PRIN MICROECONOMICS ECON 101
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Ms. Ari Lesch
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This 21 page Class Notes was uploaded by Ms. Ari Lesch on Saturday September 26, 2015. The Class Notes belongs to ECON 101 at Iowa State University taught by Staff in Fall. Since its upload, it has received 14 views. For similar materials see /class/214443/econ-101-iowa-state-university in Economcs at Iowa State University.
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Date Created: 09/26/15
REVIEW QUESTIONS 1 2 Economic efficiency is attained when no Pareto improvements are possible a A Pareto improvement This is a voluntary exchange so both parties must bene t b A Pareto improvement Going to the movie is a voluntary decision for both you and your friend so both of you must gain c Not a Pareto improvement since you were harmed although this could become a Pareto improvement if your friend compensates you for your loss through a side payment In a perfectly competitive market with no market failure providing less than the equilibrium quantity cannot be economically efficient because provision of an extra unit of the good increases total net benefits In a perfectly competitive market with no market failure providing more than the equilibrium quantity cannot be economically efficient because reducing output by one unit will increase total net benefits False A price of 0 would maximize market consumer surplus The economically efficient price maximizes the sum of market consumer surplus plus market producer surplus a Criminal law limits exchanges to those that are voluntary Voluntary exchanges lead to Pareto improvements Involuntary exchanges such as robbery always harm at least one party b Property law gives precisely defined enforceable rights over goods If property rights are poorly defined people waste resources trying to take away another person s propertyian activity that makes at least one party worse offiinstead of devoting resources to Pareto improvements c Contract law enhances efficiency by extending the range of Pareto improvements that can take place In particular it enables Pareto improvements that involve the future actions of some other party d Tort law deals with relationships between people or businesses not linked by contracts It creates incentives for businesses and individuals to account for the effects of their actions on others thereby engaging in fewer acts that hurt others and enhancing efficiency Tort law also protects against fraud thereby reducing the transactions costs associated with doing business D Antitrust law helps sustain and improve competition in industry by preventing certain practices that would limit competition and prevent Paretoimproving production from taking place The three major types of market failure discussed in the chapter are monopoly power extemalities and the existence of public goods Antitrust legislation or regulation could correct monopoly power Taxes regulation and tradable permits could correct extemalities Government provision of public goods could correct the failure of markets to provide these goods The Coase theorem addresses market failure due to eXtemalities When side payments can be negotiated and arranged without cost the private market will solve the externality problem on its own In the case of negative extemalities if the free rider problem is extensive enough it can shrink the side payment to losers until it isn t large enough to compensate losers and still leave the gainers better off In that case the private arrangement will break down and the efficient outcome will not be achieved In the case of positive eXtemalities the free rider problem keeps individuals from voluntarily making side payments to provide a good to strangers Again if it is extensive enough side payments won t be large enough to provide the good in efficient quantities Marginal cost measures the cost to the producer of producing another unit of a good while marginal social cost measures the full cost of producing another unit of a good including the marginal cost to the producer anal any harm caused to third parties The Coase theorem does not apply to most cases of air pollution because of the large number of people involvediit is very costly to determine the gains and losses for each one get them all together and then develop a solution that would please everyone A pure public good is one that is nonrivaliconsumption by one person does not affect the amount available to be consumed by othersiand nonexcludableithere is no way to force consumers to pay for the good A pure private good by contrast is rival and excludable a Breakfast at a coffee shop mostly excludable mostly rival b Medical care to treat a highly contagious disease mostly excludable although considerable benefits also accrue to the population at large which is less likely to catch the disease mostly nonrival c Efforts to maintain homeland security mostly nonexcludable mostly nonrival d A movie shown in a theater with mostly empty seats mostly excludable mostly nonrival e Teaching young children not to steal mostly nonexcludable most of the benefits accrue to others who do not pay by taking the time to teach their children not to steal mostly nonrival Introduction to Economics Consumer s Surplus 10 Introduction Economics is clearly important to electricity markets because it was economic principles that motivated them in the rst place And so it is appropriate in a course like BB 458 to introduce some basic economic thinking If you have already taken a course in economics then some of this will be a review for you Much of the below material was adapted from standard economics textbooks l 2 3 We begin our discussion of economics by distinguishing between 2 major sub elds micro economics amp macroeconomics One immediately feels from the words themselves that microeconomics relates to small and macroeconomics relates to large But that is not a complete picture More appropriately microeconomics focuses on the decisions of individual units rms companies households individual consumers within an economy macroeconomics focuses on the behavior of entire economies looking at for example determination of total investment and consumption how central banks manage money and interest rates what causes international nancial crises Our interest is microeconomic ie we want to see for an electricity market how individual prices are set what it means to have an ef cient electricity market how an electricity market can achieve ef ciency simply om the selfinterested actions of its individual agents We do not have time in this course to treat this topic as you would in a course dedicated to microeconomics at ISU it is called Econ 101 but we will establish the following essential concepts Supply and demand functions Consumers surplus Producers surplus Market ef ciency Market equilibrium Competitive equilibrium In this set of notes we will look at the rst 2 topics 20 Demand functions and Consumer Surplus A demand curve characterizes the manner in which the demand of a good will change as its price changes holding constant all other factors that in uence consumers willingness or ability to pay for the good Figure 1 illustrates a demand curve for MP3 players where x denotes number of players demanded 30 Price MP3 Player 20 x Demand Number of MP3 Players demanded per hour Fig 1 Demand curve for MP3 Players Note the demand curve indicates that the demand will increase as the price decreases This is the case for most kinds of goods When this is the case we say that the demand is elastic ie it will change with price What does the demand curve for electric energy that you and I use in our homes look like On an hour by hour basis it appears as in Fig 2 since we will consume the demand we want independent of the price Here x denotes the number of kWhrs demanded 060 050 040 030 Price kwhr 020 x Demand Number of kWhrs used Fig 2 Demand curve for Residential Energy This is an example of an inelastic demand ie a demand that is insensitive to price However we may also consider that there exist some electricity consumers particularly in industry that behave elastically Figure 3 illustrates such a consumer where above 40 MWhr they will shut down all production and only power the security lights requiring only 1 MWhr at 40 MWhr or below they will produce requiring 7 MWhrs if the price goes to 20 MWhr or lower they will initiate a separate production facility requiring an additional MWhr for a total of 8 MWhrs 60 40 30 Price MWhrs 20 l 2 3 4 5 6 7 8 x Demand Number of MWhrs used Fig 3 Elastic Demand Let s consider 110W1 that the industrial consumer is able to quantify the satisfaction or happiness of the plant manager denoted by U as a function of the amount of energy the plant consumes in an hour x and the money that it has at the end of that hour y A given bundle xy provides a level of satisfaction expressed by the socalled utility function for the plant given by U05 V95 y 1 Where vx quanti es in dollars the satisfaction associated With the amount of energy consumed x It is the utility function for energy We Will require vx to be an increasing and concave function and v00 1 The remainder of this section was adapted from notes developed by Oscar Volij of Iowa State University 5 Let s assume that the company has an amount of money m to use for the hour and that it faces an energy price of p This means there exists the following constraint on what the company can do during the hour y P95 m 2 The company has to nd the amount of energy to consume that maximizes its satisfaction Uxy but it must do so subject to the constraint identified in 2 that is the company wants to solve the following problem mxaxvx y st y px m 3 One way to solve this is to by forming the Lagrangian mmvltxgty Aypx m and then applying rst order conditions 8Fx 341 8vx lp0gtm ip 8x 8x 8x m 1 A 0 gt A 1 8y aFltxyigt lt4 x m 0 81 y I9 From the rst two equations above we obtain V39x P 5 Another way to solve this is to substitute the constraint into the objective function eliminating y resulting in maXUx maXvx m px x x 6 Taking rst derivatives with respect to x and setting to 0 yields I I Vx PO 3 V902 7 Recalling that vx expresses utility satisfaction for x then v x expresses the change in utility per unit change in x otherwise known as the marginal utility for energy It provides an upper bound to what the company should be willing to pay for one more unit of energy If they have to pay more then it means that the value of what they can do with that energy will be less than what they have to pay for it 7 And so that we see that 5 expresses the following condition to guarantee that the company will maximize their total utility U x y the willingness to pay for each additional unit of energy should equal the price paid for that energy In other words when the upper bound to what the company is willing to pay for one more unit of energy exactly equals the price they pay for that energy their total utility satisfaction om energy plus the remaining money will be maximized Here is one more articulation of the above idea 3 It always pays the consumer to buy more of any commodity whose marginal utility measured in money exceeds its price the marginal cost of the commodity to the consumer and less of any commodity whose marginal utility is less than its price When possible the consumer should buy the quantity of each good at which price p and marginal utility v are exactly equal because only these quantities will maximize the net total utility the consumer gains from the purchases given the fact that the money available must be divided among all the goods purchased We call 5 the inverse demand function ie it expresses price as a function of demand 8 The demand function then expresses demand as a function of price Example 1 Let vx 60x x2 Find the inverse demand function and the demand function vx 60x x2 v39x 60 2x and so the inverse demand function is p 60 2x To obtain the demand function we solve for x p 30 XP 2 I have plotted the 2 functions in Figs 1 and 2 below Inverse demand function 0 5 10 15 20 25 30 Demand x Fig 1 Inverse demand function Demand function x 0 10 20 30 40 50 60 Price p Fig 2 Demand Function Question Consider that the company has a choice of participating in the electric energy market or not Will it bene t by doing so The answer to this question depends on the difference between its total utility when it participates and its total utility when it does not where total utility is given by l repeated here for convenience UOCJ VOC y 1 Let s denote the total utility when it participates in the market U par 35 y it does not participate in the market Unol x 3 If it does participate and the energy price is p then it obtains an amount of energy equal to xp and the amount of money it Will have is by 2 ympxp Then the company s total utility ie its xy bundle is given by Uparxy Uxpm pm 8 If it does not participate then it receives no electric energy and it has m dollars And so the company s total utility ie its xy bundle is given by U0 m Unol x Z m 9 The difference then is given by the consumer surplus at price p We Will denote the consumer surplus as CSp It is expressed as the difference between 8 and 9 Upar x7 Una x7 U mp m pxltpgt Um m 10 Using 1 above we can express 10 as C509 yxp m pm W m 11 U xltpgtm pxltpgt Ult0mgt Observing the addition and subtraction of m C509 vxp pm W 12 Rearranging C509 vxp v0 pm 13 Recall the fundamental theorem of calculus b Fb Fa j F xdx This allows us to write the rst two terms of 13 as xp vltxltpgtgt vltogt vltxgtdx 14 Substitution of 14 into 13 results in xp mm i v ltxgtdx mp 15 Equation 15 has a nice graphical interpretation illustrated by Fig 3 where we assume a price p results in a demand X Observe that the rst term of 15 corresponds to the area under the pv x curve om 0 to x which is the entire area shaded by vertical lines The second term of 15 corresponds to the lower box not shaded by horizontal lines lower side OX and lefthandside 0p V X Consumer surplus Second term pXp 0 x x Fig 3 Consumer surplus The consumer surplus is the gap or difference between the total utility of the energy and its total market value The surplus arises because we get more than we pay for The reason we get more than we pay for is because the price we pay is equal to the value to us of the last unit of energy the marginal value Figure 4 discretizes Fig 3 to illustrate V X Consumer surplus Second term pXp Fig 4 Consumer surplus When we purchase the rst unit step 1 at price 19 we are very happy because that rst unit is worth a lot more to us than what we pay as indicated by its high value of v x The purchases of the second third and fourth units also make us happy although not quite as happy as the rst unit made us But when we purchase the fth unit it provides us with a level of satisfaction that we assess is exactly equal to the price we paid We will want that unit because otherwise we will be giving up some surplus but we want no additional unit beyond that The inverse demand curve is also a way of rethinking the law of diminishing marginal product which we de ned in our notes on Cost Curves to be as follows For almost all processes the rate of increase in output decreases as the input increases assuming other inputs are xed The above statement is really om the producer s perspective But it may be restated from the consumer s perspective where it is called the law of diminishing marginal utility Additional units of a commodity are worth less and less to a consumer in money terms As the individual s consumption increases the marginal utility of each additional unit declines Example2 In example 1 we were given the utility function for energy as Vx 6096 62 and we determined the inverse demand function as P p 60 2x and the demand function as x07 2 30 3 Assume that the price of energy is set at 30 so that the corresponding demand is x3030215 What is the corresponding consumer surplus The consumer surplus is given by xp Csp Jv39xdx pxp 0 15 15 I60 2xdx 301560x x20 450 0 26015 152 450 2900 225 4502675 4502225 Question Suppose the price of energy is dropped om p0 to p1 What happens to the consumer s surplus When the price is p0 the consumer buys x0 and the consumer surplus is om 15 x0 C5020 I v39ltxgtdx poxo 0 16 When the price is p1 the consumer buys x1 and the consumer surplus is om 15 x1 C8091 I v39ltxgtdx p1x1 0 17 So we want to compute the amount the consumer surplus has increased Subtracting 16 from 17 to get the change in consumer surplus we have CSltp1gt C5090 jv39oodx pm Jv39oodx poxo 0 0 IV39OOdX plxl P0xo Now I know a trick and that is to add and subtract p 1x0 to the above expression resulting in 18 Xi CSP1 CSP0 JVxdx P1x1 Poxo Plxo Plxo 19 Let s rearrange the terms Xi CSP1 CSP0 JVxdx P1x1 Plxo Poxo Plxo x0 Xi CSltP1gt CSp0 JVxdx p1x1 p1x0 poxo p1x0 20 Finally let s factor 19 om the second term and x0 from the third term resulting in Capo Capo v39ltxgtdx p1x1 xo p0 p1xo x0 Additional CS due to savings from reduction in price from buying old amount X0 21 Ef J Additional CS due to increased utility from buying old amount X0 Equation 21 says that the change in the consumer s surplus can be decomposed into two parts The savings from the reduction in price that we enjoy from buying the old amount yellow and The increased utility due to the additional purchased amount red We can see why if we return to our picture V X Old consumer surplus Additional CS due to savings from reduction in price from buying old amount X0 Additional CS due to 1ncreased utility from buying 7 an additional amount XlXo P1 0 x0 x1 x Fig 5 Change in consumer surplus due to price drop Additional homework problem Problem 4 2 As in our example 1 and 2 let Vx60Xx2 with P 60 2x and x07 2 30 g Recall that in example 2 we computed the consumer surplus at p30 x15 to be 225 a How much energy is obtained when p40 b Compute the consumer surplus when the price is 40 c What is the change in consumer surplus when the price is raised from 30 to 40 1 Determine the loss due to buying the new amount of energy at the higher price If the consumer loses this amount of money who gets it e Determine the decreased utility due to the decreased purchased amount f Draw a graph of the inverse demand function and illustrate on it The loss due to buying the new amount of energy at the higher price The decreased utility due to the decreased purchased amount The consumer surplus at the higher price 1 P Samuelson and W Nordhaus Economics 17th edition McGrawHill 2001 2 A Dillingham N Skaggs and J Carlson Economics Individual Choice and its Consequences Allyn and Bacon 1992 3 W Baumol and A Blinder Economics Principles and Policy Dryden Press 1994
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