Question

Consider an economy described by the following equations:

Y=C+I+G+NX,

Y=8,000

G=2,500

T=2,000

C=500 + 0.75(Y−T)

I=900−50r

NX=1,500−250ϵ

r=r∗=8.

1. In this economy, solve for private saving, public saving, national saving, investment, the trade balance, and the equilibrium exchange rate.
2. Suppose now that G is cut to 2,000. Solve for private saving, public saving, national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you find.
3. Now suppose that the world interest rate falls from 8 to 3 percent. (G is again 2,500.) Solve for private saving, public saving, national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you find.

Answer 1

Consider an economy described by the following equations:

Y=C+I+G+NX,

Y=8,000

G=2,500

T=2,000

C=500 + 0.75(Y−T)

Putting, Y = 8000 and T = 2000 we get

C = 500 + 0.75×(8000 - 2000)

or, C = 5000

I=900−50r

NX=1,500−250.e

r = r* = 8

Now let us answer the following questions one by one.

(a) Private Savings is

Sp = Y - T - C

or, Sp = 8000 - 2000 - 5000

or, Sp = 1000

Private savings is 1000.

Public Savings is

Sg = T - G

or, Sg = 2000 - 2500

or, Sg = -500

Public savings is -500. There is government budget deficit.

And, National Savings is

S = Sp + Sg = 1000 - 500

or, S = 500

National savings is 500.

Investment is

I = 900 - 50.r = 900 - 50×8

or, I = 500

Investment is 500.

Hence, Trade Balance is

TB = NX

or, TB = S - I

or, TB = 500 - 500

or, TB = 0

Trade balance is 0.

Hence, we put

NX = 0

or, 1500 - 250.e = 0

or, e = 6

Equilibrum exchange rate is 6.

(b) Now, G is cut to G1 = 2000.

Now,

Private Savings will not be affected. It will remain same as before i.e.

Sp1 = Sp = 1000

Private savings remains same at 1000.

Public Savings will be

Sg1 = T - G1 = 2000 - 2000

or, Sg1 = 0

Public savings is zero. Hence, the government budget is balanced.

The National Savings will be

S1 = Sp1 + Sg1 = 1000 + 0

or, S1 = 1000

National savings will increase to 1000.

Investment will remain same as before i.e.

I1 = I = 500

Hence, Trade Balance will be

TB1 = NX1

or, TB1 = S1 - I1 = 1000 - 500

or, TB1 = 500

There will be trade surplus of 500.

Hence, NX1 = 500

or, 1500 - 250.e1 = 500

or, e1 = 4

As there is trade surplus, hence there will be more import and less export to make the trade balance again zero. Hence, exchange rate falls to 4.

(c) Now, world interst rate falls from 8 to 3 percent.

Hence, r = r* = 3

But G = 2500

Public and Private savings will remain same as part (a). Hence

Sp2 = Sp = 1000 and

Sg2 = Sg = -500

National Savings will remain same as part (a) i.e.

S2 = S = 500

Investment will be

I2 = 900 - 50.r

or, I2 = 900 - 50×3

or, I2 = 750

As rate of interest fell, investment rises to 750.

Trade balance will be

TB2 = NX2

or, TB2 = S2 - I2 = 500 - 750

or, TB2 = -250

There will be trade deficit of 250.

Now, NX2 = -250

or, 1500 - 250.e2 = -250

or, e2 = 7

As there is trade deficit, export should increase and import should decrease. Hence, exchange rate imcreases to 7.

Hope the solutions are clear to you my friend.