Q1. A mathematical Keynesian model is shown as follows (20 pts): Goods market: Y

Question

Q1. A mathematical Keynesian model is shown as follows (20 pts):

Goods market:

Y = C + I + G + NX

C = 600 + 0.75*DI (DI: disposable income = Y - T)

I = 1000 - 2000*r (r: inerest rate)

G = 1100

NX = 600 - 0.1*Y

T = 0.2*Y (a proportional income tax system)

Money market:

Real money supply: ( MP )S = 1000

Real money demand: ( MP )d = 2500 - 10000*r1 (r: inerest rate)

a) How large is the equilibrium GDP?

b) Is the govenemnt running a budget surplus or deficit when Y is in equilibrium? How large is it?

c) Is there a trade surplus or deficit when Y is in equilibrium? How large is it?

d) Suppose the potential GDP (i.e., the maximum amount of product an economy can produce; it’s also called full-employment GDP tha corresponds to the NRU) equals 6400, what kind of economic problem may occur in the economy and what policy actions should be taken to solve this problem?

e) How large is the new govement spending needed to achieve the potential level of GDP? [Hint: Equate money supply with demand to solve for interest rate r. Substitute r to investment equation to find I. Add up C, I, G and NX to find total spending, which is a function of Y. Equate this spending equation with Y to find equilibrium GDP (i.e., solve for Y).]

Explanation / Answer

1. a.

Money market equilibrium:

Money supply = Money demanded

1000 = 2500 - 10000r

10,000r = 1,500

r= 0.15

T = 0.2Y

(Y- T) = Y – 0.2Y = 0.8Y

C = 600 + 0.75(0.8Y) = 600 + 0.6Y

I = 1,000 – 200r = 1,000 – 2,000 (0.15) = 700

G = 1100

NX = 600 – 0.1Y

Y = C + I + G + NX

    = 600 + 0.6Y + 700 + 1100 + 600 – 0.1Y

    = 3,000 + 0.5Y

Answer: Equilibrium GDP is 3,000 + 0.5Y high.

b.

Equilibrium GDP means country’s total purchase is equal to total production. Therefore, there is no budget surplus or deficit while GDP is in equilibrium.

c.

Equilibrium GDP means country’s total purchase is equal to total production. Therefore, there is no trade surplus or deficit while GDP is in equilibrium.

d.

If the potential GDP is 6,400, the real GDP would be as below:

Y = 3,000 + 0.5 (6,400)

    = 3,000 + 3,200

    = 6,200

Real GDP is less than the potential GDP because of inflation problem.

Real GDP = Potential GDP – Inflation

Inflation should be controlled by reducing money supply in the market. It could be done by increasing the interest rates.

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