For the following problems solve for the equilibrium levels of C, I, T, and X. Also find the budget surplus or deficit, as well as other variables asked for.

Model 1 - Simple Keynesian Equilibrium Problem

Let Y = C + I + G + X

C = 1000 + .6Y

I = 800

G = 1000

X = 0

Solve for:

a. the equilibrium level of Y

b. the Keynesian multiplier, k

c. the new equilibrium Y, if G is increased by 200

Model 2 - Keynesian Equilibrium Problem

Let Y = C + I + G + X

C = 1000 + .6(Y-T)

T = 900

I = 800

G = 1000

X = 0

Solve for:

a. the equilibrium level of Y

b. the Keynesian multiplier, k

c. the new equilibrium Y, if T is changed so as to balance the budget

Model 3. Still more complex multiplier problem

Let Y = C + I + G + X

C = 1000 + .6(Y-T)

T = -500 + .2Y

I = 820

G = 1000

X = 0

Solve for:

a. the equilibrium level of Y

b. the Keynesian multiplier, k

c. The recessionary or inflationary gap if potential GDP is 6200

Model 4. The Killer problem

Let Y = C + I + G + X

C = 1000 + .6(Y-T) (where T are taxes)

I = 800

G = 1000

X = 1100 - .18Y (we import 18 percent of marginal income)

T = -500 + .2Y (Income tax, 20 percent marginal tax rate)

Solve for:

a. the equilibrium level of Y

b. the Keynesian multiplier, k

c. the new equilibrium Y, if G is reduced by 70