Macroeconomic

Winter Term 2017 Assignment 2 Due: Drop Box 2nd Floor Dunning Hall by 12 noon on Thursday, 16 February No late submissions will be accepted No “Photocopied” answers will be accepted Group submissions of four only will be accepted The assignment is worth 100 points Section A (40%): Short questions Read the following statements and indicate whether they are True, False or Uncertain. Briefly, but carefully, explain the economic intuition behind your answer using diagrams and examples where appropriate. All answers have equal value. NO MARKS WILL BE GIVEN FOR UNSUPPORTED WORK. A.1 The empirical evidence on the strength of the income versus the substitution effect cited in the text (page 437) indicates that, if anything, the income effect dominates. This in turn suggests that a rise in interest rates will tend to raise consumption spending, making it more difficult for central banks to control inflation by using interest rates to slow aggregate demand. A.2 Ricardian equivalence implies that consumers will not respond to a tax cut, preferring instead to save part of their income to pay for future tax increases. Given this, a policy of lowering taxes to stimulate demand will be ineffective. A.3 Shifts over time in the relationship between inflation and unemployment (the Phillips Curve) have been due solely to changes in expected inflation. A.4 A shift inward in the Beveridge can be taken as evidence that the labour market is functioning more efficiently. Section B (60%): Long questions B1. (30%) Consumption function with credit constraints and lump-sum taxes Consider an economy with two groups of consumers, the less well off, who have no initial wealth and are credit constrained (they cannot borrow or lend to smooth consumption) and the rich who have an initial endowment of wealth in period 1 of V1 and who can borrow or lend to smooth consumption. For simplicity, each has the same level of labour income in period 1 (Y1 L ). The two different consumption functions for period 1 are: C1 p = Y1 L -T1 (1) 2 C1 r =? V1 +Y1 L -T1 + Y2 L -T2 1+ r ? ? ? ? ? ?, 0 <1 (2) Equation (2) is the same as (18) in the main text (page 434). The coefficient ? is as defined by equation (17) in the text (page 433). For convenience assume that the population is normalized to one and that the fraction of poor people is µ. 1. Derive the economy’s aggregate consumption function defined as: C1 = µC1 p +(1-µ)C1 r (3) In addition, evaluate the marginal propensity to consume out of disposable income: ?C1 ? Y1 L ( -T1) Compare your results with an economy in which there are no credit-constrained households (e.g., µ = 0). Would a reduction in the number credit-constrained households increase or decrease consumption? Explain your reasoning. Suppose now that the government enacts a debt-financed reduction in current taxes (T1 ); that is, they keep planned spending unchanged. Assume as well that the public understands that the government will be raising taxes in the future in order to balance its budget and in particular to pay down the debts incurred in period 1. That is, all consumers are Ricardian and realize that: dT1 + dT2 1+ r = 0 (4) The above follows from the condition of the inter-temporal budget constraint for the government. 2. Derive the effect that this policy will have on present consumption ( C1 ). Compare as well, this situation to one where there are no credit-constrained households. Has the government’s policy helped or hindered credit-constrained consumers? In other words, has welfare increased or decreased? The other option for the government is to lower government spending by an amount equal to the tax cut. 3 3. Derive the effect on C1 of two different scenarios: a. A temporary tax cut financed by a reduction in G1 (that is, dG1 = dT1 and dG2 = dT2 = 0 ) b. Compare the above results to a permanent cut in government spending (that is, dG1 = dT1 = dG2 = dT2 ). In this case, you can assume that r = f . How are your results affected by the existence of credit-constrained consumers? B2. (30%) Aggregate demand The goods market equilibrium condition is given by: (1) The variables are as defined in the text (equation (13), page 456). The coefficients are given by: The coefficient m! =1/(1- DY ) >1is the Keynesian multiplier, while DY , Dr and Deare partial derivatives of the private demand, , where is confidence. The variables with bars represent long-run values. Remember that r and are the real current and long-run risky or market interest rates, respectively. At the central bank, diligent hard-working economists have found a definition of money that proves to be stable in relation to Y, i and P, where i is the short-run nominal rate of interest. The money demand equation is given by: L(Y, i) = kY ? e-ßi where k > 0; ? > 0 and ß > 0 (2) At any point in time, the real demand for money equals the real supply (M/P): kY ? e-ßi = M P (3) 1. Based on equations (2) and (3), derive a monetary-policy rule for the central bank. In other words, the central bank will use what it knows about the money demand function to set its short-term policy rate (i p ). Qualitatively, how does such a rule differ from the Taylor Rule (equation (21), page 461 in the text)? 2. Illustrate, using a diagram (similar in spirit to that used in class) how the aggregate demand (AD) curve is derived from the interaction of the central bank’s policy rule with the goods market equilibrium condition (equation (1) y - y =a1(g - g)-a2 (r - r)+ v a1 = m! G Y ? ? ? ? ? ?, a2 = -m! Dr Y ? ? ? ? ? ?, v = m! e De Y (lne - lne ) D = D(Y + , r - , e + ) e r 4 above). Then, using the monetary policy rule and the goods market equilibrium condition, derive algebraically the AD curve in the following form: y - y =a (p - p *) +? v -a2?ˆ +a1 ( (g - g)) (4) 3. Find expressions for the coefficients a and ? in terms of the underlying parameters of the system. Next write the AD curve with (p – p* ) on the left-hand side and then discuss how its slope is related to ß, the interest rate elasticity of money demand and ? the income elasticity of money demand. Discuss as well how these two slopes would affect how shocks shift the AD curve written with (p – p* ) on the left-hand side. During the 1970s and early 80s, both Canada and the United States experimented with using a monetary policy rule based on estimated money-demand functions. In Canada’s case, the interest elasticity of money demand (in absolute value) was higher than that of the United States ( ßCAN > ßUSA ), although each was estimated to be less than one. At the same time, the income elasticity for each was roughly the same (?CAN ??USA ). 4. To examine the role played by different vales of ß’s, assume that Canada and the United States start out with the same inflation rate and output level (in per capita terms) and that they both face identical SRAS curves. This is illustrated in the diagram below, where two AD curves have been plotted. In answering the following three questions use the diagram and be sure to support your answers. a. Which curve would represent Canada’s and which the United States’ and why? b. If there were a common short-run negative supply shock (SRAS moves up and to the left), what would be the initial effect on inflation and output in each country? Explain why the effects would be different. c. If there were a common positive demand shock (say v rises), what would be the initial effects on both inflation and output in each country? Again, explain why they would be different. [Hint: In answering parts b. and c. you should make reference to the monetary rule you derived in part 1.] 5 AD and SRAS p y y SRAS AD AD – p = p*