Inter Microecon ECON 3020
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ECON 3020 INTERMEDIATE MICROECONOMICS HUSSAIN FALL 2008 CHAPTER 2 SUPPLY AND DEMAND This set of notes covers topics from Chapter 2 of the textbook pages 10 56 You must read these notes in conjunction with relevant sections from Chapter 2 This chapter provides a useful overview of demand curves supply curves and the market equilibrium We then talk about the concepts of price sensitivity and comparative statics DEMAND AND QUANTITY DEMANDED Demand is the quantity of a good or service that consumers demand or are willing to buy Quantity demanded on the other hand is the amount of the good or service that consumers are willing to buy at a given price during a specific period of time such as daily or monthly while holding all the other demand factors constant Demand factors are the variables that affect peoples quantity demanded or purchasing decisions The most common demand factors include i Consumers tastes and preferences ii Consumers personal income iii Information iv Prices of related goods and services and v Government actions policies and regulations A demand function shows the relationship between the quantity demanded of a good and its price and other demand factors A general form of the demand function is given by QDppspcTY 1 In equation 1 Q is the quantity demanded of the good p is the price per unit of the good 05 is the price per unit of a substitute1 good pc is the price per unit of a complementary2 good T is the taste towards the good and Y is the income of the consumers 1 Two goods are substitutes when they provide consumers the same or mostly similar services eg Coke Classic and Pepsi 2 Complementary goods are goods that must be used or consumed together eg toothbrush and toothpaste Page 1 LAW OF DEMAND AND THE DEMAND CURVE A demand curve is a plot of the demand function such as equation 1 above where we only show a negative relationship between the price of the good and the quantity demanded of the good This negative relationship between the price of a product and its quantity demanded is also known as the law of demand Consider a linear demand function for processed pork in Canada Moschini and Meilke 1992i Q171 20p20pb3pc2Y 2 In equation 2 Q is the quantity of pork demanded in million kilograms of dressed cold pork carcass weight per year p is the price per kilogram of pork in Canadian dollars pb is the price per kilogram of beef a substitute 0C is the price per kilogram of chicken p is the income of consumers in dollars per year The important questions are 0 How do we transform the above demand function to a two variable demand equation that can be plotted in a graph with only two variables 0 What is the slope of the demand curve Does it conform to the law of demand 0 What are the factors that will create shifts in and movement along this demand curve SUPPLY AND QUANTITY SUPPLIED Supply is the quantity of a good or service that producers produce or are willing to sell Quantity supplied on the other hand is the amount of the good or service that producers are willing to sell or supply at a given price during a specific period of time such as daily or monthly while holding all the other supply factors constant Similar to quantity demanded supply factors are the variables that affect producers quantity supplied or production decisions The most common supply factors include Page 2 i Costs of production ii Production technology iii Prices of related goods and services and iv Government actions policies and regulations A supply function shows the relationship between the quantity supplied of a good and its price and other supply factors A general form of the supply function is given by QDPCA 3 In equation 3 Q is the quantity supplied of the good p is the price per unit of the good C is the price per unit of the input to production and A is the state of technology used by the firm to produce the good LAW OF SUUPLY AND THE SUPPLY CURVE A supply curve is a plot of the supply function such as equation 3 above where we only show a positive relationship between the price of the good and the quantity supplied of the good This positive relationship between the price of a product and its quantity supplied is also known as the law of supply Now consider a linear supply function for processed pork in Canada Moschini and Meilke 1992y Q17840p 60ph 4 In equation 4 Q is the quantity of processed pork supplied per year p is the price per kilogram of processed pork and oh is the price of a hog Again the important questions are How do we transform the above supply function to a two variable supply equation that can be plotted in a graph with only two variables What is the slope of the supply curve Does it conform to the law of supply What are the factors that will create shifts in and movement along this supply curve Page 3 MARKET EQUILIBRIUM Equilibrium in a particular market such as the market for Nike running shoes or the market for iPods is a situation that is characterized by the equality of quantity demanded and quantity supplied and as a result a lack of tendency to change When the specific market is in equilibrium both consumers and producers are satisfied consumers are willing to purchase the exact amount of goods and serVices that the producers are willing to produce and sell Remember that equilibrium is essentially a static concept or simply a snapshot of the world Our objective is to understand the following 0 How do we represent market equilibrium in a graph 0 What happens if the market happens to start outside of equilibrium 0 Given demand and supply functions such as equation 2 and 4 how do we mathematically solve for equilibrium price and quantity in a market 0 What happens to market equilibrium when there is a shift in either the demand or the supply curve 0 What happens to market equilibrium when there is a shift in both the demand and supply curves at the same time Page 4 NUMERICAL PROBLEMS 1 Consider an economy represented by the following demand and supply functions Demand QD 24 2P Supply Q5 5 7F i Mathematically solve for the equilibrium price and quantity ii Plot the demand and supply functions in a graph and show the equilibrium price and quantity 2 Consider another economy represented by the following demand and supply functions Demand QD 171 20P20Pb 3PC 2Y Supply Q5 178 40F 60Fl i Mathematically solve for the equilibrium price and quantity if Pb4 PE 3 Y 12500 and Ph 150 ii Plot the demand and supply functions in a graph and show the equilibrium price and quantity iii What is the effect on equilibrium price and quantity if the price of hogs increases to 175 that is we now have Ph 175 Page 5 PRICE SENSITIVITY ELASTICITY Shapes of demand and supply curves determine how much equilibrium prices and quantities change due to an external shock could be a shift in demand curve or supply curve In other words the shapes of demand and supply curves determine the responsiveness of equilibrium price and quantity An elasticity is a summary measure of the percentage change in one variable due to a given percentage change in another variable holding other variables constant For function of the form 2 f X y the elasticity E of z with respect to x is AZ 7 dz X L Eg 3X 2 5 X In equation 5 E is the percentage change in z E is the percentage change in X and at the z X AZ dz limit when AX is very close to zero E approaches the partial derivative a In economics we will mostly calculate elasticity for very small changes in x Elasticity of demand It is the percentage change in quantity demanded of a good in response to a given percentage change in price of that good This elasticity measure is computed at a specific point along the demand curve The formula for price elasticity of demand is given by AQQ3Qf APP Q 6 8 In equation 6 P is the price of the good Q is the quantity demanded of the good g g is the slope of the demand curve Demand is elastic if the value of elasticity is greater than one inelastic if the value is lesser than one and unit elastic if the value is equal to one Page 6 OTHER TYPES OF ELASTICITIES Income elasticity It is the percentage change in quantity demanded due to a given percentage change in income Income elasticity of demand is given by 8 AQQ3QZ Y AYY aYQ 7 Typically the value of income elasticity is positive for normal goods the value of income elasticity is greater than one for luxury goods and the value of income elasticity is negative for inferior goods Crossprice elasticity It is the percentage change in quantity demanded of a good in response to a given percentage change in the price of another good For instance for two goods x and y cross price elasticity is given by AQXQX 90X Py APyPy aPy Q 8 Two goods x and y are compliments when the value of cross price elasticity is negative and the two goods are substitutes when the value of cross price elasticity is positive Elasticity of supply It is the percentage change in quantity supplied due to a given percentage change in price The elasticity of supply is measured as AQQaQE 9 APP E9P Q In equation 9 Q is the quantity supplied of the good P is the price of the good and g g is the slope of the supply curve Page 7 NUMERICAL PROBLEMS 1 Calculate and interpret the elasticity measure if the demand curve is given by Q 286 20F 2 Calculate and interpret the income elasticity of demand at the equilibrium point that is Q 220 and Y 125 if the demand curve is given by the following equation Q171 20P20Pb 3PE 2Y 3 Calculate and interpret the cross price elasticity of pork and beef at the equilibrium point that is Q 220 if the demand curve is given by the following equation Q171 20P20Pb 3PE 2Y 4 Calculate and interpret the price elasticity of supply at the equilibrium point that is Q 220 and P 330 if the supply curve is given by the following equation Q 88 40F i Moschini Giancarlo and Karl Dr Meilkei 1992 Production Subsidy and Countervailing Duties in Vertically Related Markets The HogPork Case Between Canada and the United States American Journal ongriculmral Economics 74 95196li Page 8 ECON 3020 INTERMEDIATE MICROECONOMICS HUSSAIN FALL 2008 CHAPTER 5 CONSUMER WELFARE AND POLICY ANALYSIS This set of notes covers topics from Chapter 5 of the textbook pages 130 167 You must read these notes in conjunction with relevant sections from Chapter 5 The main topics to be covered in this set of lecture notes include i how do we measure consumer welfare and especially changes in consumer welfare ii the compensating and equivalent measures of consumer welfare and iii applying these measures to look at the effects of a government policy MEASURING CONSUMER WELFARE Economists and policy makers have always been and will always be interested to know how to compare changes in welfare across a broad group of consumers such as how has a community of consumers been affected better or worse off as a result of a given government action or regulation Recall from previous chapters that the one of the most important building block of consumer theory is the utility function But individual utility functions are not observable in the market and it is not possible to compare utility values such as utils of satisfaction across consumers As a result we will introduce and discuss the following three measures of calculating changes in consumer welfare all of which will show changes in consumers welfare measured in dollars 0 Consumer surplus 0 Compensating variation 0 Equivalent variation As long as we can somehow estimate a demand curve for the particular good in question we can calculate the above measures of surplus But keep in mind that by saying a demand curve can be estimated we are implicitly assuming that 0 Consumers preferences are well behaved 7 follows all the assumptions we talked about in Chapter 3 0 When preferences are well behaved they can be translated to a well defined utility function The indifference curves ensure that we can solve the constrained utility maximization problem and solve for the above demand curve for the product Page 1 CONSUMER SURPLUS Welfare or surplus is the additional amount of satisfaction or benefit a consumer obtains from consuming a unit of a good over and above the cost of purchasing that unit of the good In other words if you are buying a unit of a good at a price which is lower than the benefit you derive from that unit you are better off buying the unit of the good Your true willingness to pay referred to as WTP is more than the actual price you pay in the market Consumer surplus is a dollar measure of the sum of the per unit surpluses from zero unit of the good to the number of units bought at the market equilibrium price An individual s consumer surplus is measured by the area under the inverse demand curve and above the market price from zero units to the number of units the consumer buys COMPENSATING AND EQUIVALENT VARIATION Consider a situation where a consumer Joe is at his equilibrium 7 the tangency between his indifference curve and the budget constraint Now consider an increase in price of one of the goods that Joe is buying 0 Compensating variation is the amount of money that is needed to fully compensate for Joe s loss in utility arising from the price increase In other words this is amount of money needed to keep Joe fixed at his previous indifference curve Equivalent variation is the amount of income that could be taken from Joe to leave him or her equally worse off as the price increase In other words this is amount of money needed to keep Joe fixed at his new indifference curve Both these measures are calculating how better or worse off Joe is after the price increase The important difference between the two is that compensating variation is calculated at the original utility level and equivalent variation is calculated at the new utility level Page 2 EFFECTS OF A GOVERNMENT QUOTA Consider we start the analysis at a point where Joe is at his consumer equilibrium 7 tangency between his indifference curve and budget constraint Joe is buying only the two goods i music CDs and ii movie DVDs at the equilibrium Suppose the government imposes a quota on the number of music CDs Joe can buy the question is how does this policy effect Joe s welfare Or how can we measure the amount by which Joe s welfare decreases PRACTICE EXERCISES Suppose that the following equations represent the monthly supply and demand curves for beef products in Laramie Demand QD 100 2P Supply Q5 5 2F a Calculate the equilibrium price and quantity of beef products in Laramie b Draw the demand and supply curves and calculate the area for consumer surplus c Calculate the change in consumer surplus if the equilibrium price increases by 1 Page 3 ECON 3020 INTERMEDIATE MICROECONOMICS HUSSAIN FALL 2008 CHAPTER 6 FIRMS AND PRODUCTION This set of notes covers topics from Chapter 6 of the textbook pages 168 200 You must read these notes in conjunction with relevant sections from Chapter 6 The main topics to be covered in this set of lecture notes include i production ii short run and long run production and iii returns to scale WHAT IS A FIRM A firm is an organization or entity that converts a collection of inputs such as labor land manufacturing equipment or machinery in to output something which can be sold in the market for a price or something which has value to consumers For example a restaurant buys raw ingredients cooks them and serves them as food we buy for a given price Just to get an idea in the United States firms produce 82 of the national output US gross domestic product Note here that we will solely be dealing with for profit firms 7 firms which produce an output to sell and thereby earn profits From here on when we write firms we mean for profit firms In most countries ownership of these firms can have one of three legal forms 0 Sole proprietorship 7 a firm owned and operated by a single individual 0 Partnership 7 a business jointly owned and run by two or more people who are under some kind of partnership agreement 0 Corporation 7 owned by a group of shareholders in proportion to the numbers of shares of stock they hold Shareholders elect a board of directors and they run the corporation Both partnerships and sole proprietorships have personal liability in that the owner or the partners is are personally responsible for the firm s debts Assets of the owners can be used to pay back the debt of the firm To be precise sole owner has unlimited liability and partners have shared liability In case of a corporation we have something called limited liability Personal assets of the shareholders will not be taken to pay back the corporation s debts in case of bankruptcy The maximum the shareholders can lose is the amount they invested in the stocks Page 1 WHAT DO THE OQNERS WANT Owners want to maximize profit 7 the difference between the total revenues and total costs For a firm using a single input profit can be written as Profit TE 2 Total Revenue TR 7 Total cost TC 2 Price of the good x Quantity sold 7 Price of input x Quantity of input So the firm s objective is to maximize total profit by choosing to produce as much as they can while minimizing the cost of production In other words the firm wants to produce as efficiently as possible THE PRODUCTION PROCESS The production process simply refers to a technology which the firm uses to transform a set of inputs in to a final product output to be sold in the market for a price The most important parts of this transformation process can be outlined as Input An input is anything that goes in to a production process eg a factory building or a human labor Mostly we are considering the following two broad classes of inputs 0 Capital K 7 fixed or long lived input such as a building a factory or a machine 0 Labor L 7 human services such as those provided by skilled workers managers or engineers Output The final good that we consumers buy at the market at a certain price For example clothing shoes and food items etc Production function A relationship between quantities of different inputs used and the maximum units of output that can be produced A firm producing output q using only inputs K capital and L labor will have a production function of the form qfLK 1 Page 2 Consider a firm with a production function as follows q 2 2K L 2 We substitute different values for the inputs used and the production function tells us the maximum output that can be produced for those quantities of inputs used If K 2 and L 3 then 7 is the maximum number of output units that can be produced with this production function or technology given in equation 2 Short and long run It is a period of time so short that at least one of the inputs cannot be varied Such a factor that cannot be varied is called a fixed input and the opposite is called a variable input In case of our simple two input production function above K is a fixed input in the short run and L is a variable input Long run on the other hand is a time frame long enough for firms to be able to vary all inputs Essentially there are no fixed inputs in the long run 7 all factors of production are variable PRODUCTION IN THE SHORT RUN In the short run we have one variable input labor L and one fixed input capital K We can think of the fixed input situation as the number of machinery or factory buildings the firm owns 7 cannot change these numbers in the immediate future So firm s short run production function is q m1 3 In equation 3 I is the fixed amount of capital and L is the variable labor input Effectively we are saying that the firm can only increase amount of labor input to increase output in the short run This short run production function is also referred to as the total product of labor function and is sometimes denoted by TPL Page 3 AVERAGE AND MARGINAL PRODUCT OF LABOR Marginal product It is the change in total product due to a one unit change in the labor input holding all other inputs constant The formula for marginal product is given by aq 6mm MPL aL 6L 4 Average product It is the total output or total product of labor divided by the number of units of labor The formula for average product of labor is given by L1 APL fL 5 Practice exercise A computer assembly firm s production function is q 01LK 3L2K 01L3K What is its short run production function if capital is fixed at I 10 Give the formulas for its marginal product of labor and its average product of labor In the following table we will calculate the above three labor products from data we have on fixed capital labor and total product of labor and then plot the relevant curves to look at their properties K Page 4 IMPORTANT PROPERTIES OF THE THREE CURVES M PL reaches a maximum at 10 workers per day TPL reaches a maximum at 20 workers per day where M PL 2 0 0 The APL reaches a maximum at 15 workers per day When MPL is above APL APL is rising When M PL is below APL APL is falling Law of diminishing marginal returns or diminishing marginal product It states that if the firm continues to raise one input workers per day keeping all other inputs and technology constant at their existing levels then the increases in output will be smaller and smaller In other words if we look at the TPL curve above we see that the TPL curve is positively sloped but the slope is decreasing as we move further away from the origin 3 1 Practice exercise Consider a firm whose production function is given by q LIKE Calculate the average and marginal product of labor holding capital fixed at K K PRODUCTION IN THE LONG RUN Recall in the short run one input K was fixed In the long run however both our inputs L and K can be varied So we are back to a production function of the form q fLK L 5K 5 6 Note that we don t have K any more From the definition of a production function a firm can use different combinations of L and K to produce output Practice exercise Calculate some combinations of L and K all of which result in a production of 36 units Page 5 ISOQUANTS An isoquant is a curve consisting of input combinations all of which produce a given level of output efficiently So along an isoquant we are using different L and K combinations to produce the same level of output For the production function in equation 6 an isoquant can by defined by q Lo5Ko5 36 7 The word isoquant comes from two different words 7 iso meaning single and quant means quantity All the combinations of L and K which will result in an output of 36 units can be plotted to obtain the isoquant for 36 units PROPERTIES OF ISOQUANTS Property 1 Similar to a consumer a firm actually has a family of isoquants 7 isoquants which are further away from the origin represent higher levels of output Property 2 lsoquants cannot cross 7 violates the assumption of efficient production Property 3 lsoquants slope downward 7 if isoquants were positively sloped firms would raise both inputs at the same time to strictly increase output Only if isoquants are negatively sloped then firms will have to substitute one input for the other and output will be constant along an isoquant Property 4 lsoquants cannot be fat Page 6 SHAPES OF ISOQUANTS The curvature of an isoquant shows the degree of substitutability between the two inputs The W0 extreme cases are Perfect substitutability Isoquants will be straight lines Generally these production functions will be linear in nature These isoquants correspond to linear production functions of the form qLK Zero substitutability Inputs only can be used in fixed proportions there is zero substitutability between the inputs Inputs can actually be thought of as complements to each other in the production process This will give rise to L shaped isoquants These isoquants correspond to fixed proportions production functions of the form q min L K Imperfect substitutability Isoquants are convex to the origin inputs are substitutes or complements only to a limited extent Most of our analysis will involve isoquants of this shape and they are definitely more interesting and realistic than the above two cases These isoquants correspond to the production functions shown in equation 6 SLOPE OF AN ISOQUANT AND DIMINISHING MRTS The slope of an isoquant shows the degree to which a firm can substitute between inputs while keeping output unchanged The slope is also known as the marginal rate of technical substitution MRTS and for a convex isoquant the slope decreases as we use more of L in production or as we move further away from the origin The M RTS tells us how many units of K the firm can substitute with an additional unit of L while keeping output constant And since isoquants are downward sloping MRTS is negative The formula for M RTS is given by MPL MPK dK MRTS E 8 For our convex to the origin isoquants each additional labor allows the firm to replace smaller and smaller units of capital 7 so M RTS falls as we move down along the curve increasing labor 7 Page 7 this decline in the MRTS in absolute value as the firm increases labor illustrates diminishing marginal rates of technical substitution Practice exercise What is the marginal rate of technical substitution for a general Cobb Douglas production function of the form q AL le RETURNS TO SCALE So far our analysis has been limited to changing only one input and the corresponding effect on output When we increased labor we have also decreased capital movement along an isoquant What happens to output if the firm increases all its inputs proportionately The answer lies in something called returns to scale 0 Increasing returns to scale The production technology is said to exhibit increasing returns to scale if a doubling of all the inputs more than doubles output 0 Constant returns to scale The production technology is said to exhibit constant returns to scale if a doubling of all the inputs also doubles output 0 Decreasing returns to scale DRS The production technology is said to exhibit decreasing returns to scale if a doubling of all the inputs less than doubles output 0 Remember Do not confuse diminishing MRTS with decreasing returns to scale Practice exercise Under what conditions does a general Cobb Douglas production function q AL le exhibit decreasing constant increasing returns to scale Page 8 PRACTICE PROBLEMS i D U By studying Will can produce a higher grade GW on an upcoming economics exam His production function depends on the number of hours he studies utility maximization problems A and the number of hours he studies supply and demand problems R Specifically GW 2 25A03936R03964 His roommate David s grade production function is GD 251402512015 a What is Will s marginal productivity of studying supply and demand problems What is David s b What is Will s marginal rate of technical substitution between studying the two types of problems What is David s Suppose that the production function is given by q L34K14 a What is the average product of labor holding capital fixed at 1 b What is the marginal product of labor c Does this production function have increasing constant or decreasing returns to scale In the short run a firm cannot vary its capital K 2 but it can vary its labor L It produces output q Explain why the firm will or will not experience diminishing marginal returns to labor in the short run if its production function is a q 10L K b q Lo5Ko5 The production function for the automotive and parts industry is q L03927K03916M03961 where M is energy and materials based loosely on Klein 2003 What kind of returns to scale does this production function exhibit What is the marginal product of energy and materials Mark launders his white clothes using the production function q B 20 where B is the number of cups of Clorox bleach and G is the number of cups of a generic bleach that is half as potent Draw an isoquant for 10 clothes using the given production function What is the M RTS at each point along this isoquant Page 9 ECON 3020 INTERMEDIATE MICROECONOMICS HUSSAIN FALL 2008 CHAPTER 1 INTRODUCTION This set of notes covers topics from Chapter 1 of the textbook pages 1 9 You must read these notes in conjunction with Chapter 1 This chapter provides an introduction to some of the most important concepts and definitions that will be covered in detain in this class WHAT IS ECONOMICS Every society has scarce resources and we have to use these limited resources to meet different goals Economics is the study of how to use limited resources efficiently for the achievement of alternative ends The three most important questions facing any society are What to produce 7 Should we produce more guns or more butter Society faces a trade off producing more guns means producing less butter How to produce 7 Should we use more labor or more capital Producers have to switch between different production techniques and input combinations always looking for the cheapest production technology Who gets what is produced 7 Who gets to consume what is produced 7 more for one means less for someone else MICROECONOMICS AND MACROECONOMICS Microeconomics is the study of how an individual decision maker eg an individual consumer or a firm uses scarce resources to maximize hisher personal benefits Benefits can be thought of as measured by units of satisfaction for a consumer or dollar profits for a firm Macroeconomics on the other hand is the study of the economy as a whole Page 1 SOME IMPORTANT CONCEPTS AND DEFINITIONS 0 Who makes the decisions 7 a centralized economic system e g the former Soviet Union or a market based economic system e g the United States 0 In a centralized system economic decisions are commanded and controlled by the government And in a market based economic system market decides everything Price is the critical link between what to produce how to produce and who gets what is produced in a market economy 0 Models 7 simplification of reality 7 used to analyze complex relations between important economic variables in a straightforward manner We use these models in microeconomics to better understand why individuals behave in certain ways and why they make certain choices in certain circumstances Most of what we will be doing in this class will be based on learning and understanding simplified models of economic decision making 0 Models are built by making assumptions about the real world and then these models are tested by comparing their predictions with what is happening in reality 0 Economic decisions are always made under a constrained situation 7 individuals are maximizing their satisfaction subject to an income constraint firms are maximizing profits subject to using a specific technology 0 Positive economics vs normative economics 7 a testable hypothesis about cause and effect as opposed to thinking about whether something is good or bad Page 2 ECON 3020 INTERMEDIATE MICROECONOMICS HUSSAIN FALL 2008 CHAPTER 11 MONOPOLY This set of notes covers topics from Chapter 11 of the textbook pages 360 401 You must read these notes in conjunction with relevant sections from Chapter 11 The main topics to be covered in this set of lecture notes include i monopoly profit maximization ii monopoly market power and elasticity iii welfare effects of monopoly iv cost advantages that create monopoly and natural monopolies and V government actions that create and discourage monopolies MONOPOLY A monopoly is a single seller of a product for which there is no close substitute Unlike a competitive firm a monopoly is not a price taker 7 monopolist s own demand curve is the market demand curve And lastly a monopolist faces a downward sloping demand curve which implies that it does not lose all its customers if it raises price by a small margin But just like a perfectly competitive firm a monopolist also chooses to produce where marginal revenue equals marginal cost to maximize profits So profit is maximized for a monopolist when the following necessary condition is satisfied d d E RQ E CQMR MC 1 The sufficient condition for a profit maximum is also the same as before d2zQ d2RQ dZCQ lt 0 2 sz sz sz Equation 2 is identical to the sufficiency condition for profit maximum of a competitive firm It states that at the optimum it must be the case that the slope of the marginal revenue curve must be less than that of the marginal cost curve Page 1 MARGINAL REVENUE AND THE DEMAND CURVE For a monopolist marginal revenue curve will be always below the demand curve for any positive quantity Recall that total revenue for a monopolist is given by RQPQ Q The marginal revenue for the monopolist can be obtained by differentiating the above expression with respect to Q dP MR P EQ 3 l l l l dP Since the slope term above is negative for a monopolist s demand curve that is Elt0 marginal revenue will always be lower than price for all positive quantities Also remember that elasticity cf is given by Equation 3 can also be rearranged as follows MRP11 4 if From equation 4 it is straightforward to see that as elasticity increases marginal revenue gets closer and closer to the price Practice exercise Derive and plot the marginal revenue curve for the inverse demand function PQ 24 Q What is the monopolist s profit maximizing level of output if we combine a short run cost function given by C QQ2 12 with the above inverse demand curve Plot the results and explain Page 2 MARKET POWER Market power is the ability of a monopolist to charge a price above marginal cost and earn a positive profit Question is how much above its marginal cost a monopoly can set its price Combining the profit maximization condition and equations 3 and 4 we can write MRP11MC 6 5 According to equation 5 the higher the value of elasticity the lower the difference between price and marginal cost Consider a case where cf approaches negative infinity perfectly elastic according to equation 5 the ratio approaches 1 As expected more elastic the demand curve greater the threat for the monopolist to lose buyers when price is raised If there are a lot of close substitutes for the monopolist s output then consumers demand will be more elastic and monopolist will have lower market power Consider that the US Postal Service USPS had a monopoly in overnight delivery services until 1979 Now Federal Express United Parcel Service and many other firms compete with USPS for overnight delivery services Because of this competition USPS s market power has reduced over the years Another way to measure market power is to use the Lerner Index or price markup1 This index is calculated by the ratio of the difference between price and marginal cost to the price that is MC b Recall that for a competitive firm price always equals marginal cost so the Lerner P Index is always zero for a competitive firm For a monopolist however the bigger the difference between price and marginal cost the larger the Lerner Index And bigger the Lerner Index the greater the market power for the monopolist Using equation 5 we can express the Lerner Index as follows 1 This index has been named after its inventor Abba Lerner Page 3 MC Ml 6 p 6 Values for the Lerner Index range from 0 to 1 for a profit maximizing firm because MC 20 p 2 MC and 0 S p MC S p It can be seen from equation 6 that the index value increases for a monopolist as demand become more inelastic or less elastic What is Lerner Index value if cf 5 and what happens to the Lerner Index value if cf 2 Practice exercise Apple s constant marginal cost of producing its top of the line iPod is 200 its fixed cost is 736 million and its inverse demand function is p600 ZSQ where Q is units measured in millions What is Apple s average cost function Assuming that Apple is maximizing short run monopoly profit what is its marginal revenue function What are its profit maximizing price and quantity profit and Lerner Index What is the elasticity of demand at the profit maximizing level Show Apple s profit maximizing solution in a figure WELFARE EFFECTS OF MONOPOLIES Monopoly output is lower than perfectly competitive output and monopoly price is set above the marginal cost of production and thus the perfectly competitive price level So a monopolist s output choice has an associated loss to the society or a dead weight loss The dead weight loss associated with a monopoly will discussed in class using a diagram and using the diagram we will fill the following table Consumer surplus C5 Producer surplus P5 Page 4 Practice exercise What happens if the government imposes a specific tax of 239 8 per unit on a monopoly Assume that the monopoly faces the inverse demand function PQ 24 Q How does the monopoly change its profit maximizing quantity and price Use a figure to show how the tax affects tax revenue consumer surplus producer surplus welfare and deadweight loss COST ADVANTAGES AND MONOPOLY A monopoly may exist because a firm enjoys a cost advantage over potential rivals This type of situation mostly arise when i the firm controls a key input of production ii the firm enjoys access to better technology or better techniques for organizing production and iii the firm is able to develop newer and better production methods the newer method might be so much better that it gives the firm a distinct advantage over other firms NATURAL MONOPOLY A market has a natural monopoly if one firm can produce the total output of the market at a lower cost than several firms could With a natural monopoly it is more efficient to have one firm producing than many firms Believing that they are natural monopolies governments frequently grant monopoly rights to individual firms or public utilities to sell essential goods and services like water gas electricity etc Consider a situation where the cost for a firm to produce an output level of q is given by C q In this case a natural monopoly exists if CQltCqiCqzCqn 7 In condition 7 Q q1 q2 qquot is the aggregate output of any n 2 2 firms and this condition holds for all levels of output A natural monopoly exists in this case because it is more efficient cheaper cost of production for the monopoly firm to produce the total output of Q Natural monopolies usually have cost advantages due to increasing returns to scale Any firm with increasing returns to scale will have a declining average cost curve So when a new firm can never compete with the incumbent firm the monopoly as the new firm will always have to start production at a higher level of costs Page 5 GOVERNMENT ACTIONS AND MONOPOLY In the United States the USPS is a good example of a government created monopoly The constitution explicitly grants the government the right to establish a postal service In most cases governments create monopolies by preventing competing firms from entering a market or in other words by creating barriers to entry These barriers to entry can be enacted in one of three ways i making it difficult for new firms to obtain a license to operate 7 until recently many US cities required that new hospitals or other inpatient facilities demonstrate the need for a new facility to obtain a certificate of need which allowed them to enter the market ii granting a firm right to operate as a monopoly 7 very common for governments to grant monopoly rights to a private company to run a public utility and iii auctioning the rights to a monopoly The second way that governments create and sustain monopolies is by the issuance of patents If a firm cannot prevent imitation by keeping its discovery secret it may obtain government protection to stop other firms from duplicating its discovery and entering the market Virtually all countries provide this kind of protection through a patent which is an exclusive right granted to the inventor to sell a new and useful product process substance or design for fixed period of time So the patent in effect makes the inventor a monopoly in that market for a specified number of years US patents usually last for 20 years from the date when the inventor files for such protection Patents obviously result in monopolies and dead weight losses for the society But a common justification cited for such protection is to stimulate research into new areas and these research efforts often cost hundreds of millions of dollars GOVERNMENT ACTIONS TO REDUCE MONOPOLY POWER Governments can also take steps to curb monopoly power in a particular market Two of the common methods for controlling a monopoly include i using regulations such as a ceiling on the price charged by the monopolist and ii encouraging competition in the market where the monopoly is operating for example implementing policies to eliminate barriers to entry if the government created the monopoly through its own policies to begin with As another example consider a situation where the government opens domestic monopoly markets to international trade and thereby increases competition in these industries and discouraging monopolies Page 6 PRACTICE PROBLEMS 1 D U 4 Show that the elasticity of demand is unitary at the midpoint of a linear inverse demand function and hence that a monopoly will not operate to the right of this midpoint The inverse demand curve that a monopoly faces is p 100 Q The firm s cost curve is C Q 10SQ What is the profit maximizing solution How does your answer change if CQ100SQ The inverse demand curve that a monopoly faces is p 10Q 0395 The firm s cost curve is C Q SQ What is the profit maximizing solution Suppose that the inverse demand function for a monopolist s product is p 9 Its cost function is CQ 10 100 4QZ Q3 a Draw marginal revenue and marginal cost curves At what output does marginal revenue equal marginal cost 5 l l l l l H 127139 What is the profit max1mrz1ng output Check the second order condition d QZ at the monopoly optimum Page 7
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