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Unformatted text preview: Economics 154a, Spring 2005 Intermediate Macroeconomics Problem Set 8: Answer Key April 11, 2005 1. Do numerical problem #4 on p. 425 in Chapter 11 of the textbook: An economy is described by the following equations: Desired Consumption C d = 300 + 0 . 5( Y T ) 300 r ... (a) Write the equation for the aggregate demand curve. ... ANSWER : The IS curve is given by Y = C d + I d + G = 300 + 0 . 5( Y 100) 300 r + 100 100 r + 100 = 450 + 0 . 5 Y 400 r . This can be rewritten as . 5 Y = 450 400 r , or Y = 900 800 r . The LM curve is M/P = L, or 6300/P = 0.5Y  200r. To find the aggregate demand curve, substitute the LM curve into the IS curve to eliminate r. To do this, multiply both sides of the LM curve by 4 to get 25 , 200 /P = 2 Y 800 r , or 800 r = 2 Y (25 , 200 /P ). Then substitute this in the IS curve: Y = 900 800 r = 900 [2 Y (25 , 200 /P )]. This can be rewritten as 3 Y = 900 + (25 , 200 /P ), or Y = 300 + (8400 /P ). (b) Suppose that P=15. What are the shortrun values of output, the real interest rate, consumption, and investment? ANSWER :With P = 15, the AD curve is Y = 300+(8400 / 15) = 860. From the IS curve, 860 = 900 800 r , which has the solution r = 0 . 05. Consumption is C = 300 . 5(860 100) (300 × . 05) = 665. Investment is I = 100 (100 × . 05) = 95. (c) What are the longrun equilibrium values of output, the real interest rate, con sumption, investment, and the price level? ANSWER :In the long run, Y = 700. From the IS equation, 700 = 900 800 r , which has the solution r = 0 . 25. The LM curve then is 6300 /P = (0 . 5 × 700) (200 × . 25) = 300, which has the solution P = 21. Consumption is C = 300 . 5(700 100) (300 × . 25) = 525. Investment is I = 100 (100 × . 25) = 75. In addition, do part (d) below: (d) Suppose that the economy is the longrun equilibrium in part (c) and G increases from 100 to 110 (T remains fixed at 100). Determine the new shortrun equilib rium values of Y , r, C, and I (P remains fixed at its initial value). Calculate the 1 multiplier on government spending (i.e., the change in Y divided by the changemultiplier on government spending (i....
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This homework help was uploaded on 04/06/2008 for the course ECON 154 taught by Professor Bjoernbruegemann during the Spring '07 term at Yale.
 Spring '07
 BjoernBruegemann
 Macroeconomics

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