FIRST PUBLIC EXAMINATION

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1 A10282W1 FIRST PUBLIC EXAMINATION Preliminary Examination for Philosophy, Politics and Economics Preliminary Examination for Economics and Management Preliminary Examination for History and Economics SECOND PUBLIC EXAMINATION Honour School of Engineering, Economics and Management (Part B) Honour School of Materials, Economics and Management (Year 2) INTRODUCTORY ECONOMICS TRINITY TERM 2015 Monday, 22 June :30-12:30 Please start the answer to each question on a separate page. There are 10 questions in this paper. Answer four questions: three from Part A and one from Part B. All questions attract the same number of total marks. For multipart questions, the weight assigned to each part is indicated in square brackets. Candidates should show knowledge of both Microeconomics and Macroeconomics by answering at least one question on Microeconomics and at least one on Macroeconomics. Candidates may use a calculator as specified by the Department of Economics. Do not turn over until told that you may do so. 1

2 Part A Answer three of the six questions in this section. 1. [Microeconomics] Consider two perfectly divisible goods, x 1 and x 2, which a consumer can purchase in any amounts she wishes. Suppose that her preferences are described by the utility function u = logx 1 + 2logx 2 (a) Show that her Marshallian/uncompensated demands for the two goods are x 1 = 1 m 3 p 1 x 2 = 2 m 3 p 2 where p 1 and p 2 denote the prices of the two goods and m is the available budget. [15%] (b) Suppose that the prices of both goods are 1 and that she has 2 to spend. What will her demand for each good be? [15%] (c) Draw a diagram showing the budget constraint, the chosen bundle and the indifference curve (place good one on the vertical axis). [15%] (d) Now suppose that these goods are only available in discrete, indivisible, integer amounts (0, 1, 2, ). Suppose that both prices remain at 1 and the consumer budget remains 2. What will her demands be? Explain your answer. [15%] (e) Show using a diagram (good one on the vertical axis) that the consumer will be worse off as a result of this indivisibility. [15%] (f) Using the prices p 1 = 1 and p 2 = 1 calculate a money-metric measure of the welfare cost of indivisibility. Draw a diagram illustrating your calculation. [25%] A10282W1 2

3 2. [Microeconomics] At present children s clothes are not subject to tax in the UK. In an effort to raise tax revenue the government is considering introducing a specific duty on children s hats. The table provides you with some information on the hat market in the year Annual Sales Revenue 27m Average price of a hat 9 Estimated aggregate elasticity of demand for hats -3/2 (a) Assuming linearity, derive the market demand curve and inverse demand curve. [15%] (b) Assuming the supply of hats is perfectly elastic, derive the inverse market supply curve. [15%] (c) Draw and label a supply and demand curve diagram illustrating the current equilibrium (with price on the vertical axis). [10%] (d) Suppose the government sets the tax at 2 per hat. (i) Calculate the new equilibrium price and quantity. (ii) Calculate the revenue raised by the tax. (iii) Calculate the deadweight loss, the change in consumer surplus, and the change in producer surplus. Provide an explanation for the effective incidence of the tax. (iv) Draw and fully label a diagram (with price on the vertical axis) illustrating the incidence of the tax. [30%] (e) Show that the revenue maximising tax rate is 3 per hat. [15%] (f) At what level should the government set the hat tax if it wishes the revenue raised to exactly offset the associated deadweight loss. [15%] A10282W1 3 turn over

4 3. [Microeconomics] Consider a market for a homogeneous good with a demand curve Q = 12 P. The marginal costs of production are 6. Suppose there is just one firm in the market: a monopolist. (a) What is marginal revenue? How and why does it differ from price P? [10%] (b) Draw the demand curve and marginal revenue curve. Indicate the point on the demand curve where the price elasticity of demand equals -1. Indicate on the demand curve the points associated with the lowest and highest elasticities. [15%] (c) Indicate on the diagram the monopolist s choice of output, assuming that the monopolist maximizes profit. Calculate the monopolist s choice of output. Does the monopolist produce too little output from society s point of view? What is the social cost of monopoly relative to perfect competition? Explain your answer. [25%] (d) Suppose the monopolist maximizes revenue instead of profit. Calculate the output that the monopolist sets. Indicate this on the diagram. Who wins and who loses when the monopolist changes from profit maximization to revenue maximization? What is the loss to society from monopoly now, relative to perfect competition? Comment on the social desirability of revenue maximization generally. [25%] (e) Suppose now that there are two firms in the market, each with marginal cost 6. The demand curve is as given above. Suppose the firms choose outputs to maximize profits, and set Nash equilibrium outputs, i.e. they compete as in the standard Cournot duopoly model. i. Compute total output in Cournot Nash equilibrium. ii. Is output higher or lower now than when there was a profit maximizing monopoly? Explain your answer. iii. In this example which is better for society: Cournot competition (with profit maximizing firms) or a revenue maximizing monopolist? Is this answer true more generally? (Hint: consider the case where marginal costs are zero). [25%] A10282W1 4

5 4. [Macroeconomics] Consider a small open economy with perfect capital mobility, described by the following functions C = C(Y T) I = I(r) G = G NX = NX(e) (M/P) d = L(Y, r) (M/P) s = (M/P) where C is consumption, I investment, G government spending, NX net exports, (M/P) d demand for real money balances, (M/P) s supply of real money balances, Y income, r interest rate, T taxes, P price level, and e the exchange rate. The exchange rate is expressed as units of foreign currency per unit of domestic currency, such that a rise in e represents an appreciation/revaluation of the domestic currency. Assume that this economy is initially at the natural level of output and prices are fixed. The country operates a floating exchange rate regime. (a) Explain why the interest rate in this economy is determined by the world interest rate, r (i.e. r = r ). [10%] (b) Using the model above, explain, with the aid of diagrams, the effects of each of the following changes on income: i. a decrease in money supply, ii. an increase in autonomous investment, iii. a decrease in the demand for real money balances, iv. a rise in the world interest rate. [50%] (c) What could be behind the changes in part (b)? Provide one example for each of the parts (ii) to (iv). [15%] (d) Suppose now that the price level is no longer fixed. Taking that into account, derive diagrammatically an aggregate demand curve for this economy. [10%] (e) Using the aggregate demand curve derived in (d) show, using a diagram, how the economy adjusts from the short-run equilibrium found in (b)(i). [15%] A10282W1 5 turn over

6 5. [Macroeconomics] Consider an economy that can be represented by the following relationships: C = α + β(y T) I = γ δr G = G where C is consumption, Y is income, T are lump-sum taxes, I is investment, r is the real interest rate and G is government spending. a) Solve for the equilibrium level of income as a function of parameters, exogenous variables and the real interest rate. Derive the slope of the IS curve. [15%] b) Suppose the government decides to change the tax system to a proportional income tax system, so that: C = α + β(y(1 t)) where t is the tax rate. Does the slope of the IS curve change? Provide economic intuition for your answer. [20%] c) Returning to the original specification at the start of the question, suppose consumption now additionally depends negatively on the real interest rate. What effect does this have on the effectiveness of monetary policy? [20%] d) With the consumption function given at the start of the question, how do the marginal and average propensities to consume change as disposable income changes? Does the evidence support these predictions? [25%] e) How and why do models of inter-temporal consumption such as the life-cycle hypothesis and the permanent income hypothesis produce different empirical predictions to those given in part (d)? [20%] A10282W1 6

7 6. [Macroeconomics] The Phillips curve in the Kingdom of the North is: π = π e 2(u 0.06) where π is inflation, π e is expected inflation and u is the unemployment rate. There are no supply shocks in the economy. The Governor of the Central Bank of the Kingdom of the North (from House Stark) can choose between inflation of 2% or 4% a year. For simplicity, assume that these are the only two possible values for inflation. The Governor s preferences over inflation and unemployment are described by a loss function: (π 0.02) 2 + u 2 which says there are losses whenever inflation deviates from its target rate of 2% (i.e. 0.02) or whenever unemployment is above zero. (a) Assume that expected inflation is π e = 2%. Will the central bank choose inflation of 2% or 4%? Explain. [15%] (b) If agents have rational expectations, what will inflation, expected inflation and unemployment be in the Kingdom of the North? [25%] (c) The Kingdom of the North is considering forming a monetary union with the Kingdom of the Rock. In that monetary union, the central bank would be under the control of the authorities of the Kingdom of the Rock (from House Lannister), who prefer an inflation rate of 2% regardless of unemployment. So, in that monetary union, inflation would always be 2%. If agents continue to have rational expectations, what would be the rate of unemployment in the Kingdom of the North? [15%] (d) The preferences of the Governor from House Stark are different to those of the Governor from House Lannister. Is that a problem if the Kingdom of the North joins the monetary union? Explain. [25%] (e) What does this parable tell us about recent problems in the Euro Area? [20%] A10282W1 7 turn over

8 Part B Answer one of the four questions in this section. 7. [Microeconomics] Critically compare the use of non-tradable emissions quotas as a means of controlling environmental problems versus the use of Pigouvian taxation. 8. [Microeconomics] The concept of Nash equilibrium is often used as a guide to help predict how economic agents will behave in strategic interactions. Explain what Nash equilibrium is and why it is useful. 9. [Macroeconomics] Why, after the Euro Area crisis, did some countries suffer a greater rise in unemployment than others? 10. [Macroeconomics] Is 80% a worrying ratio of government debt to GDP? A10282W1 8 Last page