Answer ALL questions in Sections A and B. Answer ONE question from Section C. Answer ONE question from Section D.

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1 UNIVERSITY OF EAST ANGLIA School of Economics Main Series UG Examination ADVANCED TOPICS IN ECONOMICS ECO-6007Y Time allowed: 3 hours Answer ALL questions in Sections A and B. Answer ONE question from Section C. Answer ONE question from Section D. Each Section (A-D) carries 25 marks. Notes are not permitted in this examination. Do not turn over until you are told to do so by the Invigilator. ECO-6007Y Module Contact: Dr Ben McQuillin, ECO Copyright of the University of East Anglia Version 1

2 SECTION A Page 2 1. Three individuals (dining together in a restaurant) are trying to choose a bottle of wine to share. There are four types of wine on the wine-list, and each individual s weak preference relation over the four alternatives is an ordering. The individuals preference orderings must be somehow combined to make a group decision. a) Suppose the group uses the following social preference function to determine their joint ( social or group ) preferences over the four alternatives. In the social preference relation, any one alternative (x) will be strictly preferred to any other (y) if and only if at least two individuals strictly prefer x to y. Which one of the axioms in Arrow s Impossibility Theorem (universal domain, Pareto efficiency, non-dictatorship, or independence of irrelevant alternatives) is contravened by the social preference function? (Briefly explain your answer.) [5 marks] b) Now suppose the group uses the following social choice function to make their actual choice. They will not choose any alternative that is ranked, by any one individual, strictly lower than all the other alternatives (i.e. any alternative that is somebody s least preferred ). If more than one alternative is nobody s least preferred then, from these remaining alternatives, they will choose the one which is ranked highest by the oldest member of the group. (If the oldest member ranks more than one remaining alternative equal-highest, then they will choose alphabetically between these.) Which one of the axioms in the Gibbard-Satterthwaite Theorem (surjectivity, non dictatorship, or strategy-proofness) is contravened by the social choice function? (Again, briefly explain your answer.) [4 marks] 2. Assume a large number of workers, and a large number of prospective employers, all of whom are risk-neutral. Workers are of two types: one-third are H- types (with high productivity) and two-thirds are L-types (with lower productivity). Both types have a true value to employers: H-types are worth 80,000 and L-types are worth 20,000. A worker s type is observed by herself but hidden from prospective employers. However, employers can stipulate within any offered contract that a worker needs some quantity (y) of post-16 educational qualifications. Post-16 qualifications do not increase (or decrease) any specific worker s productivity. The cost of obtaining a quantity y of such qualifications for L-types is given by cl(y) = 30y, and for H-types is given by ch(y) = 15y. In this screening model, what contracts will be offered in equilibrium? (Briefly explain your answer.) [8 marks] ECO-6007Y Version 1

3 Page 3 3. Adele is an accountant, Bruce is a business-analyst, and Chrissie is a computerscientist. Working alone, Adele can earn 40,000, Bruce can earn 20,000, and Chrissie can earn 50,000 per year. But they realise that by setting up a small business-services firm they can increase their earnings. A company comprising Adele and Bruce will earn 110,000; Adele and Chrissie will earn 100,000; Bruce and Chrissie will earn 90,000. A company comprising all three will earn 160,000. a) Present this situation as a cooperative game. [2 marks] b) What is the Shapley value of the game? [3 marks] c) Does the Shapley value, in this case, lie in the core? (Briefly explain your answer.) [3 marks] SECTION B 4. Use the static AS-AD model assuming zero ongoing inflation (i.e. nominal and real interest rates coincide), a closed economy, and an initial equilibrium in which the level of real output corresponds to the natural rate of employment determined by the imperfect-competition model of the labour market. Answer all the following questions: a) Assume that the Central Bank reduces its stock of assets by selling domestic government bonds by means of open market operations. Describe the effects of this intervention on the following variables: - Real output in the short run - The price level in the short run - The interest rate in the short run Also describe the mechanisms operating on the labour market, the financial market, and the goods market, that cause each of the short run effects that you set out above. [10 marks] b) Describe the effects of the monetary intervention considered in question (a) on the following variables: - Real output in the medium run - The price level in the medium run - The interest rate in the medium run Also describe the mechanisms operating on the labour market, the financial market, and the goods market, that cause each of the medium run effects that you set out above. [10 marks] c) Does the monetary intervention considered in question (a) affect the unemployment rate in the medium run? Explain your answer by briefly discussing the general properties of the imperfect-competition model of the labour market that are relevant to your answer. [5 marks] TURN OVER ECO-6007Y Version 1

4 SECTION C Page 4 5. How reasonable is Expected Utility Theory as a model for decision making in the context of risk and uncertainty? Do the Allais-paradoxes show that we should be using a different model? 6. What is meant by an incentive contract in the context of a principal-agent model? Why does such a contract not, typically, entirely eliminate the inefficiency associated with hidden actions? 7. Discuss whether the Nash Bargaining Solution seems more reasonable as a description of what should happen (i.e. a normative claim), or as a description of what would happen (i.e. a positive claim), when two players are determining how to divide a cooperative surplus. 8. Using at least one of Alvin Roth s applications of matching mechanisms to illustrate your answer, explain the significance of stability and of truth-revelation in the context of matching-market design. SECTION D 9. Define the expectations-augmented Phillips Curve, explain why it has been used to explain the US data in the s, and discuss its consequences for policies that make the unemployment rate deviate from its natural level. 10. Describe the monetary interventions enacted by the ECB (European Central Bank) in response to the 2008 Global Crisis, and discuss the effectiveness of such policies in connection with the recently observed levels of interest rates. Discuss the possibility of using fiscal policy to speed up the recovery. 11. Compare the traditional Keynesian consumption function with modern consumption theories in which households are forward looking and choose consumption plans according to intertemporal optimization. Explain how the predictions of the two theories differ and discuss the empirical evidence on income sensitivity. END OF PAPER ECO-6007Y Version 1

5 Advanced Topics in Economics (ECO-6007Y) 2016/17 Main Series Exam - Exam Feedback In this document we provide sketch answers for all questions that appeared in the 2016/17 main series exam. The overall frequency distribution for marks is given below. The overall average mark was (up from in 2015/16), and the median was (up from 59.00). The question that posed greatest problems for students was the first question on the paper: question 1(a). Only 19 (out of 100) students answered this broadly correctly. This contributed to performances being generally lower on Section A than on other sections in the exam. The average marks were 12.17, 16.96, and (out of 25) for Sections A, B, C and D respectively. Advanced Topics in Economics /17 Main Series Exam Marks (Frequency Distribution) In the following, the exam questions are shown in black text and sketch answers are then given in blue text. SECTION A 1. Three individuals (dining together in a restaurant) are trying to choose a bottle of wine to share. There are four types of wine on the wine-list, and each individual s weak preference relation over the four alternatives is an ordering. The individuals preference orderings must be somehow combined to make a group decision. a) Suppose the group uses the following social preference function to determine their joint ( social or group ) preferences over the four alternatives. In the social preference relation, any one alternative (x) will be strictly preferred to any other (y) if and only if at least two individuals strictly prefer x to y. Which one of the axioms in Arrow s Impossibility Theorem (universal domain, Pareto efficiency, non-dictatorship, or independence of irrelevant alternatives) is contravened by the social preference function? (Briefly explain your answer.) [5 marks]

6 The SPF contravenes universal domain. The SPF fulfils Pareto efficiency, because if all individuals strictly prefer x to y then, in the social preference relation, x will be strictly preferred to y. It fulfils nondictatorship, because for any individual there is a possibility of being out-voted. It fulfils IIR, because the social preference over x and y depends only on individual preferences over x and y. But it violates universal domain because (due to the Condorcet paradox), for some combinations of individual preferences the social preference relation will be intransitive and therefore not an ordering. b) Now suppose the group uses the following social choice function to make their actual choice. They will not choose any alternative that is ranked, by any one individual, strictly lower than all the other alternatives (i.e. any alternative that is somebody s least preferred ). If more than one alternative is nobody s least preferred then, from these remaining alternatives, they will choose the one which is ranked highest by the oldest member of the group. (If the oldest member ranks more than one remaining alternative equal-highest, then they will choose alphabetically between these.) Which one of the axioms in the Gibbard-Satterthwaite Theorem (surjectivity, non-dictatorship, or strategy-proofness) is contravened by the social choice function? (Again, briefly explain your answer.) [4 marks] The SCF violates strategy-proofness. The SCF fulfils surjectvity, because any bottle of wine could be socially chosen; and non-dictatorship because even the oldest member of the group may not get her firstpreference (if somebody else ranks it lowest). But it is not strategy-proof because (for example) a diner who knows her least preferred is the same as somebody else s, my state her second-least preferred as least-preffered in order to guarantee one of her top-two choices. 2. Assume a large number of workers, and a large number of prospective employers, all of whom are risk-neutral. Workers are of two types: one-third are H- types (with high productivity) and two-thirds are L-types (with lower productivity). Both types have a true value to employers: H-types are worth 80,000 and L-types are worth 20,000. A worker s type is observed by herself but hidden from prospective employers. However, employers can stipulate within any offered contract that a worker needs some quantity (y) of post-16 educational qualifications. Post-16 qualifications do not increase (or decrease) any specific worker s productivity. The cost of obtaining a quantity y of such qualifications for L-types is given by cl(y) = 30y, and for H-types is given by ch(y) = 15y.

7 In this screening model, what contracts will be offered in equilibrium? (Briefly explain your answer.) [8 marks] In an equilibrium it must be that no contracts being offered make a loss (for the employers), no contracts not being offered make a profit, and (by deduction), no contracts being offered and accepted make a positive profit. To fulfil this we will have two contracts, (w* L, y* L) accepted by all the L-types, and (w* H, y* H) accepted by all the H-types, with: w* L = 20,000 [lower leads to profits, higher leads to losses] w* H = 80,000 [ditto] y* L = 0 [otherwise (w* L-ε, 0) would be accepted and profitable] y* H = (80,000-20,000)/30 = 2,000 [if higher, then (w* H-ε, y* H-ε) would be accepted and profitable, if lower then the L-types would accept this contract.] To be thorough, we should check that, given the above, the contract (( 80, ,000 + ), 0) - i.e. a contract aiming to attract all workers in the context above - is not now profitable. And indeed it isn t, because it pays 50,000 + for an average prodctivity of just 80,000 ⅓ + 20,000 ⅔ = 40, Adele is an accountant, Bruce is a business-analyst, and Chrissie is a computerscientist. Working alone, Adele can earn 40,000, Bruce can earn 20,000, and Chrissie can earn 50,000 per year. But they realise that by setting up a small business-services firm they can increase their earnings. A company comprising Adele and Bruce will earn 110,000; Adele and Chrissie will earn 100,000; Bruce and Chrissie will earn 90,000. A company comprising all three will earn 160,000. a) Present this situation as a cooperative game. [2 marks] We can present this as a TU game in characteristic function form, (N,v), with: N = {A, B, C}, v(a) = 40,000, v(b) = 20,000, v(c) = 50,000 v(ab) = 110,000, v(ac) = 100,000, v(bc) = 90,000, v(abc) = 160,000 b) What is the Shapley value of the game? [3 marks] Ordering: A s marginal cont. B s mariginal cont. C s marginal cont. ABC 40,000 70,000 50,000 ACB 40,000 60,000 60,000 BAC 90,000 20,000 50,000 BCA 70,000 20,000 70,000 CAB 50,000 60,000 50,000 CBA 70,000 40,000 50,000 Average: 60,000 45,000 55,000

8 Based on the calculation above, the Shapley value is given by (φ A, φ B, φ C) = (60000, 45000, 55000). c) Does the Shapley value, in this case, lie in the core? (Briefly explain your answer.) [3 marks] The Shapley value, in this case, does not lie in the core, because we have φ A + φ B < v(ab). SECTION B 4. Use the static AS-AD model assuming zero ongoing inflation (i.e. nominal and real interest rates coincide), a closed economy, and an initial equilibrium in which the level of real output corresponds to the natural rate of employment determined by the imperfect-competition model of the labour market. Answer all the following questions: a) Assume that the Central Bank reduces its stock of assets by selling domestic government bonds by means of open market operations. Describe the effects of this intervention on the following variables: - Real output in the short run - The price level in the short run - The interest rate in the short run Also describe the mechanisms operating on the labour market, the financial market, and the goods market, that cause each of the short run effects that you set out above. [10 marks] By selling domestic bonds, the central bank withdraws liquidity from the market and thus restricts money supply. Therefore, the short run effects include (i) a decrease in real output, (ii) a decrease in the price level, and (iii) an increase in the interest rate. The decrease in liquidity generated by the monetary contraction of the Central Bank generates, according to the theory of liquidity preference, an excess supply of bonds on the financial market, which (reduces bond prices and, consequently) increases market interest rates. In the goods market, the increase in the interest rate depresses investment and thus reduces aggregate demand. In the short run, reduced aggregate demand decreases output below the equilibrium level, and pushes unemployment above the natural level. In the labour market, underemployment induces a reduction in the nominal wage requested by workers and, hence, a reduction in the output price charged by firms. b) Describe the effects of the monetary intervention considered in question (a) on

9 the following variables: - Real output in the medium run - The price level in the medium run - The interest rate in the medium run Also describe the mechanisms operating on the labour market, the financial market, and the goods market, that cause each of the medium run effects that you set out above. [10 marks] The medium-run effects of the monetary contraction include (i) no effect in real output, (ii) a proportional decrease in the price level, and (iii) no effect on the interest rate. In the medium run, the decrease in the price level that is observed in the short run is incorporated in the expectations of wage setters: as firms reduced prices, workers will supposedly accept cuts in nominal wages since they face lower-than-expected prices in subsequent rounds of negotiations. As nominal wages decline, they induce further reductions in actual prices on the side of firms, and the catch-down between actual and expected prices ends up into a new equilibrium in the labour market featuring a lower nominal wage, a lower output price charged by firms, but the same real wage as before the shock. Graphically, in the medium run the AS curve shifts downward repeatedly until the AD-AS equilibrium corresponds to the natural level of real output (the same as before the monetary intervention), which is however associated to a lower price level than before the monetary intervention. That is, money is neutral in the medium run. In the financial market, the interest rate goes back to the same level as before the monetary intervention because the price level decreases so as to increase real money supply after the initial contraction: when the economy is back to the same level of real output, real money supply is back to the same level observed before the monetary intervention (while nominal money is lower). Graphically, the LM shifts right to the pre-shock position in the medium run. Since output and the interest rate are, in the medium run, the same as before the monetary intervention, investment is unchanged as well. c) Does the monetary intervention considered in question (a) affect the unemployment rate in the medium run? Explain your answer by briefly discussing the general properties of the imperfect-competition model of the labour market that are relevant to your answer. [5 marks] In the medium run, according to the AD-AS model with imperfect competition, unemployment is back to the natural rate. The main characteristic driving the result of money neutrality in the medium run is the fact that the natural equilibrium of the labor market is characterized by a level of unemployment that is exclusively determined by technology, endowments, market structure (i.e., existence of mark-ups) and other institutional factors (e.g., level of unemployment benefits, regulation, employment protection ) since these are the determinants aggregate real supply when there is no

10 mismatch between actual and expected prices and wages. This theory hinges on the idea that such mismatches may arise in the short run and such fluctuations may well be induced by monetary and fiscal policy, in addition to other types of demand-side shocks like consumers confidence and expectations but vanish in the medium run as economic agents are supposed to learn, sooner or later, the actual prices and wages that will prevail in future negotiations. SECTION C 5. How reasonable is Expected Utility Theory as a model for decision making in the context of risk and uncertainty? Do the Allais-paradoxes show that we should be using a different model? [We were looking for explanations of: What is expected utility? What conditions do preferences (including in the context of risk and uncertainty) need to fulfil in order to be representable by utilities? What are the Allais paradoxes? There should then have been some interpretative discussion about the Allais paradoxes Do they imply that we should be using a different model (such as prospect theory)? Or are they (the paradoxes) just special cases, akin to optical illusions? Or, perhaps, even if the paradoxes are real are there good arguments (such as those of Gul and Pesendorfer) for continuing to base economic models on the idealized rationality reflected in EUT?] 6. What is meant by an incentive contract in the context of a principal-agent model? Why does such a contract not, typically, entirely eliminate the inefficiency associated with hidden actions? [We were hoping to see an explanation of the principal-agent problem itself perhaps with a stylized example, and then perhaps a derivation of an appropriate incentive contract for such an example. Ideally, there might have been a demonstration that this contract remains inefficient. Crucially, however, there had to be an explanation that the incentive contract transfers risk from the principal to the agent, and yet the agent is (we assume) more likely to be risk averse. In the best essays there would be some discussion of the real-world applicability of this problem.] 7. Discuss whether the Nash Bargaining Solution seems more reasonable as a description of what should happen (i.e. a normative claim), or as a description of what would happen (i.e. a positive claim), when two players are determining how to divide a cooperative surplus. [We were hoping to see an explanation of what is a bargaining problem, and then an

11 explanation of the Nash bargaining solution: an explanation of the axioms (efficiency, symmetry, IIR and scale-covariance), and a definition of the solution (as the outcome in the bargaing set that, relative to the default allocation or threat point, maximizes the product of utility gains). Then, in discussing whether the solution is more compelling from a normative or from a positive perspective, good essays may have considered the axioms one by one: i.e. do the axioms seem like conditions of fairness, or of ideal rationality, or do they seem like descriptions of what we would expect? The may also have mentioned the Nash programme : for example, the fact that a Rubinstein-type non-cooperative bargaining model supports the solution. What implications does this have for the solution s (normative/positive) status?] 8. Using at least one of Alvin Roth s applications of matching mechanisms to illustrate your answer, explain the significance of stability and of truth-revelation in the context of matching-market design. [Alvin Roth has been involved in the design of clearing houses (in the US) that assign junior doctors to hospitals (the National Residency Matching Program, in the US), children to junior state schools (in Boston), older children to high schools (in New York City) and also that facilitate chains of kidney-exchanges (initially through the New England Kidney Exchange), Students were expected to focus on any one of these. Stability in this context means that the matching created is in the core. Without stability, there is a likelihood that some agents will try to circumvent the clearing house. On the other hand, if we really only care about one side of the market, stability can conflict with strong Pareto efficiency (from the perspective of agents on this side of the market). Truth revelation means that it is a weakly dominant strategy for agents to declare their true preference ordering to the clearing house. Without this property, the clearing house becomes difficult to use, unfairly advantages agents who know how to play the system, and fails to reveal useful information about (for example) which schools are truly popular. On the other hand, there are theorems that show no mechanism to be wholly strategy-proof: perhaps the best that can be achieved can be to make the mechanism strategy proof from one side of the market. (By treating one side as proposers in a Gale-Shapley algorithm, the mechanism becomes strategy proof for this side of the market; which is what Roth et al did for Boston Schools.)] SECTION D 9. Define the expectations-augmented Phillips Curve, explain why it has been used to explain the US data in the s, and discuss its consequences for policies that make the unemployment rate deviate from its natural level. In the s, inflation became more persistent in the US, leading to a reassessment of the nature of the Phillips Curve. Originally, the Phillips Curve was

12 considered to be a stable negative empirical relationship between inflation and unemployment rates. This is what Phillips in the UK, and Solow and Samuelson in the USA, discovered when they looked, in the late 1950s, at the joint behaviour of unemployment and inflation. But the reason for the apparent stability of the Phillips Curve was that inflation was not persistent within the time sample used in empirical studies. When inflation is not very persistent, expected inflation does not depend very much on past inflation. Thus, the standard approach to rationalize the existence of a stable Phillips Curve was a simple transformation of existing static short-run models: the aggregate supply curve, a positive relationship between output and price levels, was redefined as a negative relationship between inflation and unemployment rates. However, as inflation became more persistent in the 1970s and 1980s, the data did not show a stable Phillips Curve anymore. To explain this fact, economists began to use a modified Phillips Curve, called "expectations-augmented Phillips Curve" in which expectations of inflation were based more and more on past inflation. In this new framework, the Phillips Curve takes the form of a relation between unemployment and the change in inflation. High unemployment leads to decreasing inflation; low unemployment leads to increasing inflation. The natural unemployment rate is then redefined as the unemployment rate at which the inflation rate remains constant (sometimes called NAIRU). When the actual unemployment rate exceeds the natural rate of unemployment, the inflation rate typically decreases; when the actual unemployment rate is less than the natural unemployment rate, the inflation rate typically increases. As a consequence, policies that drive the unemployment rate below its natural level will induce increasing inflation: stable inflation will only be achieved by letting the unemployment rate be equal to its natural level for a while. By the same token, disinflation policies aiming at stabilizing the inflation rate at a low level will bear the cost of keeping for some time unemployment rates above their natural level. 10. Describe the monetary interventions enacted by the ECB (European Central Bank) in response to the 2008 Global Crisis, and discuss the effectiveness of such policies in connection with the recently observed levels of interest rates. Discuss the possibility of using fiscal policy to speed up the recovery. The ECB responded to the crisis through a mix of conventional and non-conventional monetary policies aimed at expanding liquidity. Conventional: official interest rates were cut in a sequence of steps, bringing the main refinancing rate down to 1%. Non-conventional: (i) European banks were granted unlimited liquidity at a fixed interest rate at maturities of up to a year. (ii) The ECB granted cash to banks in exchange for a wider range of assets owned by commercial banks at their ECB accounts. (iii) Covered bonds: the ECB bought securities issued by commercial banks. (iv) More recently, the ECB embarked on Quantitative Easing (QE), buying directly long-term bonds, private sector obligations and loans made by banks to households with long maturity; the idea is to reduce longer-term interest rates further

13 out on the yield curve and, perhaps, encourage investments through this channel. Effectiveness: Since the end of 2008, conventional monetary policies reduced official interest rates down to zero. The implied liquidity trap (agents become indifferent between bonds and money so that money supply expansions do not reduce interest rates further and, hence, cannot encourage investment to raise aggregate demand) made central banks conventional policies ineffective. This is why unconventional measures have been used further. However, unconventional measures like (i)-(iii) only increase liquidity temporarily (6 months, 1 year); regarding (iv), the evidence on the effectiveness of Q.E. is mixed. Is fiscal policy an option? In principle yes but the government budget constraints matter in several countries. In many European Countries, the ratio of government debt to GDP has markedly increased in the recent decades. High debt implies that, sooner or later, either taxes will have to increase or spending will have to decrease, or the government will be unable to repay the debt back. And when investors become worried about repayment of the debt, they start asking for higher interest rates on government bonds, making it even harder for the government to repay the debt. These worries could lead to higher interest rates in a number of European countries, which would then force national governments to reduce budget deficits and thus limit the potential for using fiscal policy to speed up the recovery. 11. Compare the traditional Keynesian consumption function with modern consumption theories in which households are forward looking and choose consumption plans according to intertemporal optimization. Explain how the predictions of the two theories differ and discuss the empirical evidence on income sensitivity. The traditional "Keynesian" consumption function postulates that consumption is a positive function of current disposable income with a fixed marginal propensity to consume. It is a relationship between flows (consumption and current income) and, as such, does not take into account the impact on current consumption of stocks like the households' financial assets and the so-called human wealth (the present-value of all expected net labour earnings of the household). An important implication of assuming a Keynesian consumption function is that consumption levels are extremely sensitive to shocks on current income. Modern consumption theories based on forward-looking consumers and intertemporal optimization predict, instead, that consumption depends on both wealth and current income. Wealth is the sum of non-human wealth (financial wealth and housing wealth) and human wealth.