Question

Fantasy Island is a closed economy and is characterized by the following equations: Consumption: C = 4000+ 0.75(Y-T) Investment: I = 2000 - 5000r Government spending: G = 3500 Budget surplus = 500 Real money demand: L = 0.4Y - 2500i, where i=r+ Expected inflation: Tº = 0 Production function: Y = 10 K12L 1/2 The nominal money supply = 7250 Note: Interest rates, i and r, are expressed in decimal points, i.e., ifr=0.5, then r = 50%. Suppose the IS-LM model can be to describe the economy of Fantasy Island and answer the following questions. Keep your answer to TWO decimal points if necessary. a) Derive the IS and LM equations for this economy. (4 points) b) Suppose, in the long-run, 2000 (real) units of capital are utilized and 2000 workers are employed. Calculate the resulting full-employment values of real output, real interest rate, consumption, the government budget balance, and the price level. (5 points) c) Suppose the economy is initially in its long-run equilibrium as shown in part B above. Now, autonomous consumption suddenly (and permanently) falls by 10%. Calculate the resulting (new short-run equilibrium values of real output, real interest rate, investment, consumption, and the real money supply. Determine the unemployment rate that results in short-run equilibrium. (6 points) d) Suppose, as well, we are also told that when the economy was in long-run equilibrium (in part B (above), 120 people were unemployed. Further, when the shock hit the economy (in part C, above ) in net terms no people have exited/entered the labour force. In light of this new information determine the unemployment rate that results in the short-run equilibrium from part C. What portion this unemployment is represented by cyclical unemployment and what portion is comprised of those in the natural rate (level of) unemployment (NRU). (4 points) Hint: Cyclical unemployment is the level of unemployment that results from deviations of output from the full-employment level. e) Determine the (new) LR equilibrium values of real output, real interest rate, investment, consumption, and the real money supply that result due to the shock described in part C (above). 6 points)

Answer 1

Budget Sweplus : Tea = 500 .T 500+ G : 1000 IS curve: Y. C+ I + GP = 4000 +0.75 (Y - 1000) .: + 2000 - 5000r + 3500 = 4000-3000 +0:757 + 5500-5000 av, 0:25 Y = 6500 - 5000r :: Y = 25000 - 2000or! LM curre : M = t . ar 7250 - 0:47 - 2500 i 0 4 X - As iertae , and tezo, iar :r: 18125 + 62507 b) for K = 2000, 1:2000; P=10(2000)* (2000) = 20000 - 26000 - 20000 20000 ' oigo 0:3 :: C = 4000 +0.75( 20000-4000) - 16000 ::T-G = 500 .20000 - 6250 10.30) 18125 :.p's site's Boots

I co New autonomous nomous consumption. consumption : (1.0.1)× 4000 . = 3600 New consumption function : nsumption function :c= 3600+ 1: Y = 24.900 - 2000or new is. - 600 +0:759 , short nun p=1 Equilibrium: Pali : i :. Y18125 + 6250 ramm is = L M 2000or :18125 + 6250r :or, .. 2625or =6275 :. r = 0.24 . : . Y = 19600 :. I : 800 is c = 15700 :: = 7250 :.1 = (60) † .19.208 iiü = 2000-1920*8 = 3.96. 2000 Total labor force : 2000 +120 = 2120 . Nrü : 2120-2000 x 100 =566% current unemployment : 21 4x100 i 2120 = 9:4º7. :. cyclical u : 9.99% - 5'66%. - 3.74% 2120 - 192008

1. e) At long run equilibrium; i = 20000 UN u :. Ti 24400 - 20000 = 0:22 20000 :: I = 2000 - 5000(0.22) = 900 .:. c : 16000 is = 0'4(20000)- 2500 (0:22) = 7450