Question $2(35$ points$)$ Chapters $7,11$ & $12$

The closed economy of Temptation Island is characterized by the following equations:

Consumption: C $=6000+0\mathrm{.}85($Y $$ T$)$

Investment: I $=1500300$r

Government spending: G $=5000$

Taxes: T $=4500$

Real money demand: L $=0\mathrm{.}65$Y $500$i

Expected inflation: $$e $=0$

Production function: Y $=$ K$1/2$L$1/2$

The nominal money supply $=35000$

Note: Interest rates, both i and r$,$ are expressed in percentage points, i$.$e$.,$ if r $=5\mathrm{.}5,$ then the real interest

rate is interpreted as being equal to $5\mathrm{.}5\%.$

Suppose the IS$-$LM model can be to describe Temptation Island, and answer the following questions.

Keep your answer to at least THREE decimal points if necessary.

a$)$ Derive the IS and LM equations for this economy. $(4$ points$)$

b$)$ Suppose we are in the base period, so the price level is fixed at $1\mathrm{.}00.$ Calculate the resulting

short$-$run equilibrium values of real output, real interest rate, investment, consumption, the

government budget balance, and price level. $(3$ points$)$

c$)$ Suppose, in the long$-$run, $64000($real$)$ units of capital are utilized and $36000$ workers are

employed. Calculate the resulting full$-$employment values of real output, real interest rate,

investment, consumption, the government budget balance, and the price level. $(3$ points$)$

d$)$ Suppose the government decides to change the level of taxation to create budget surplus of $600.$

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. $(6$ points$)$