202 Fall 10, PS 4 Discuss

202 Fall 10, PS 4 Discuss - ECO 202, Lyons Fall 2010...

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ECO 202, Lyons Fall 2010 PROBLEM SET IV DISCUSSION SHEET CHAPTER 12 Problem 1: Begin, as usual, by finding PAE, given the information in the problem, remembering to plug in the interest rate as a decimal fraction (0.10, rather than 10%). PAE = C + Ip + G + NX = [2,600 + 0.8(Y - 3,000) - 10,000•0.10] + [2,000 - 10,000•0.10] + [1,800] + [0] = [2,600 + 0.8Y -2,400 - 1,000] + [2,000 - 1,000] + [1,800] = 2,000 + 0.8Y Solve for equilibrium (i.e., where PAE = Y): PAE = Y = 2,000 + 0.8Y => 0.2Y = 2,000, so PAE = Y = 10,000 . Graphically, you will observe that a plot of the expenditure line PAE = 2,000 + 0.8Y, crosses the equilibrium line (PAE = Y) where Y = 10,000. Problem 2 (a & b): a) Given the results of problem 1, if potential output, Y*, is equal to 12,000, then the economy is suffering a recessionary gap, and monetary policy should be expansionary, which means acting to lower the real (and nominal) interest rate. There are two ways to proceed: i) The recessionary gap is 2,000, so the Fed must lower the interest rate by enough to increase autonomous expenditures by 400 (that is, given the expenditure multiplier of 5 derived from the mpc of 0.8). Two components of expenditure are interest-rate-sensitive -- autonomous consumption and investment. The interest-sensitive components are -10,000• r in each case, so together the impact of r is –20,000• r . We want PAE = 400 = -20,000• r , so r = –0.02. That is, the interest rate must be reduced by two percentage points from 10% to 8% . ii) Solve the equation in problem 6 for r after substituting Y* = 12,000 for Y: Y*= 12,000 = PAE = [2,600 + 0.8(12,000 -3,000) -10,000• r ] + [2,000 - 10,000• r ] + [1,800] + [0] 12,000 = [2,600 + 7,200 - 10,000• r ] + [2,000- 10,000• r ] + [1,800] 20,000• r = 2,600 + 7,200 + 2,000 + 1,800 - 12,000 = 13,600 - 12,000 = 1,600 Thus, r = 1,600/20,000 = 0.08, or 8%. * Lowering the real interest rate by 2% is correct policy. b) If Y* = 9,000, the Fed should raise the interest rate to eliminate the expansionary gap. Using the method of a) i) above: Since the gap is 1,000 and the multiplier is 5, autonomous expenditures must fall by 200. A 1% increase in the interest rate will accomplish this end, since –20,000•0.01 = –200.
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This note was uploaded on 10/20/2011 for the course ECO 202 taught by Professor Normmiller during the Spring '08 term at Miami University.

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202 Fall 10, PS 4 Discuss - ECO 202, Lyons Fall 2010...

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