241 Technology Improvement in technology used to produce good X 2 SX a Worsening of technology used to produce good X SX 9 2242 Input Prices T Price 1 Price 5on 5qu input for good x Input for good x 2243 Prices of Joint Products sxo SXF T PriceJ i Prlcejomtpmductofgoodx cunt pmduct ofgood x 2244 Prices of Substitutes in Production T Prlcesubsutute m produouon for good X SX F i Prlcesubsutute m produouon for good X 2 SK a Exercise 22 S1 S2 and S3 represent three of Krispy Kreme Donut s supply curves for donuts Starting from point E indicate which is the most likely movement in response to the speci ed change Price of donuts in dollar P1 00 I P0 50 B F H P025 D G S I 5392 5 4 Donutx per Day Use il Information 1 Donuts and snack cakes are substitutes in production 2 Donuts and donut holes are joint products 3 With present technology Krispy Kreme can make 100 donuts per hour 4 Donuts are made With sugar our water an oven and labor Sugar costs 100 per pound Flour costs 050 per pound Water costs 1 cents per gallon Labor costs 500 per hour The oven costs 200 per hour to run 5 Start each scenario at point E on supply curve S2 at a price level of 050 per donut Scenarios 1 The price of sugar changes to 075 per pound 2 The price of snack cakes decreases 3 The price of donut holes decreases 4 The price of labor increases to 750 5 The price of snack cakes increases 6 The oven gets clogged with donut mix As a result only 75 donuts can be made per hour 7 The price of donut holes increases 8 The price of donuts increases 9 The price of donuts decreases TOPIC 2 DEMAND SUPPLY AND MARKET EQUILIBRIUM 23 MARKET SUPPLY 231 De nition Market Supply the amount of a good that all potential producers are able and willing to offer for sale at each price level during a given period of time ceteris paribus 232 SHIFT VARIABLES FOR MARKET SUPPLY We derived the market supply curve by horizontally summing the rms supply curves at each price Therefore shifts in the market supply curve are the result of shifts of the constituent firms supply curves We39ll adopt a similar convention to that we employed with market demand if we are discussing market supply curves then we39ll assume all the firms react in a similar fashion so we can meaning illy speak of shifts of market supply in response to one of our given shift variables Thus the shift variables of the market supply curve for a given market are the same as those that shift the firms supply curves however remember this is only an assumption If you later take other economics courses be aware different assumptions may apply As with market demand curves we ll add one additional shift variable for the market supply curve the number of firms If the number of firms increases ceteris paribus then market supply increases the market supply curve shifts to the right If the number of firms decreases ceteris paribus then market supply decreases the market supply curve shifts to the left Exercise 23 Firm 1 and Firm 2 s supply tables for cappuccino are given below If Firm 1 and Firm 2 are the only two potential sellers of cappuccino use the information given below to derive the market supply table for cappuccino Firm l39s Supply Firm 239s Supply Market Supply Price Quantity Price Quantity Price Quantity per Supplied Supplied Supplied cup cupsday 300 6 300 4 300 250 5 250 3 250 200 3 200 2 200 150 2 150 l 150 100 l 100 0 100 75 0 75 0 75 TOPIC 2 DEMAND SUPPLY AND MARKET EQUILIBRIUM 24 MARKET EQUILIBRIUM 241 De nition Market Equilibrium A price quantity combination where the market quantity demanded is equal to the market quantity supplied 242 Equilibrium price The price where market quantity demanded is equal to market quantity supplied 243 Price as an allocation mechanisms See class notes 244 Disequilibrium and Adjustment 2441 Surplus If the prevailing market price is above the equilibrium price then the quantity supplied will exceed the quantity demanded This results in a surplus It is measured as quantity supplied minus quantity demanded at a price above the equilibrium price We can also refer to this as a situation of excess supply where QS gt Qd When a surplus exists rms produce and try to sell more than buyers are willing to purchase This causes inventories to accumulate Eventually rms lower prices in an attempt to reduce oversized inventories Lower prices cause rms to produce less and buyers to purchase more This process continues until we reach equilibrium Thus if the market is functioning effectively price serves as a mechanism to equate quantity supplied and quantity demanded 2442 Shortage If the market price is below the equilibrium price then the quantity demanded will exceed the quantity supplied This results in a shortage It is measured by quantity demanded minus quantity supplied at a price below the equilibrium price In this case at the prevailing market price the quantity demanded is greater than the quantity supplied Qd gtQS This means buyers are willing and able to purchase more of the good at the prevailing market price than suppliers are willing and able to offer Inventories will be depleted Seeing that the shelves are going bare rms will raise their prices As rms raise prices they are willing to produce and supply more of the good recall the Law of Supply and consumers are willing to buy less recall the effects of a price increase under the Law of Demand Again this process continues until we ve reached a market equilibrium Prices again have served as the medium for equating quantity supplied and quantity demanded 245 Supply and Demand have different shift variables Note that the factors that shift supply and demand are different In this sense supply and demand are independent This implies that if one of demand s shift variables changes then the supply curve does not also shift The only things that shift supply are the supply curve s shift variables 246 What to know about market demand market supply and equilibrium gtW H the relationship between individual and market demand horizontal summation change in quantity demanded vs change in demand shift variables for individual and market demand and direction Note when dealing with market mctions we39ll assume for now all individual mctions are shifted in same direction how to construct market demand or market supply tables if I give you two or three individual demand tables or rm supply tables complements substitutes law of demand and law of supply def of demand function and supply mction change in supply vs change in quantity supplied shift variables for firm and market supply and direction def of market equilibrium shortage surplus how to determine equilibrium if given market supply and demand in table form how to allocate market equilibrium allocation among demanders and firms Exercise 24 Use the following information to determine the market equilibrium price quantity combination Also determine the quantities each consumer demands at the equilibrium price as well as the quantity each rm supplies Consumer A s Consumer B s Market Demand Market Supply Firm l39s Supply Firm 239s Supply Demand Demand Price Quantity Price Quantity Price Quantity Price Quantity Price Quantity Price Quantity Demanded Demanded Demanded Supplied Supplied Supplied 300 0 300 1 300 300 300 6 300 4 250 1 250 2 250 250 250 5 250 3 200 2 200 3 200 200 200 3 200 2 150 3 150 4 150 150 150 2 150 1 100 4 100 5 100 100 100 1 100 0 75 5 75 6 75 75 75 0 75 0 l The equilibrium pricequantity is P 39 2 How much does Consumer A consume at the equilibrium price 3 How much does Consumer B consume at the equilibrium price 4 How much does Firm 1 supply at the equilibrium price 5 How much does Firm 2 supply at the equilibrium price TOPIC 2 DEMAND SUPPLY AND MARKET EQUILIBRIUM 25 MARKET EQUILIBRIUM ADJUSTMENTS TO MARKET DEMAND AND MARKET SUPPLY SHIFTS See class notes and the text Exercise 25 Using Supply and Demand Models The September 18 2001 edition of the Wall Street Journal p A6 contains an article entitled Decline in Air Travel May Lower Prices For Heating Oil but Not Those at Pump Below you ll be asked to use the supply and demand model to explain some of the WSJ s predictions 1 The dwindling demand for jet iel could save consumers from higher heatingoil prices this winter a Using the supply and demand graph for jet iel below indicate the initial market equilibrium on the appropriate axes label the market equilibrium price P1 and market equilibrium quantity Q1 b Then draw in a new demand curve label it D2 indicating a reduction in the demand for jet fuel Label the new equilibrium price P2 and the new equilibrium quantity Q2 on the appropriate axes The Jet Fuel Market Price of jet fuel per gallon 51 D1 Gallons of jet c le per day As a result of the change in demand the equilibrium price of j et iel has d The WSJ goes on to say that re ners probably will reduce jetfuel production by 250000 barrels per day or about 15 and shift that production into heating oil This quote suggests that a re nery can switch quotom producing jet iel to home heating oil This would imply that jet iel and home heating oil are Indicate the initial market equilibrium for home heating oil on the graph below Label the equilibrium price P1 and the equilibrium quantity Q1 on the appropriate axes The Home Heating Oil Market Price of home heating oil per 31 gallon D1 Gallons of home heating oil per day Draw on the graph above the appropriate new demand or supply curve if colder temperatures cause the demand for home heating oil to increase disturbing the initial home heating oil market equilibrium Label the new curve S2 or D2 as appropriate and label the new equilibrium price P2 and the new equilibrium quantity Q2 In moving to the new equilibrium the price of home heating oil If the changes you described in parts c and d above occur at the same time as the change you found in f what can we conclude about the new equilibrium price of home heating oil Why The WSJ article goes on to talk about the gasoline market if more consumers turn to the highways strong demand could keep prices high where re nery problems have crimped supply a Midwest re nery is reported to have blown up a Using the supply and demand graph for gasoline below indicate the initial market equilibrium on the appropriate axes label the market equilibrium price as P1 and market equilibrium quantity as Q The Gasoline Market Price of gallon of gasoline 51 D1 Gallons of gasoline per day b If consumers drive more as they reduce air travel the demand for gasoline will increase Indicate this new level of demand on the graph above as D2 c If consumers drive more as they y less then car travel and air travel are likely goods d If a refinery blows up then the number of suppliers has and supply will e Draw in a supply curve indicating the re nery s destruction Label it 8 Show the market equilibrium if D2 and 82 are the appropriate supply and demand curves Label the new market equilibrium price P2 and the new market equilibrium quantity Q2 f Compared to the initial equilibrium P1 Q the market equilibrium price of gasoline has to reach P2 40 TOPIC 3 DEMAND AND SUPPLY ISSUES AND EXTENSIONS 31 ELASTICITIES 3 1 0 Introduction Recall that the demand curve is the relationship between the price of a good and the quantity demanded of the same good holding all other factors constant An interesting question is how responsive is quantity demanded to changes in price How responsive is consumption to changes in income or the price of other potentially related goods To answer this question economists have formulated the concept of the elasticity There are many different types of elasticities each of which describes the responsiveness of a quantity measure to changes in a particular related variable We ll study the following 1 the own price elasticity of demand 2 the cross price elasticity of demand 3 the income elasticity of demand 4 the price elasticity of supply The general form of the elasticity is change of the quantity of some good change of some related variable First we ll brie y discuss the interval of measurement then we ll discuss each of the four elasticity measure listed above 311 The interval of measurement If the elasticity is measured at a point meaning the measurement is change of the quantity of some goodchange of some related variable at a given point either a price and quantity combination of good X along the demand curve for good X for the own point price elasticity of demand a quantity income combination for the point income elasticity of demand a quantity of X price of a related good combination the point cross price elasticity of demand or the quantity and price of a good on the supply curve of the good point price elasticity of supply we call this a point elasticity If the elasticity is measured over an interval using two endpoints for calculating the elasticity measure we call this an arc elasticity 312 The Own Price Elasticity of Demand We measure the degree of responsiveness of quantity demanded of a good say good X to changes in price of the same good PX with the own price elasticity of demand The own price elasticity of demand for good X signified by eQleX is the ratio of the percentage change 41 of the quantity demanded of a good to the percentage change of the price of the same good measured along a given demand curve ie holding everything else constant The own price elasticity of demand provides a measure of how responsive quantity demanded is to price changes over a particular range of price change on a given demand curve This range can be either a particuliar point for a point elasticity or an interval for an arc elasticity 3121 Interpretation The interpretation of eQxiPX is the percentage that quantity demanded would change in response to a 1 increase in the price of good X along a given demand curve 3122 Arc own price elasticity of demand If we are interested in a measure of the responsive of the quantity demanded of X due to a price change of good X over an interval along a demand curve we compute the arc own price elasticity of demand for good X This is computed as Qxl 9 9 9 8 Pia Pm QRquot le Px0 where QXI is the nal quantity demanded of X QXO is the initial quantity demanded of X PX is the nal price of X PXO is the initial price of X This tells us on average how responsive is quantity demanded of good X to price changes of good X over the speci ed interval of this demand curve 3123 The point own price elasticity of demand If we are interested in a measure of the responsiveness of quantity demanded of X to a price change of good X at a specific point on the demand curve for good X we compute the point own price elasticity of demand for good X This is computed as qu Where p is the price of good X at the speci ed point on the demand curve of good X q is the quantity of X at the speci ed point on the demand curve of good X the ratio AqAp is the inverse of the slope of the demand curve of good X at the point of interest 313 The Cross Price Elasticity of Demand This concept measures how responsive is consumption of a good say good X to changes 42 in the price of some other good say good y Symbolically it is represented as eijPy 3131 Interpretation The interpretation of 8QXle is by What percentage would consumption of good X change in response to a 1 increase in the price of good y The cross price elasticity of demand is positive if the goods are substitutes The cross price elasticity of demand is negative if the two goods are complements A cross price elasticity of demand of 0 would be referred to as the case of unrelated goods 3132 Arc cross price elasticity of demand formula Qxl on 9x1 90 Pyj Pyo 39quot y PPy Where QXI is the nal consumption of X QXO is the initial consumption of X Pyl is the nal price of y Py is the initial price of y 314 The Income Elasticity of Demand This concept measures the responsiveness of consumption of a good say good X to changes in income It is represented as symbolically as SQXJ 3141 Interpretation The income elasticity of demand tell us by What percentage does consumption of a good change in response to a 1 increase in income If the good is a normal good the income elasticity of demand will be positive If the good is inferior the income elasticity of demand will be negative 43 3142 The Arc Income Elasticity of Demand Formula Q on 9x1 920 8 11 10 Qquot 11Io Where QXI is the nal consumption of X QXO is the initial consumption of X I1 is the nal income level and I0 is the initial income level 315 The Price Elasticity of Supply of Good X The price elasticity of supply of good X measures the responsiveness of the quantity supplied of good X to changes in the price of good X 3151 Interpretation By What percentage does quantity supplied change in response to a 1 increase in the price of the good 3152 Arc Price Elasticity of Supply Formula Q on Q1Qa Pad Paco arc price elasticity of supply of good x le PM Where QXI is the nal quantity Supplied of X QXO is the initial quantity supplied of X PX is the nal price of X PXO is the initial price of X This tells us on average how responsive is quantity supplied to price changes over the speci ed interval of this supply curve 316 Range of values See your class notes 317 Which curve is more elastic from the same graph See your class notes 44 318 A descriptive convention 8 l gt 1 we refer to as elastic 8 1 we refer to as unit elastic 8 l lt l we refer to as inelastic Refer back to your class notes to see where on a demand curve these descriptions are more likely to apply 45 Exercise 31b worth one point on test 2 If the price charged to park in the student parking lot goes from 250 to 350 the quantity demanded number of student parking spaces decreases quotom 1000 to 950 per day a What is the arc own price elasticity of demand for student daily parking over this range b Is the demand curve for daily student parking spaces elastic unit elastic or inelastic over the range of this price change Over a different segment of the demand curve for student daily parking spaces the own price elasticity of demand is measured as 2 If the price of student parking spaces decreases by 5 in this interval by what percent and in which direction will the number of student parking spaces demanded change Direction 1 or change If the price of MARTA tokens increases from 150 to 250 the number of student parking spaces demanded changes from 975 to 1025 a What is the arc crossprice elasticity of demand for student parking spaces with respect to the price of MARTA tokens b What is the relationship between MARTA tokens and student parking spaces These two goods are goods If Sean s income increases from 10000 to 50000 then he buys 100 MARTA tokens rather than his preVious 200 MARTA tokens per year a What s Sean s arc income elasticity of demand for MARTA tokens b Are MARTA tokens inferior or normal good for Sean As the price of a student parking space increases from 250 to 350 the quantity supplied number of student parking spaces increases from 1050 to 1150 a What is the arc elasticity of supply of student parking spaces over this portion of the supply curve of student daily parking spaces b Is the supply curve for daily student parking spaces elastic unit elastic or inelastic over the range of this price change 46 TOPIC 4 THE FIRM PRODUCTION AND THE COST OF PRODUCTION 41 THEORY OF THE FIRM See text and in class notes 47 Exercise 41A Referring to the article An Offer You Can t Re ise The Economist February 6 1999 pp 6869 answer Q1 and Q2 below Your answers should be concise no more than three sentences per question and grammatically correct Q1 What distribution channel is ATampT planning to use to deliver its products Q2 How does ATampT s strategy incorporate economies of scope 48 Exercise 41B After attending a seminar on corporate governance the Board of Directors of Screw U Enterprises Inc hereafter referred to as SUE awarded Screw U s CEO Stanley Grabowski stock options Previously Mr Grabowski had received only a xed salary of 100000 these options represent an addition to this salary and an attempt by SUE s Board of Directors to align Mr Grabowski s financial interests with those of shareholders These options allow Mr Grabowski to purchase 1000 shares of SUE s stock at a price of 10 per share on October 31 2013 and he plans to sell any shares purchased through this option plan on that same day October 31 2013 The options expire after October 31 2013 in other words he either exercises the options on October 31 2013 or he losses them SUE s stock currently sells for 10 per share Q1 Q2 How much would Stanley profit from these options if SUE s stock price is 999 on October 31 2013 but rises spectacularly to reach 100 per share on October 31 2014 Answer Dollars How much would Stanley profit from these options if SUE s stock price is 11 on October 31 2013 but then plummets to 25 per share on October 31 2014 Answer Dollars The CFO of SUE presents Mr Grabowski with two projects for his consideration Project A will raise the stock price to 11 by October 31 2013 but will likely result in a stock price decline thereafter to 25 on October 31 2014 Meanwhile Project B will cause the stock s price to decline to 9 on October 31 2013 followed by an increase in SUE s stock price to 100 on October 31 2014 Considering only the options he currently holds which project A or B is Mr Grabowski likely to approve he can only approve one or the other Circle one Project A Project B Continue to Q4 and 5 49 Ex 41B Continued Q4 Q5 Day Tradin Tom likes to get in and out of a position If he buys SUE s shares now he ll sell then on October 31 2013 Meanwhile Auntie Sarah holds SUE shares in her widows and orphans md and doesn t plan to sell her shares until October 31 2014 Who is more likely to pro t if Mr Grabowski s decisions are driven by a desire to pro t from his options Day Tradin Tom Auntie Sarah Circle one What incentive system would you suggest for aligning the interests of management with those of longterm shareholders we ll de ne longterm shareholders as those holding shares for three years or more TOPIC 4 THE FIRM PRODUCTION AND THE COST OF PRODUCTION 42 PRODUCTION OVERVIEW See text and inclass notes 420 INTRODUCTION Previously we39ve concentrated on the behavior of consumers First we began with the consumer39s budget constraint and indifference map We used that information to derive first the individual39s demand curve and nally the market demand curve for a commodity Now we39ll study in a similar fashion the supply side of the economy where the agent we39ll focus on is the rm First we39ll define the production function and then show how it can be represented as an equation table or graph 421 Definition Production Function the relationship between combinations of inputs used in a time period and the maximum output that can be produced using each input combination in the time period given the state of technology 422 We can represent a production mction as an equation For example let q 10 K12 L 1 2 where q is the quantity of a commodity produced in a set period of time K is the quantity of capital used in the production process of q during the time period L is the quantity of labor used in the production process of q during the time period 423 We can also represent a production mction as a table Note the above equation represents a different production mction than does the table below TAB LE 41 Hypothetical production mction for widgets Widgets per month Units of Capital used in 424 Finally if we are using only two inputs we can represent a production mction graphically using an isoquant map 4241Definition Isoquant the set of all combinations of inputs that when used efficiently will produce a certain level of output Each level of output each quantity will have it39s own isoquant The Marginal Rate of Technical Substitution of Labor for Capital MRTSLK is defined as the amount of capital we can take away from the rm while we add a single unit of labor and still produce the same amount of output It is equal to the absolute value of the slope of an isoquant at a given input combination The MRTSLK is also equal to the ratio of the MPPL to MPPK that is MPPLMPPK or MPLMPK in the shorthand notation you39ll most often see 4242 Variable vs Fixed proportion production and isoquants Variableproportions production function when a firm can use different input combinations to produce the same amount of output For example quotom Table 41 the firm can use 2 workers and 3 units of capital to produce 470 widgets The rm can also use 3 workers and 2 units of capital to produce 470 widgets Most production mctions you encounter will be variable proportions production mctions Properties of Variable Proportion Production Function lsoquants 1 If both inputs have positive MPPs the isoquants will be downward negatively sloping 2 If both inputs have positive MPPs isoquants to the right and above represent higher levels of output 3 Two isoquants can never intersect 4 Isoquants are generally convex smiling in our terminology This shape means the MRTSLK becomes smaller as we increasingly add more and more labor and reduce the amount of capital used along an isoquant Fixedproportion production functions occurs when producing a given quantity of output requires a certain ratio between inputs There is no quottradingoftquot of one input for another In this case adding more than the required amount of the input does not allow us to produce more or reduce the amount of other inputs We39ve simply wasted the additional amount of the input we added Production mctions of this type are represented by L shaped isoquants TOPIC 4 THE FIRM PRODUCTION AND THE COST OF PRODUCTION 43 SHORT RUN PRODUCTION Firms have to buildplants negotiate supplier contracts and hire labor Often certain inputs are easier to vary than others This leads to the distinction between short run and long run production In the short run at least one input into the productive process is xed The inputs that we are not able to vary in the short run are called fixed inputs The inputs we can change are called variable inputs In the long run the rm is able to adjust all the inputs used in the productive process Therefore in the long run all inputs are variable inputs At least one input is xed in the case of short run production Usually when the inputs are labor and capital capital such as plant property and equipment is assumed to be the xed input and labor is assumed to be the variable input To determine short run production we use a production mction in one of it39s many forms First we identify the xed inputs Fixed inputs will not vary during our short run analysis Let39s say we use the information from Table 41 We are told capital is xed at 2 units Below we39ll list the amounts of output possible with capital xed at two units as we progressively add units of labor beginning with 0 units of labor We also need to de ne two other important concepts the Average Physical Product of Labor and the Marginal Physical Product of Labor 431 Average Physical Product The Average Physical Product of Labor APPL is total output divided by the amount of labor used to product the corresponding amount of total output In equation form this is ME APPL LABOR To determine the average physical product of any variable input take the total output and divide by the amount of the variable input used to produce the corresponding total output 432 Marginal Physical Product The Marginal Physical Product of Labor MPPL is the additional output produced in response to a one unit increase in the amount of labor employed To compute the marginal physical product of labor nd the total output for the worker of interest let39s say the second worker Then find the total output corresponding to one less worker in this case the first worker The marginal physical product of the second worker is the difference between the total output corresponding to the second worker and the total output corresponding to the rst worker ceteris paribus TABLE 42 APPL and MPPL EXERCISE Units of Number of Output Average Physical Marginal Physical Note that the APPL and the MPPL are dependent on the quantity of the xed input Verify this by comparing the marginal and average physical product of the 2nd worker when capital equals 1 versus the APPL and MPPL when capital equals 2 units from Table 41 433 Total Average and Marginal Product Curves We can graphically represent the relationships between a the amounts of a variable input employed and either the resulting total output or average physical product of the variable input and marginal physical product of the variable input Using the data below in Table 43 we can graph these relationships with the variable input number of workers per period on the horizontal axis Graph TP versus number of workers on one graph then graph APP and MPP of labor versus number of workers on another graph Put labor on the horizontal axis See Figure 41 when you39re nished to check your answer TABLE 43 APPL and MPPL Graphing Exercise Units of Number of Output Average Physical Marginal Physical 4331 A Few Relationships between the TP APP and MPP curves 1 APP is always rising as long as MPP is above APP Conversely APP will fall when MPP is below APP Hence if MPP starts above APP and then declines to eventually intersect APP this intersection will take place where APP is at a maximum 2 TP is maximized where MPP nally meets the horizontal intercept where MPP finally diminishes to 0 3 The slope at a given point on the TP curve is the MPP for that unit of input 4 The slope of a line drawn from the origin to a point on the TP curve is the APP for the corresponding amount of the variable input 434 THE LAW OF DIMINISHING MARGINAL RETURNS or why is the TP curve shaped like that The convex increasing slope section of the TP curve re ects the effects of specialization and division of labor Rather than one worker or few workers performing all productionrelated tasks the workers specialize in certain functions In Figure 41 the convex section where specialization and division of labor dominate is the area from 0 to 3 units of labor input By looking at the lower panel of Figure 41 you can verify that the MPPL is at it39s maximum when 3 workers are utilized The concave frowning in our terminology section re ects the Law of Diminishing Marginal Returns This law states that when we hold technology and all other inputs constant some formulations say at least one input constant but we39ll adopt the stricter quotall other inputs constantquot version then as we continue to add a constant amount of an input eventually the resulting change in total product the marginal product will decrease Reasons for this phenomenon are congestion and coordination costs In Figure 41 diminishing marginal returns set in after the third worker The fourth worker adds less to total output than did the third the fifth worker adds less to total output than did the fourth etc Note that the Law of Diminishing Marginal Returns does not assume we hire the most productive workers first The usual convention is to assume workers have similar productive capabilities Congestion and coordination costs overwhelming specialization and division of labor effects or division of labor effects and specialization gains have been exhausted drives the Law of Diminishing Marginal Returns Short Run Production and Cost Example W 50 and r 20 APPL MPPL TFC TVC SRTC SRMC AFC SRAVC SRATC 5 5 Source Byrnes and Stone Economics edition p 516 Total Product of Labor Number ofWorkers perWeek Marginal and Average Physical Products ofLabor Number ofWorkers perWeek Exercise 43 ShortRun Production Capital K Labor L Output Q 0 0 75 1 Fill in the blanks in the table above 2 With What sized labor force does this production function begin to exhibit diminishing marginal returns 61 TOPIC 4 THE FIRM PRODUCTION AND THE COST OF PRODUCTION 44 LONG RUN PRODUCTION In the long run the rm is able to vary all inputs The rm would then be interested in knowing how total output responded to proportional increases in all inputs This concept is captured by returns to scale RETURNS TO SCALE analysis asks the question if all inputs are increased by a certain proportion for example by 100 or by any xed proportion the only requirement being all inputs have to be increased by the same proportion then by what proportion does the maximum possible output increase There are three possible cases 441 INCREASING RETURNS TO SCALE If maximum total output increases by a LARGER proportion than the proportional increase of all inputs then the production mction exhibits INCREASING RETURNS TO SCALE over that portion of the production function Here the division of labor and specialization gains cause the rm to become more productive as we increase the scale of the rm 442 CONSTANT RETURNS TO SCALE If maximum total output increases by THE SAME proportion as the proportional increase of all inputs then the production mction exhibits CONSTANT RETURNS TO SCALE over that portion of the production mction 443 DECREASING RETURNS TO SCALE If maximum total output increases by A SMALLER proportion than the proportional increase of all inputs then the production function exhibits DECREASING RETURNS TO SCALE over that portion of the production mction Increasing coordination costs and the exhaustion of any gains from specialization or division of labor tend to cause decreasing returns to scale 444 A Usual Case Often we will observe a rm39s production mction exhibits increasing retans to scale at very low levels of production constant retmns to scale at slightly higher levels of production and decreasing returns to scale at very high levels of production 62 NAME Exercise 45 Output Total Fixed Total Total Cost Marginal Cost Average Average Average Total units per Cost Variable Cost per month per unit Fixed Variable Cost Cost month per month per month Cost per unit per unit per unit 0 30 0 1 30 40 2 30 70 3 30 90 4 30 120 5 30 160 6 30 210 7 30 270 63 TOPIC 5 51 INDUSTRY STRUCTURE OVERVIEW INDUSTRY STRUCTURE AND ITS IMPLICATIONS INDUSTRY STRUCTURE OVERVIEW Perfect Monopolistic Oligopoly Monopoly Competition Competition Number of Many buyers Many buyers Few sellers One seller Firms and sellers and sellers Product type homogeneous differentiated either no close homogeneous or substitutes differentiated Barriers to entry None None Signi cant Signi cant LR profit None None Possible LR Possible LR profit profit 65 Example 52 Output Total Total Total Cost Marginal Average Average Average Price Total Marginal Profit Marginal units Fixed Variable SBmonth Cost Fixed Variable Total Cost SBunit Revenue Revenue SBmonth Profit month Cost Cost unit Cost Cost unit month unit unit month SBmonth SBunit SBunit 0 60 0 1 60 30 2 60 49 3 60 65 4 60 80 5 60 100 6 60 124 7 60 150 8 60 180 9 60 215 10 60 255 11 60 300 12 60 360 Exercise 52 Market Price is 45unit Output Total Total Total Marginal Average Average Average Price Total Marginal Profit Marginal units Fixed Cost Variable Cost Cost Fixed Variable Total SSunit Revenue Revenue SSmonth Profit month SSmonth Cost SSmonth SSunit Cost Cost Cost SSmonth SSunit SSunit montlr SSunit SSunit SSunit 60 0 1 60 30 2 60 49 3 60 65 4 60 80 5 60 100 6 60 124 7 60 150 8 60 180 9 60 215 10 60 255 11 60 300 12 60 360 Example 54 Monopoly in the Short Run Output Total Total Total Margina Average Average Average Price Total Marginal Total Marginal units Fixed Variable Cost 1 Cost Fixed Variable Total per Revenue Revenue Profit Profit per Cost Cost per per Cost Cost Cost unit per per per per month per per month unit per per per month unit month unit month unit unit unit unit 0 30 0 120 1 30 40 110 2 30 70 100 3 30 90 90 4 30 120 80 5 30 160 70 6 30 210 60 7 30 270 50 1 The pro t maximizing outputprice combination is P unit and Q units 2 The amount of profit at the profit maximizing combination is month
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