SUMMER TERM 2017 ECON1604: ECONOMICS I (Combined Studies)

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1 SUMMER TERM 2017 ECON1604: ECONOMICS I (Combined Studies) TIME ALLOWANCE: 3 hours Answer ALL questions from Part A, ONE question from Part B, and ONE question from Part C. Correct but unexplained answers will not receive high marks. Questions in Part A carry five percent of the total mark each, and questions in Parts B and C carry twenty-five percent of the total mark each. In cases where a student answers more questions than requested by the examination rubric, the policy of the Economics Department is that the student s first set of answers up to the required number will be the ones that count (not the best answers). All remaining answers will be ignored. PART A Answer ALL questions from this section. A1 Suppose that the demand function for a good is Q = p + 20p s + Y, where p is the price of the good, Q is the quantity demanded, p s is the price of another good, and Y is the consumer s income. If initially p is 2 per unit, p s is 1 per unit, and Y is 100, then calculate the following three quantities: price elasticity of demand, cross-price elasticity of demand, and income elasticity of demand. Comment on the values of the elasticities. A2 Suppose the market for grass seed can be expressed as: Demand: Q D = 100 2p, Supply: Q S = 3p. If government imposes a 5 specific tax per unit sold to be collected from sellers, what is the price consumers will pay? How much tax revenue is collected? What fraction is paid by sellers? A3 Suppose that left shoes and right shoes must be purchased separately. Ingrid needs an equal number of each type of shoe and has a budget of 100 for shoes. Left shoes always cost 1. If right shoes cost 19 each, how many of each will Ingrid buy? If the price of right shoes increases to 49 each, how will Ingrid react? Explain your answer by drawing the indifference curves and budget lines. A4 Carmela s pasta factory employs workers and pasta machines according to the following production function f(l, K) = L 1/2 K 1/2. The hourly cost of capital is 10 and the hourly cost of workers is 40. Write out the Lagrangian for the cost-minimization problem. Suppose Carmela wishes to produce 1000 units of pasta. How much labour and capital should she employ? How much will it cost to produce 1000 units? An order arrives doubling the amount of pasta Carmela needs to produce. Assuming she is unable to purchase more capital, how much will it cost to meet the new production level? ECON TURN OVER

2 A5 Suppose anyone with a driver s licence is capable of supplying one trip from the airport to the downtown business centre on any given day. The long-run supply curve of such trips is horizontal at p = 50, which is the average cost of such trips. Suppose daily demand is Q = p. Calculate the change in consumer surplus, producer surplus and social welfare if the city government requires those people supplying such trips to possess a special licence, and the government will issue only 300 licences. A6 The demand for money is given by Md = Y (0.3 i), where Y = 100 and the supply of money is 20. What is the equilibrium interest rate? If the central bank wants to set i to 7%, at what level should it set the supply of money? Explain how the central bank can bring in this change in the supply of money. A7 Suppose there is a simultaneous increase in government spending and an increase in the money supply. Explain what effect this particular policy mix will have on output and the interest rate. Based on your analysis, do we know with certainty what effect this policy mix will have on investment? Explain using the IS-LM model. A8 Explain how a reduction in the proportion of contracts that are indexed affects the relationship between changes in the unemployment rate and inflation. A9 Assuming the Marshall-Lerner condition holds and using the ZZ/Y and NX graphs, explain what effect a real appreciation will have on output, exports, imports, and net exports. Clearly label all curves and clearly label the initial and final equilibria. A10 Explain what effect each of the following events will have on the IS curve in a flexible exchange rate regime: (1) an increase in foreign output; (2) a reduction in the foreign interest rate; and (3) an increase in the domestic interest rate. ECON CONTINUED

3 PART B Answer ONE question from this section. B1 A consumer can buy two goods, X and Y. Her utility function is U(X, Y ) = 20X 1 2 Y 1 2. The prices of the two goods are p X = 1 and p Y = 4 (both in per unit), and her exogenous income is m = 400 (in ). (a) Solve the consumer s utility-maximisation problem to obtain the optimal consumption bundle and maximised utility level. (b) Repeat part (a) with a different price with a different price for good X, namely p X = 2. (c) In part (b), what part of the total change in consumption of good X from part (a) is due to the substitution effect? How much of the change in consumption of good X is due to the income effect? (d) What is the minimum extra income that should be given to the consumer under prices p X = 2 and p Y = 4 so that her maximised utility is equal to that in part (a)? (e) What kinds of income adjustment is offered in part (d), cost of living adjustment or a true cost of living adjustment? What can be the problem to implement this kind of adjustment, e.g., by government? ECON TURN OVER

4 B2 The industry demand function for a particular good is D(p) = 24 p, where p is the price of the good (in /unit) and D(p) is the industry-wide quantity demanded. Suppose that there are n identical firms in this perfectly competitive industry, each with cost function C(q) = 9 + q 2, where q(p) is each firm s output and S(p) = nq(p) is the industry-wide quantity supplied. (a) Determine the average cost, average variable cost, average fixed cost, and marginal cost of each firm. (b) Find each firm s supply function, the industry supply function, and the equilibrium price and quantity in this industry. (c) What is the profit earned by each firm? In the long run, how many firms will be in this industry? Explain your answer in terms of a typical firm s profit. (d) Calculate the consumer surplus, producer surplus, and total surplus when the profit per firm is constrained to be zero. (e) Now assume that the government restricts the number of firms in the industry to one (therefore the industry is no longer a perfectly competitive one). Determine the new equilibrium price and quantity in this industry as well as the profit earned by each firm. What is the deadweight loss to society from this restriction? ECON CONTINUED

5 PART C Answer ONE question from this section. C1 Suppose you are asked to model unemployment in an economy with search frictions. Unemployed workers move into jobs at a rate f, which depends on job vacancies (v), a job search effectiveness parameter (i), and an index of mismatch (mm). Employed workers lose their jobs at a rate s. The labour force (L) is taken to be constant. (a) Derive expressions for the unemployment inflow and outflow, and the evolution of the unemployment rate. Obtain the steady state unemployment rate, and explain how the resulting structural relationship between the unemployment rate and the number of vacancies leads to the Beveridge curve. (b) Explain how the labour market determines the relationship between the number of vacancies and the unemployment rate (the job creation curve). (c) Take f = v +i mm, i = 0.1, mm = 0.2 and s = 0.1. Assuming that the job creation curve is described by v = 10u, derive equilibrium levels for u and v, where u is the unemployment rate. (d) Suppose now that, due to some economic event, there are increases in both the separation rate and the mismatch rate, so that s = 0.4 and mm = 0.5. Describe what happens to the Beveridge and job creation curves. What would be the new equilibrium levels for the unemployment rate and the number of vacancies? (e) Give some examples of possible economic events that might lead to increases in either s, mm or both. Suggest any possible remedial actions that the government might consider in such an event. ECON TURN OVER

6 C2 Consider the Mundell-Fleming model for a small open economy with floating exchange rates: IS: Y = C(Y T ) + I(Y, i) + G LM: IRP: i = i. M = P Y L(i), IM(Y, ɛ) ɛ + X(Y, ɛ), Here, for the domestic economy, C is the consumption function, Y is domestic (real) GDP, T is government taxes, I is investment, G is government spending, IM is imports, X is exports, M is the nominal money stock, P is the domestic price level and L(i) is the liquidity function. The domestic and foreign interest rates are i and i respectively and Y is foreign (real) GDP. The real exchange rate is given by ɛ and you may assume that price levels remain constant throughout. (a) State the Marshall-Lerner condition with any necessary assumptions for it to be valid. Explain the dynamics of the effects of a sudden depreciation in the domestic currency on the trade balance. (b) Suppose the economy is experiencing a situation where output is at its natural level but there is a large trade deficit. The policy makers goal is to reduce the trade deficit while leaving output unchanged.what type of exchange rate policy and/or fiscal policy can be used to achieve this goal? Explain using graphs and words. (c) Is fiscal policy more effective at stimulating the economy under fixed exchange rates or floating exchange rates? Explain your answer using a graph and words. (d) Let the economy be in a liquidity trap (i = i = 0) with high and growing national debt. Show graphically using the Mundell-Fleming model and explain in words how a loss of confidence in the economy from foreign investors could lead to an increase in output. ECON END OF PAPER