ans6154a

ans6154a - Economics 154a, Spring 2005 Intermediate...

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Unformatted text preview: Economics 154a, Spring 2005 Intermediate Macroeconomics Problem Set 6: Answer Key March 28, 2005 1. Numerical Problem # 4 on Chapter 10: An economy has the following AS-AD curves: AS Curve y = 300 + 30( M/P ) AD Curve Y = Y + 10( P- P e )... (a) What are the equilibrium levels of the price level, P , and output, Y ? ANSWER : P e = 60. Setting AD = AS to eliminate Y , we get 300+30( M/P ) = 500+10( P- P e ). Plugging in the values of M and P e gives 300+(30+400 /P ) = 500+10( P- 60), or 300+(12 , 000 /P ) = 500+10 P- 600, or 400+(12 , 000 /P ) = 10 P . Multiplying this equation through by P/ 10 gives 40 P + 1200 = P 2 , or P 2- 40 P- 1200 = 0. This can be factored into ( P- 60)( P- 20) = 0. P cant be negative, so the only solution to this equation is P = 60. At this equilibrium P = P e , so Y = 500, and the economy is at full-employment output. (b) An unanticipated increase raises money supply to M = 700. ANSWER :With an unanticipated increase in the money supply to M = 700, the expected price level is unchanged at P e = 60. The aggregate demand curve is Y = 300+30( M/P ) = 300+(30 700 /P ) = 300+(21 , 000 /P ). The aggregate supply curve is Y = 500 + 10( P- P e ) = 500 + 10( P- 60) = 10 P- 100. Setting AD = AS to eliminate Y gives 300 + (21 , 000 /P ) = 10 P- 100, or 400 + (21 , 000 /P ) = 10 P , or P- 40- (2100 /P ) = 0. Multiplying through by P gives P 2- 40 P- 2100 = 0. This can be factored as ( P- 70)( P- 30) = 0, which has the positive solution P = 70. From the AD curve, Y = 300 + (21 , 000 /P ) = 300 + (21 , 000 / 70) = 600. (c) The Fed announces that the money supply will be increased to M = 700, which the public believes. ANSWER : When M = 700 and is anticipated, P = P e . Then the AD curve is Y = 300 + (21 , 000 /P ) and the AS curve is Y = 500. Setting AD = AS gives 500 = 300 + (21 , 000 /P ), which has the solution P = 105. 1 2. (a) Suppose that the discovery of a new technology increases the expected future marginal product of capital, but does not affect current productivity. Explain how and why this new technology shifts the IS curve. ANSWER : The IS curve represents the equilibrium between investment and savings. An increase in the future marginal productivity of capital raises desired future capital and therefore raises desired investment at any given interest rate....
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ans6154a - Economics 154a, Spring 2005 Intermediate...

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