Fantasy Island is a closed economy and is characterized by the following
equations:
Consumption: C = 400 + 0.80(Y – T)
Investment: I = 300 – 1500r
Government spending: G = 300
Taxes: T = 400
Real money demand: L = 0.4Y – 498i
Expected inflation: pe = 0
Production function: Y = K1/2L1/2
The nominal money supply = 707
Note: Interest rates, i and r, are expressed in decimal points, i.e., if r = 0.5, then r = 50%.
Suppose the IS-LM model can be used to describe Fantasy Island, and answer the following questions.
a) Derive the IS and LM equations for this economy.
b) Suppose we are in the base period, so the price level is fixed at 1.00. Calculate the resulting short-run equilibrium values of real output, real interest rate, investment, consumption, the government budget balance, the price level, and real money supply.
c) Suppose, in the long-run, 2000 (real) units of capital are utilized and 2000 workers are employed. Calculate the resulting long run (full-employment) equilibrium values of real output, real interest rate, investment, consumption, the government budget balance, the price level, and the real money supply.
d) Suppose autonomous consumption
and
autonomous investment both suddenly (and permanently) fall by 20%. Calculate the resulting (new) short-run equilibrium values of real output, real interest rate, investment, and consumption. Determine the unemployment rate that results in short-run equilibrium.
e) Suppose, instead, we are also told that when the economy was in long-run equilibrium (in part C, above) 100 people were unemployed. Further, when the shock hit the economy (in part D, above) no people have exited the labour force. Determine the unemployment rate that results in the short-run equilibrium from part D. What portion this unemployment is represented by cyclical unemployment and what portion is comprised of those in the natural rate (level of) unemployment (NRU).
f) When the economy returns to long-run equilibrium what unemployment rate should we expect to see? Explain why/when this makes sense.
g) Determine the (new) LR (full-employment) equilibrium values of real output, real interest rate, the price level, and the real money supply that result following the shock described in part D (above).
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