By the end of this course and having completed the Essential reading and activities you should:

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1 Examiners commentaries 2013 EC2066 Microeconomics Important note This commentary reflects the examination and assessment arrangements for this course in the academic year In 2014 the format of the examination will change as the element of choice in Section A will be eliminated. Section A will comprise EIGHT rathen than TEN questions, all of which must be answered. The format and structure of the examination may change again in future years, and any such changes will be publicised on the virtual learning environment (VLE). Information about the subject guide Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2011). You should always attempt to use the most recent edition of any Essential reading textbook, even if the commentary and/or online reading list and/or subject guide refers to an earlier edition. If different editions of Essential reading are listed, please check the VLE for reading supplements if none are available, please use the contents list and index of the new edition to find the relevant section. General remarks Learning outcomes By the end of this course and having completed the Essential reading and activities you should: be able to define and describe: the determinants of consumer choices, including inter-temporal choicees and those involving risk firms behaviour how firms behaviour differs in different market structures and may help to determine those structures how firms and households determine factor prices. be able to analyse and assess: efficiency and welfare optimality of perfectly and imperfectly competitive markets the effects of externalities and public goods on efficiency government policies aimed at improving welfare. be prepared for further courses which require a knowledge of microeconomics. 1

2 EC2066 Microeconomics Time management Section A comprises 10 questions, eight of which must be answered (accounting for 40% of the total marks). As noted above, from 2014 onwards the element of choice in Section A will be eliminated, so that it will comprise eight questions, all of which must be answered. Section B comprises six questions of which three must be answered (accounting for 60% of the total marks). Candidates are strongly advised to divide their time accordingly. On average, only nine minutes should be allocated to any individual Section A question. On average, only 36 minutes should be allocated to any individual Section B question. Key steps to improvement You need to be able to apply relevant microeconomic theory to questions that you may not have encountered before. To prepare for this, you need not only to gain a thorough understanding of microeconomic models but also (and importantly) to practise using relevant models to answer specific questions. Practice is the key, not the learning of specific answers. You should spend time planning your answers and make sure that you respond to all parts of a question and to key words like define, explain and compare. Precise and concise answers are to be preferred to vague and long-winded answers. You should be aware that, for most answers, diagrams and/or mathematical analysis are essential. These should be correct and diagrams should be well-labelled. In addition, you should always accompany them with appropriate explanations. Again, practice makes perfect. Essential reading: Important information The subject guide refers to Morgan, Katz and Rosen as the principal text. In addition to this, you should practice questions from other texts. Two auxiliary texts that are good sources for practice questions are listed below. Further, the auxiliary texts often develop applications not covered in the principal text. You should study these to broaden, as well as deepen, your understanding. In some cases, reading several treatments of the same topic might help to clarify the basic idea. You should use the auxiliary texts for this purpose as well. The coverage of game theory is often inadequate in texts. You should make sure that you understand the key ideas covered in some detail in the subject guide. Principal text Morgan, W., M.L. Katz and H.S. Rosen Microeconomics. (Boston, MA: Irwin/McGraw-Hill, 2009) second edition [ISBN ]. Referred to as MKR throughout the Examiners commentaries. Auxiliary texts Perloff, J.M. Microeconomics with Calculus. (Upper Saddle River, NJ: Pearson Education, 2011) second edition [ISBN ]. Referred to as Perloff throughout the Examiners commentaries. Pindyck, R.S. and D.L. Rubinfeld Microeconomics. (Upper Saddle River, NJ: Prentice Hall/Pearson, 2012) eighth edition [ISBN ]. 2

3 Question spotting Many candidates are disappointed to find that their examination performance is poorer than they expected. This can be due to a number of different reasons and the Examiners commentaries suggest ways of addressing common problems and improving your performance. We want to draw your attention to one particular failing question spotting, that is, confining your examination preparation to a few question topics which have come up in past papers for the course. This can have very serious consequences. We recognise that candidates may not cover all topics in the syllabus in the same depth, but you need to be aware that Examiners are free to set questions on any aspect of the syllabus. This means that you need to study enough of the syllabus to enable you to answer the required number of examination questions. The syllabus can be found in the Course information sheet in the section of the VLE dedicated to this course. You should read the syllabus very carefully and ensure that you cover sufficient material in preparation for the examination. Examiners will vary the topics and questions from year to year and may well set questions that have not appeared in past papers every topic on the syllabus is a legitimate examination target. So although past papers can be helpful in revision, you cannot assume that topics or specific questions that have come up in past examinations will occur again. If you rely on a question spotting strategy, it is likely you will find yourself in difficulties when you sit the examination paper. We strongly advise you not to adopt this strategy. 3

4 EC2066 Microeconomics Examiners commentaries 2013 EC2066 Microeconomics Important note This commentary reflects the examination and assessment arrangements for this course in the academic year In 2014 the format of the examination will change as the element of choice in Section A will be eliminated. Section A will comprise EIGHT rathen than TEN questions, all of which must be answered. The format and structure of the examination may change again in future years, and any such changes will be publicised on the virtual learning environment (VLE). Information about the subject guide Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2011). You should always attempt to use the most recent edition of any Essential reading textbook, even if the commentary and/or online reading list and/or subject guide refers to an earlier edition. If different editions of Essential reading are listed, please check the VLE for reading supplements if none are available, please use the contents list and index of the new edition to find the relevant section. Comments on specific questions Zone A Candidates should answer ELEVEN of the following SIXTEEN questions: EIGHT from Section A (5 marks each) and THREE from Section B (20 marks each). Candidates are strongly advised to divide their time accordingly. Section A Answer eight questions from this section (5 marks each). Question 1 Mary s demand curve for food is given by Q = 10 2P where Q is the quantity of food and P is the price of food. Calculate her price elasticity of demand for food at P = 2. 4 MKR Chapter 3; Subject guide Chapter 3 (Consumer theory).

5 It is straightforward to calculate the price elasticity of demand: At P = 2, ε = 4/6 = 2/3. ε = dq P dp Q = 2 P 10 2P Question 2 Andy purchases only two goods, apples (A) and oranges (R). The price of apples is 2 and the price of oranges is 4. Andy has an income of 40 and his utility function is U(A, R) = 3A + 5R What bundle of apples and oranges should Andy purchase to maximize utility? MKR Chapter 2; Subject guide Chapter 3 (Consumer theory). Since the indifference curves are straight lines (3A + 5R = constant) and the budget line is also a straight line, you should guess just by looking at the problem that it is likely to have a corner solution. You can confirm this by calculating as follows. We have MU A P A = 3 2 = 6 4 and MU R = 5. So Andy should simply consume apples. The optimal bundle is A = 20, R = 0. P R 4 Question 3 Under first-degree price discrimination, a monopolist s marginal revenue is equal to average revenue. Is this true or false? Explain your answer. MKR Chapter 13; Subject guide Chapter 8 (Competition and monopoly). This is false. The monopolist extracts full surplus, so marginal revenue coincides with the demand curve. But because of the surplus extraction, the average revenue curve is now higher than the demand curve. To see this, consider the following example. Suppose demand is given by Q = 10 P. The revenue of a monopolist who produces Q units is Q times price at Q plus the entire consumers surplus. Therefore the revenue of a first-degree price-discriminating monopolist from producing Q units, denoted by R FD (Q), is given by Since P = 10 Q, we can rewrite this as R FD (Q) = PQ + (10 P)Q. 2 R FD (Q) = (10 Q)Q + Q2 2 = 10Q Q2 2. 5

6 EC2066 Microeconomics It follows that marginal revenue is MR(Q) = dr FD(Q) dq = 10 Q = P. Thus marginal revenue coincides with the demand curve. However, the average revenue curve is now higher than the demand curve: AR(Q) = R FD(Q) Q = 10 Q 2 > P. Question 4 Consider the following game. For what values of x does each player have a dominant strategy? Explain your answer. Player 2 A 2 B 2 C 2 A 1 3,3 3,0 1,2 Player 1 B 1 2,3 1,2 0,1 C 1 0,1 2,0 x, x The coverage of game theory in MKR (Chapter 16) is not ideal. See Chapter 9 (Game theory: an introduction) of the subject guide for a detailed discussion. This is an easy question. But you should be careful to read the payoffs of players correctly. Remember that the first number in each box is the payoff of the row player (player 1) and the second number is the payoff of the column player (player 2). Once you look at the right set of numbers for each player, it should be obvious that A 1 and A 2 are dominant strategies for 1 and 2 respectively if x < 1. Question 5 If the long-run average cost is decreasing in output, the long-run marginal cost must be decreasing in output as well. Is this true or false? Explain your answer. MKR Chapter 9; Subject guide Chapter 7 (The firm). This is false. Decreasing long-run average cost (LRAC) implies that long-run marginal cost (LRMC) is below long-run average cost, but has no implication on whether the LRMC is increasing or decreasing. As the picture below shows, LRMC can be increasing while still below LRAC. 6

7 Cost LRMC LRAC Quantity Declining LRAC implies LRMC<LRAC, but as the picture shows, LRMC need not be decreasing. Question 6 As the rate of interest falls, a saver might save less but never becomes a borrower. Is this true or false? Explain your answer. MKR Chapter 4; Subject guide Chapters 3 (Consumer theory) and 5 (Saving, investment and choice over time). This is false. Many candidates attempt to answer this question by drawing a picture to start with. This is not the right way to go about answering it. A picture is not very helpful here. You need to know the logic of the answer first, and then you can show this in a picture to clarify your own understanding, but you cannot simply draw a picture and try to guess the answer from that. Let us try to identify the different effects arising from a change in the interest rate. A fall in the interest rate has two effects. Substitution effect: The price of current consumption C 0 has fallen relative to future consumption C 1, so the agent will choose a higher C 0. This implies that the saver saves less. Income effect: The saver feels poorer as the interest rate decreases. If consumption today is a normal good, the income effect implies the saver will reduce today s consumption and save more. The two effects go in opposite direction. It is clear, however, that if the substitution effect is large enough compared to the income effect, it is possible that the saver could become a borrower. Of course, if current consumption is an inferior good, both effects would go in the same direction (save less) and then it is even more likely that a saver becomes a borrower. 7

8 EC2066 Microeconomics Question 7 Consider a competitive industry with several identical firms. The total cost function of the representative firm is given by C(q) = q q 2 + q3 2 where q denotes the output of the representative firm. Derive the supply function of the representative firm, paying proper attention to the shut-down point. MKR Chapter 10.1; Subject guide Chapter 8 (Competition and monopoly). The supply function is given by the MC curve above the average cost (which is here the same as average variable cost) curve. Now, MC = 1 2q + 3q 2 /2, and AC = 1 q + q 2 /2. Therefore MC AC if 1 2q + 3q 2 /2 1 q + q 2 /2 which implies q 2 q This happens when q 1. Thus the (inverse) supply curve is given by P = 1 2q + 3q 2 /2 for q 1 Cost MC AVC (here same as AC) 1 Quantity The supply curve is the solid part of the MC curve, which is the part above AVC (here same as AC). Question 8 If lenders cannot observe the quality of projects of borrowers, the usual competitive market supply logic of lending more at higher interest rates does not always hold. Is this true or false? Explain your answer. 8

9 MKR Chapter 17; Subject guide Chapter 12 (Asymmetric information). This is true. The key idea is adverse selection, combined with the fact that loan contracts are typically limited liability contracts, so that if a project fails and gets a zero return (say), the lender gets zero return as well. As rates increase the borrowers with less risky projects (which typically earn a lower return) tend to drop out of the market. On the other hand, consider a project that succeeds with a small probability but yields a very high return when it succeeds. When it fails, the project returns zero. A borrower who invests in such a risky project is happy to obtain a loan at a high rate because he only has to pay that rate when the project succeeds. So as the rate of interest rises, the lender is faced with an increasingly worsening (i.e. riskier) pool of borrowers. Therefore the lender s profit might decrease as the interest rate increases. It follows that the lender might want to lend less (or not at all) at higher rates. Question 9 If market demand is infinitely elastic and market supply elasticity is finite, a per unit tax on suppliers creates no deadweight loss. Is this true or false? Explain your answer. MKR Chapter 11; Subject guide Chapter 8 (Competition and monopoly). This is false. There is no deadweight loss on consumers, but there is a deadweight loss in producer surplus. The picture below shows the loss. You should be careful to correctly identify the area of loss. Many candidates draw the right supply-demand picture, but then fail to identify the correct area of deadweight loss. Price Supply after tax of t per unit Supply t P Deadweight Loss Demand Q 1 Q 0 Quantity With a flat demand curve, price does not change after tax, but quatity falls, giving rise to a deadweight loss (shaded area). 9

10 EC2066 Microeconomics Question 10 Suppose an agent borrows funds and invests in a project. His effort must be monitored by lenders to ensure that the investment is successful, and monitoring is costly. If the agent borrows from several lenders, he is likely to be monitored at an inefficient level. Is this true or false? Explain your answer. MKR Chapter 18; Subject guide Chapter 13 (Externalities and public goods). This is true. The key is to understand that monitoring is a public good. If one lender monitors the borrower, all other lenders benefit as well. Once you realise the public good nature of monitoring, it should be clear that free riding incentives exist. This, in turn, implies that the overall level of monitoring would fall short of the socially efficient level. Section B Answer three questions from this section (20 marks each). Question 11 Suppose there are two identical firms in an industry. The output of firm 1 is denoted by q 1 and that of firm 2 is denoted by q 2. The total cost of production for firm i, i {1, 2}, is 10 C(q i ) = 4 q i Let Q denote total output, i.e. Q = q 1 + q 2. The inverse demand curve in the market is given by P = 10 Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. (b) Suppose the firms can collude, and maximize joint profit. Calculate the deadweight loss arising under this scenario. (c) What would be the quantities produced by each firm and market price under Stackelberg duopoly if firm 1 moves first? (d) Now suppose the production process in the industry pollutes the environment and generates a marginal social cost given by MC E = 2Q Calculate the deadweight loss arising from the Cournot-Nash equilibrium in this case. MKR Chapter 15; Subject guide Chapter 10 (Oligopoly and strategic behaviour).

11 (a) Firm 1 maximises (10 q 1 q 2 )q 1 4q 1. The first order condition is 6 2q 1 q 2 = 0 implying that the reaction function of firm 1 is given by q 1 = 3 q 2 2 Imposing symmetry, we have q 1 = q 2 = q where q = 3 q 2 which implies q = 2. Therefore the Cournot-Nash equilibrium quantities are given by q 1 = q 2 = 2 and the market price is P = 10 4 = 6. (b) If firms collude, together they maximise joint profit given by (10 Q)Q 4Q. The first order condition is 10 2Q 4 = 0 which gives us Q = 3 and therefore P = 7. To calculate the deadweight loss, note that the efficient quantity is the quantity demanded at price equal to MC. Here MC = 4, so the efficient quantity is Q = 6. Thus at the price-quantity pair (P, Q ), the deadweight loss is given by 1 2 (P 4)(6 Q ) Thus the deadweight loss under collusion is 9/2 = 4.5. Price 10 D Q = 10 - P 7 Deadweight Loss MC = Quantity Calculating the deadweight loss from collusive equilibrium. (c) Now firm 1 takes firm 2 s reaction function as given. Firm 2 s reaction function is q 2 = 3 q 1 /2. Therefore firm 1 maximises ( ( 10 q q 1 2 )) q 1 4q 1 11

12 EC2066 Microeconomics which simplifies to ( 3 q ) 1 q 2 1 The first order condition is given by 3 q 1 = 0 implying that q 1 = 3. It follows that q 2 = 3/2. The market price is /2 = 11/2 = 5.5. (d) The private marginal cost is 4, and the marginal externality cost is 2Q. Therefore the socially optimal quantity is given by which implies 4 + 2Q = P 4 + 2Q = 10 Q which implies that the socially optimal quantity is Q 0 = 2 and the associated price is P 0 = 8. At the total Cournot quantity 4, the social marginal cost is = 12, and the social marginal benefit is simply the height of the demand curve given by = 6. Therefore the deadweight loss is given by 1 2 (4 Q 0)(12 6) = 1 (4 2)(12 6) = 6 2 Price, Cost MC = 4 + 2Q Deadweight Loss P = 10 - Q 2 4 Quantity Calculating the deadweight loss from Cournot equilibrium with private marginal cost of 4 and an additional social marginal cost of 2Q. Question 12 Consider a market for used cars. There are some low quality cars and some high quality cars. Potential sellers have a car each, and there are many more buyers than possible sellers in the market. A high quality car never breaks down. A low quality car provides a poorer ride quality over longer journeys and also breaks down with positive probability. A seller values a high quality car at 9000 and a low quality car at A buyer values a high quality car at 10,000 and a low quality car at All agents are risk-neutral. 12

13 In answering the following questions, assume that the sellers get the entire surplus from trade. (a) Suppose quality is observable to sellers but not to buyers. Buyers only know that a fraction 3/5 of the cars in the market are high quality and the rest are low quality. Would cars of both low and high qualities be traded in equilibrium? Derive the equilibrium price(s) at which such trade takes place. (b) Is the market outcome in part (a) efficient? Explain your answer. (c) Now suppose low quality cars break down with probability 0.7. Recall that high quality cars never break down. Suppose the sellers of high quality cars announce a guarantee that promises a full refund if the car breaks down. Show that with this guarantee, high quality cars sell for and low quality cars sell for (d) Suppose, as in part (c), that low quality cars break down with probability 0.7. Suppose the government decides to force each seller to offer a full refund if the car sold by the seller breaks down. How does this change the market outcome? Is the market outcome efficient? Explain your answer. MKR Chapter 17; Subject guide Chapter 12 (Asymmetric information). (a) If all cars are offered for sale, the average value of buyers is = Since buyers would not pay more than 8,000 for a car, high quality sellers would not sell. Anticipating this, a buyer would know that any car being offered for sale must be a low quality car and therefore buyers would be willing to pay at most 5,000 for a car. Since sellers get the entire surplus, the equilibrium market price would be 5,000 and only low quality cars would be traded in equilibrium. (b) The market outcome is inefficient as there are gains from trade in high quality cars, but this gain is left unexploited. (c) The key idea you should understand is that to establish a separating equilibrium as described in the question, we must show that the low quality sellers would not want to mimic the behaviour of the high quality sellers. The high quality sellers have no cost of offering a guarantee. So the crucial question is whether low quality car sellers would also offer a guarantee. By offering a guarantee they could mimic the high quality sellers and sell at 10,000. But the cars would break down with probability 0.7, so that they would have to pay back 10,000 with probability 0.7. Thus the payoff of low quality sellers from offering a guarantee is = But if a seller sells without a guarantee, he reveals himself as a low quality seller and his car sells at 5,000 in equilibrium. Since 5000 > 3000, a low quality seller has no incentive to imitate a high quality seller by offering a guarantee. It follows that there is a separating equilibrium: high quality cars sell with a guarantee at the buyers valuation of 10,000 and low quality cars sell at the buyers valuation of 5,000. (d) If low quality sellers are forced to give a guarantee, the best they can hope for is to sell at 10,000 with a guarantee. But as calculated above, they get a payoff of 3,000 even if they could sell at the maximum price of 10,000. But 3000 < 4000, which is their reservation value 13

14 EC2066 Microeconomics for their cars. So low quality sellers would quit the market, and only high quality sellers would sell their cars with a guarantee at 10,000. This outcome is inefficient since there are gains from trade in low quality cars, and this gain is left unexploited. Question 13 (a) Find the pure and mixed strategy Nash equilibria of the following game. Player 2 A 2 B 2 Player 1 A 1 2,7 3,2 B 1 0,0 4,1 [8 marks] (b) Consider the following extensive-form game with two players. Player 2 moves after player 1. Each player can produce a high output or a low output. Player 1 s payoff is additionally influenced by an exogenous event which occurs with probability p [0, 1]. The payoffs are written as ((Payoff to 1), Payoff to 2). 14 i. Suppose p > 1/3. Find the subgame perfect Nash equilibrium of the game above. [6 marks] ii. Suppose, before the start of the game, player 2 has the option of committing to produce a high output (H 2 ). Making such a commitment requires player 2 to incur a cost of 1. Find the range of values of p for which it is optimal to make such a costly commitment. [6 marks] The coverage of game theory in MKR (Chapter 16) is not ideal. See Chapter 9 (Game theory: an introduction) of the subject guide for a detailed discussion. (a) The pure NE are (A 1, A 2 ) and (B 1, B 2 ). The mixed NE is as follows.

15 (b) Suppose 1 plays A 1 with probability p and B 1 with probability (1 p). Then p must be such that 2 is indifferent between A 2 and B 2. This gives us 7p = 2p + (1 p). Solving, p = 1/6. Now suppose 2 plays A 2 with probability q and B 2 with probability (1 q). Then q must be such that 1 is indifferent between A 1 and B 1. This gives us 2q + 3(1 q) = 4(1 q). Solving, q = 1/3. Therefore the mixed NE is given by 1 playing A 1 with probability 1/6 and B 1 with probability 5/6 and 2 playing A 2 with probability 1/3 and B 2 with probability 2/3. Many candidates derive the mixed strategies correctly using the method above. Some use a slightly different method: first write down the expected payoff of each player given that each plays a mixed strategy. Let Eπ 1 denote the expected payoff of player 1. Now differentiate this with respect to p and set this equal to zero. What does this do? Well, this should give us the value of q for which Eπ 1 does not depend on p (i.e. the derivative of Eπ 1 with respect to p is zero, so that the expected payoff of 1 does not change when p changes). This is precisely the value of q for which 1 would be indifferent between A 1 and B 1. For all other values of q, the derivative is either positive or negative, so that the optimal choice of p is either 1 (when the derivative is positive) or 0 (when the derivative is negative). Similarly we can find the p for which 2 is indifferent. However, it is very important to note that when you set deπ 1 dp = 0, this is not a maximisation exercise (i.e. this is not a first order condition). If you say you are maximising with respect to p, this tells the Examiners that you have not understood the exercise you are carrying out, and you are unlikely to get any credit for your answer. In general, we would encourage you to adopt the first method discussed above for deriving mixed strategy Nash equilibria. That method is the simplest, makes the underlying intuition clear and minimises the chance of making a mistake. i. A subgame perfect Nash equilibrium (which is a formalisation of the notion of credibility) is a Nash equilibrium of the whole game that also induces Nash equilibrium play in every subgame. For games of perfect information, we can obtain subgame perfect Nash equilibria using backward induction. (In more complicated games where a player does not have perfect information about moves of previous players, backward induction may not work, but such games are outside the scope of this course.) Solving backwards, we see that if 1 plays L 1, 2 s optimal action is H 2 (the payoff from H 2 is 4, while that from L 2 is 1), and if 1 plays H 1, 2 s optimal action is L 2. Therefore in any subgame-perfect equilibrium, 2 s strategy must be (H 2 if L 1 and L 2 if H 1 ). Given this, 1 compares between L 1 which yields a payoff of 3 2p and H 1 which yields a payoff of 2 + p. Now, 2 + p > 3 2p implies p > 1 3. Since this is the case given by the question, 1 s optimal choice is H 1. Therefore the subgame perfect Nash equilibrium is given by the strategy combination (H 1, (H 2 if L 1 and L 2 if H 1 )). Many candidates answer this question by saying that the subgame perfect Nash equilibrium is (H 1, L 2 ). It is very important for you to understand that this is not fully correct. You should carefully study the notion of a strategy in a dynamic game and the concept of subgame perfect Nash equilibrium from the subject guide. A strategy in a dynamic game with sequential moves (also called an extensive-form game) is a complete plan of actions, and therefore you need to specify an action for the second mover after every action of the first mover. An incomplete specification would earn you very little credit. 15

16 EC2066 Microeconomics ii. There are two crucial points to understand. First, if p < 1/3, 1 would optimally play L 1 so that 2 would get 4 simply by playing the subgame-perfect equilibrium strategy as above. In this case commitment is not useful, so the first condition is that p > 1/3. The second point to understand is that if 1 plays H 1 optimally, commitment would have no value for 2 (indeed, he would get 1 minus the cost of commitment, giving 2 a payoff of 0 but he could get 2 as above by not getting into any such commitment). Thus for commitment to have any value, it must be that without the commitment 1 would play H 1, but the commitment makes it optimal for 1 to play L 1, so that player 2 can get 4 minus the cost of commitment, giving 2 a payoff of 3. If 2 commits to playing H 2 after both L 1 and H 1, 1 plays L 1 optimally if 3 2p > 1 + p which implies p < 2 3. Thus it is optimal to make a commitment to high output if 1 3 < p < 2 3. Question 14 (a) Jean spends her income on fuel for heating her house and other goods ( other goods represents a composite of all other goods). The price of the composite of other goods is 1, and the price of heating fuel is p. The government decides to put a tax of t per unit on heating fuel. i. Suppose the government asked for a lump-sum tax that would leave Jean with the same level of utility as after the per-unit tax. Would Jean pay more or less tax under the lump-sum tax scheme compared to the per-unit tax scheme? Explain using a diagram. ii. Suppose the per-unit tax has been imposed. The local council starts a scheme to help certain residents with their fuel tax bill. Jean qualifies for the scheme, and she receives extra income equal to the amount of tax she pays. Would this make Jean s utility as high as her pre-tax level of utility? Explain using a diagram. (b) Jo has a wealth of 10,000, but faces the risk of losing 3600 with probability 0.2. An insurance company offers Jo the following scheme: in exchange for a premium of X, the insurance company would pay out 5X in the event of a loss. i. Suppose Jo s utility function is given by u(w) = ln w where w denotes wealth. What is the optimal choice of X for Jo? ii. Now suppose Jo s utility function is given by u(w) = 1 1 w where w denotes wealth. What is the optimal choice of X for Jo in this case? (a) MKR Chapter 4; Subject guide Chapter 3 (Consumer theory). 16

17 i. As the picture shows, the lump-sum tax would raise more revenue. The non-distortionary policy fares better. Another way of saying this is that the equivalent variation of a per-unit tax exceeds the tax revenue. Other Goods B A D C Budget line after lump-sum tax Budget line after per-unit tax Heating Fuel The dashed line is the original budget line. Jean consumes at A after the per-unit tax is imposed. Since the composite good has a price of 1, the vertical distance between the budget lines (segment AB) shows the amount of tax paid. An equivalent lump-sum tax would move Jean s consumption to C, implying tax revenue of CD, which is larger than AB. The non-distortionary policy raises more tax. In other words, EV of a per-unit tax exceeds tax revenue. ii. As the picture shows, Jean s utility after the tax plus extra income would not be as high as her pre-tax level of utility. The compensating variation of a per-unit tax scheme is greater than the tax-revenue (since it must also compensate for the distortion caused by the tax). So just giving back the tax-revenue is going to leave the consumer worse-off compared to the before-tax situation. 17

18 EC2066 Microeconomics Other Goods Budget line after tax plus extra income equal to tax paid C A B Budget line before tax Budget line after tax Heating Fuel Jean s consumption is initially at A, and moves to B after the per-unit tax. Since the composite good has a price of 1, the vertical distance between the budget lines (segment BC) is the amount of tax paid. If Jean receives extra income equal to tax paid, her budget line shifts up as shown, but her utility on this line is clearly less than that at point A. In other words, the CV of the per-unit tax is greater than tax revenue. (b) MKR Chapter 6; Subject guide Chapter 6 (Choice under uncertainty). For a good coverage of the expected utility model, as well as the derivation of risk premium for a risk-averse individual, see Perloff, Chapter i. For any X, the insurance company s profit is 0.8X + 0.2(X 5X) = 0 Therefore the scheme is a fair insurance scheme. Since Jo is risk averse, she would choose complete insurance. This implies X = X X which implies 5X = 3600, or X = 720. ii. The utility function is different, but this is still concave, i.e. Jo is still risk averse. Therefore, under fair insurance Jo will still choose full insurance, i.e. X = 720. Question 15 A society consists of 2 identical individuals who derive utility from a public good. The public good can be provided at a constant marginal cost of 6. Let x i denote the level of public good provision by i and let X denote the total provision of the public good. The net benefit enjoyed by individual i from providing x i units of the public good is given by where i {1, 2}. U i (x i, X) = 1 2 (10 X)2 6x i 18

19 (a) Derive the socially optimal level of provision of the public good. [6 marks] (b) If every individual optimally chooses how much public good to provide, derive the total level of provision of the public good. [7 marks] (c) Suppose n > 1 new individuals arrive in the society. The net benefit enjoyed by new individual j from providing x j units of the public good is given by V j (x j, X) = 1 3 (9 X)2 6x j Suppose every individual optimally chooses how much public good to provide. Does the total level of public good provision change compared to part (b) as a result of the new arrivals? Explain your answer. MKR Chapter 18.3; Subject guide Chapter 13 (Externalities and public goods). [7 marks] (a) The socially optimal level of provision of the public good can be found by maximising the sum of utilities: which gives us max X 21 2 (10 X)2 6X 2(10 X) 6 = 0 or X = 7, which is the socially optimal level of provision of the public good. (b) Individual 1 maximises 1 2 (10 (x 1 + x 2 )) 2 6x 1. The first order condition is which implies 10 x 1 x 2 6 = 0, x 1 = 4 x 2. Imposing symmetry, x 1 = x 2 = x where x = 4 x, or x = 2. Therefore the total level of provision of the public good is 4. (c) Each new individual j maximises where so that 1 3 (9 X)2 6x j X = Differentiating with respect to x j, we get n j=1 x j + X x j = 1. 2 x i i=1 V j = 2 (9 X) 6 = X < 0. x j 3 Therefore any new individual j optimally contributes 0. It follows that the total level of public good provision does not change compared to part (b) as a result of the new arrivals. 19

20 EC2066 Microeconomics Question 16 (a) Explain the incentive properties of residual claimant contracts relative to flat salaries in terms of reducing unobservable shirking by an employee. [10 marks] (b) Carefully explain why flat salaries are often observed, and residual claimant contracts are rarely observed. MKR Chapter 17 ; Subject guide Chapter 12 (Asymmetric information). [10 marks] The question is about a problem that arises in the employer employee relationship when the employer is unable to observe the employee s effort, giving rise to a moral hazard problem. The answer to part (a) should explain that residual claimant contracts put all risk on employees so that the incentive to take high effort is maximised. Flat salaries, on the other hand, provide complete insurance to the employees which provides zero incentive to take high effort. The answer to part (b) should point out, first, that even when an employee gets a flat salary, it need not be riskless. This is because an employee who shirks might increase the chance of getting fired (e.g. if the performance remains poor for a few periods). The fear of getting fired might act as an incentive to work hard even though the actual salary is flat. Second, if employees are more risk averse compared to employers, residual claimant contracts may not be optimal. Such contracts put a high level of risk on risk-averse employees. This might lead employees to either not participate, or require very high levels of compensation to induce participation. In this case it is efficient for the employers to absorb risk, and generate incentives through by combining flat salaries with the threat of firing for poor performance, as noted above. 20

21 Examiners commentaries 2013 EC2066 Microeconomics Important note This commentary reflects the examination and assessment arrangements for this course in the academic year In 2014 the format of the examination will change as the element of choice in Section A will be eliminated. Section A will comprise EIGHT rathen than TEN questions, all of which must be answered. The format and structure of the examination may change again in future years, and any such changes will be publicised on the virtual learning environment (VLE). Information about the subject guide Unless otherwise stated, all cross-references will be to the latest version of the subject guide (2011). You should always attempt to use the most recent edition of any Essential reading textbook, even if the commentary and/or online reading list and/or subject guide refers to an earlier edition. If different editions of Essential reading are listed, please check the VLE for reading supplements if none are available, please use the contents list and index of the new edition to find the relevant section. Comments on specific questions Zone B Candidates should answer ELEVEN of the following SIXTEEN questions: EIGHT from Section A (5 marks each) and THREE from Section B (20 marks each). Candidates are strongly advised to divide their time accordingly. Section A Answer eight questions from this section (5 marks each). Question 1 Mary s demand curve for food is given by Q = 10 2P where Q is the quantity of food and P is the price of food. Calculate her price elasticity of demand for food at P = 2. MKR Chapter 3; Subject guide Chapter 3 (Consumer theory). 21

22 EC2066 Microeconomics It is straightforward to calculate the price elasticity of demand: At P = 2, ε = 4/6 = 2/3. ε = dq P dp Q = 2 P 10 2P Question 2 Andy purchases only two goods, apples (A) and oranges (R). The price of apples is 2 and the price of oranges is 4. Andy has an income of 40 and his utility function is U(A, R) = 3A + 5R What bundle of apples and oranges should Andy purchase to maximize utility? MKR Chapter 2; Subject guide Chapter 3 (Consumer theory). Since the indifference curves are straight lines (3A + 5R = constant) and the budget line is also a straight line, you should guess just by looking at the problem that it is likely to have a corner solution. You can confirm this by calculating as follows. We have MU A P A = 3 2 = 6 4 and MU R = 5. So Andy should simply consume apples. The optimal bundle is A = 20, R = 0. P R 4 Question 3 Under first-degree price discrimination, a monopolist s marginal revenue is equal to average revenue. Is this true or false? Explain your answer. MKR Chapter 13; Subject guide Chapter 8 (Competition and monopoly). This is false. The monopolist extracts full surplus, so marginal revenue coincides with the demand curve. But because of the surplus extraction, the average revenue curve is now higher than the demand curve. To see this, consider the following example. Suppose demand is given by Q = 10 P. The revenue of a monopolist who produces Q units is Q times price at Q plus the entire consumers surplus. Therefore the revenue of a first-degree price-discriminating monopolist from producing Q units, denoted by R FD (Q), is given by Since P = 10 Q, we can rewrite this as R FD (Q) = PQ + (10 P)Q R FD (Q) = (10 Q)Q + Q2 2 = 10Q Q2 2.

23 It follows that marginal revenue is MR(Q) = dr FD(Q) dq = 10 Q = P. Thus marginal revenue coincides with the demand curve. However, the average revenue curve is now higher than the demand curve: AR(Q) = R FD(Q) Q = 10 Q 2 > P. Question 4 Consider the following game. For what values of x does each player have a dominant strategy? Explain your answer. Player 2 A 2 B 2 C 2 A 1 3,3 3,0 1,2 Player 1 B 1 2,3 1,2 0,1 C 1 0,1 2,0 x, x The coverage of game theory in MKR (Chapter 16) is not ideal. See Chapter 9 (Game theory: an introduction) of the subject guide for a detailed discussion. This is an easy question. But you should be careful to read the payoffs of players correctly. Remember that the first number in each box is the payoff of the row player (player 1) and the second number is the payoff of the column player (player 2). Once you look at the right set of numbers for each player, it should be obvious that A 1 and A 2 are dominant strategies for 1 and 2 respectively if x < 1. Question 5 If the long-run average cost is decreasing in output, the long-run marginal cost must be decreasing in output as well. Is this true or false? Explain your answer. MKR Chapter 9; Subject guide Chapter 7 (The firm). This is false. Decreasing long-run average cost (LRAC) implies that long-run marginal cost (LRMC) is below long-run average cost, but has no implication on whether the LRMC is increasing or decreasing. As the picture below shows, LRMC can be increasing while still below LRAC. 23

24 EC2066 Microeconomics Cost LRMC LRAC Quantity Declining LRAC implies LRMC<LRAC, but as the picture shows, LRMC need not be decreasing. Question 6 If leisure is a normal good, the demand for leisure rises as wage rises. Is this true or false? Explain your answer. MKR Chapter 5.1; Subject guide Chapter 4 (Labour supply and the effect of taxes). Many candidates attempt to answer this question by drawing a picture to start with. Note that a picture is not very helpful here. What you need to do is to work through the logic of income and substitution effects. In fact, the best strategy for answering questions of this sort is as follows. Start by writing down substitution effect. Try to argue for the relevant price change, which direction the relevant demand changes. Next, write down income effect and clarify the direction of this effect. The answer should be apparent from the two effects you have just identified. Let us try this here. Substitution effect: As wage rises (the price of leisure rises), the substitution effect implies that an agent would consume less leisure. Income effect Since leisure is a normal good, the income effect (here the agent is richer) implies the agent would consume more leisure. The two effects go in opposite directions. Clearly, it is possible that the substitution effect dominates, in which case the demand for leisure would fall as wage rises. Therefore the statement is false. 24

25 Question 7 In an Edgeworth Box, a reallocation of resources from the initial endowment to any point on the contract curve always constitutes a Pareto improvement. Is this true or false? Explain your answer. MKR Chapter 12; Subject guide Chapter 11 (General equilibrium and welfare economics). This is one of the simplest questions here. It should be fairly obvious that this is false. If the endowment point is already on the contract curve, any reallocation will make one agent strictly worse off. Now consider any endowment point that is not on the contract curve. Reallocations to the part of the contract curve that is preferred by both agents compared to the endowment point are Pareto improving. Reallocations to other points do not constitute a Pareto improvement. Question 8 If consumption at all dates is a normal good, savers necessarily save less if the rate of interest falls. Is this true or false? Explain your answer. MKR Chapter 4; Subject guide Chapters 3 (Consumer theory) and 5 (Saving, investment and choice over time). This is false. This is another example where drawing a picture is not very helpful. If you try to draw a picture and get your answer from that, it is very likely you will answer incorrectly. You need to know the logic of the answer first, and then you can show this in a picture to clarify your own understanding, but you cannot simply draw a picture and try to guess the answer from that. Let us try to identify the different effects arising from a change in the interest rate. A fall in the interest rate has two effects. Substitution effect: The price of current consumption C 0 has fallen relative to future consumption C 1, so the agent will choose a higher C 0. This implies that the saver saves less. Income effect: The saver feels poorer as the interest rate decreases. Since consumption today is a normal good, the income effect implies that the saver will reduce today s consumption and save more. The two effects go in opposite directions. It is clear, however, that if the income effect is larger than the substitution effect, savers would save more. 25

26 EC2066 Microeconomics Question 9 Private provision of goods that are non-excludable and non-rival leads to over-provision compared to the socially optimal level. Is this true or false? Explain your answer. MKR Chapter 18; Subject guide Chapter 13 (Externalities and public goods). This is false. Goods that are non-excludable and non-rival are public goods. You should know that private provision of public goods leads to under-provision relative to the social optimum. Question 10 The LSE requires mobile phones to be switched off in the library. Assuming this is strictly enforced, does such a restriction enhance efficiency? Explain your answer. MKR Chapter 18; Subject guide Chapter 13 (Externalities and public goods). The answer to this question depends on how you interpret the question. If you associate phones with people talking, it is clear that the answer is yes since talking in a library generates negative externality on other users. Since the social cost of talking in a library outstrips the private benefit, the restriction enhances efficiency. On the other hand, smart phones now are often used for purposes such as surfing the internet, which generates no externalities, and there is no economic case for restricting such use. If you associate these sort of uses with phones, you would have to conclude that asking users to switch off phones reduces efficiency, and the correct policy would be to ask users to put their phones in the silent mode. Either answer is acceptable so long as you clarify your own interpretation of the question. 26 Section B Answer three questions from this section (20 marks each). Question 11 Suppose there are two identical firms in an industry. The output of firm 1 is denoted by q 1 and that of firm 2 is denoted by q 2. The total cost of production for firm i, i {1, 2}, is C(q i ) = 4 q i Let Q denote total output, i.e. Q = q 1 + q 2. The inverse demand curve in the market is given by P = 10 Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price.

27 (b) Suppose the firms can collude, and maximize joint profit. Calculate the deadweight loss arising under this scenario. (c) What would be the quantities produced by each firm and market price under Stackelberg duopoly if firm 1 moves first? (d) Now suppose the production process in the industry pollutes the environment and generates a marginal social cost given by MC E = 2Q Calculate the deadweight loss arising from the Cournot-Nash equilibrium in this case. MKR Chapter 15; Subject guide Chapter 10 (Oligopoly and strategic behaviour). (a) Firm 1 maximises (10 q 1 q 2 )q 1 4q 1. The first order condition is 6 2q 1 q 2 = 0 implying that the reaction function of firm 1 is given by q 1 = 3 q 2 2 Imposing symmetry, we have q 1 = q 2 = q where q = 3 q 2 which implies q = 2. Therefore the Cournot-Nash equilibrium quantities are given by q 1 = q 2 = 2 and the market price is P = 10 4 = 6. (b) If firms collude, together they maximise joint profit given by (10 Q)Q 4Q. The first order condition is 10 2Q 4 = 0 which gives us Q = 3 and therefore P = 7. To calculate the deadweight loss, note that the efficient quantity is the quantity demanded at price equal to MC. Here MC = 4, so the efficient quantity is Q = 6. Thus at the price-quantity pair (P, Q ), the deadweight loss is given by 1 2 (P 4)(6 Q ) Thus the deadweight loss under collusion is 9/2 =

28 EC2066 Microeconomics Price 10 D Q = 10 - P 7 Deadweight Loss MC = Quantity Calculating the deadweight loss from collusive equilibrium. (c) Now firm 1 takes firm 2 s reaction function as given. Firm 2 s reaction function is q 2 = 3 q 1 /2. Therefore firm 1 maximises ( ( 10 q q 1 2 )) q 1 4q 1 which simplifies to ( 3 q 1 2 ) q 1 The first order condition is given by 3 q 1 = 0 implying that q 1 = 3. It follows that q 2 = 3/2. The market price is /2 = 11/2 = 5.5. (d) The private marginal cost is 4, and the marginal externality cost is 2Q. Therefore the socially optimal quantity is given by which implies 4 + 2Q = P 4 + 2Q = 10 Q which implies that the socially optimal quantity is Q 0 = 2 and the associated price is P 0 = 8. At the total Cournot quantity 4, the social marginal cost is = 12, and the social marginal benefit is simply the height of the demand curve given by = 6. Therefore the deadweight loss is given by 1 2 (4 Q 0)(12 6) = 1 (4 2)(12 6) =

29 Price, Cost MC = 4 + 2Q Deadweight Loss P = 10 - Q 2 4 Quantity Calculating the deadweight loss from Cournot equilibrium with private marginal cost of 4 and an additional social marginal cost of 2Q. Question 12 Consider a market for used cars. There are some low quality cars and some high quality cars. Potential sellers have a car each, and there are many more buyers than possible sellers in the market. A high quality car never breaks down. A low quality car provides a poorer ride quality over longer journeys and also breaks down with positive probability. A seller values a high quality car at 9000 and a low quality car at A buyer values a high quality car at 10,000 and a low quality car at All agents are risk-neutral. In answering the following questions, assume that the sellers get the entire surplus from trade. (a) Suppose quality is observable to sellers but not to buyers. Buyers only know that a fraction 3/5 of the cars in the market are high quality and the rest are low quality. Would cars of both low and high qualities be traded in equilibrium? Derive the equilibrium price(s) at which such trade takes place. (b) Is the market outcome in part (a) efficient? Explain your answer. (c) Now suppose low quality cars break down with probability 0.7. Recall that high quality cars never break down. Suppose the sellers of high quality cars announce a guarantee that promises a full refund if the car breaks down. Show that with this guarantee, high quality cars sell for and low quality cars sell for (d) Suppose, as in part (c), that low quality cars break down with probability 0.7. Suppose the government decides to force each seller to offer a full refund if the car sold by the 29