The following equations describe an economy:
C = 1000 + 0.8YD - 10i
I = 1400 - 10i
G = 1000
TA = 2000
L = 2Y - 100i
M = 12000
P = 2
Where C is consumption, YD is disposable income, i is the interest rate as a percentage, I is investment, G is government spending, TA is lump-sum taxes, Y is income, L is demand for real money balances, M is the nominal money supply, and P is the price index. Notice that consumption is postulated to be negatively related to the interest rate.
[ 8 points] Derive the equations that describe the IS and LM curves. Show your work.
[10 points] Solve for the equilibrium levels of (a) income, (b) interest rate, (c) consumption, and (d) investment. Show your work.
[ 6 points] Derive the aggregate demand (AD) curve for the economy. Show your work.
Suppose that the government increases transfer payments by 525 billion.
[ 5 points] Determine the size of the horizontal shift of the IS curve; that is, how much can output increase if the interest rate is maintained at the same level as in part (c). Show your work.
[ 6 points] Find the change in the equilibrium income when the equilibrium change in the interest rate is taken into account. Show your work.
[ 5 points] Based on your calculations from questions 4 and 5, how much is the crowding out effect on output? Note: start your answer by defining what is meant by crowding-out effects of expansionary fiscal policy. Show your work.
[10 points] If the Federal Reserve System intends to eliminate the above crowding-out effect completely, how much should the real money supply increase by? Show your work.