Question

Consider the following short-run model of an open economy:

Y = C+I+G+NX
C = 100+(2/3)(Y-T)
I = 200
NX = X-(1/E)IM
X = (1/E)400
IM = (1/6)E Y

Domestic and foreign prices are constant with P=P^*=1. Thus, the real exchange rate is equal to the nominal rate E.

The policy makers want to achieve the following targets for output, consumption and net exports: Y^T=1200, C^T=780 and NX^T=0. Show how these targets can be achieved using government consumption (G), taxes (T) and the exchange rate (E) as policy instruments. It must be clear from your answer how it has been derived.

Answer 1

Objective: Y = 1200, C = 780, NX = 0

Equation 1 : Y = C+I+G+NX

Equation 2 : C = 100 + (2/3)(Y-T)

Equation 3 : I = 200

Equation 4 : NX = X-(1/E)IM

Equation 5 : X = (1/E)400

Equation 6 : IM = (1/6)EY

Equation 7 : P = 1

Using Equation 5 and 6, substituting in Equation 4

NX = (1/E)400 - (1/E)(1/6)EY

NX = 400/E - Y/6

Setting NX = 0

we have,

400/E = Y/6

Setting Y = 1200

E = 400*6/1200 = 2

Now, Setting, Y = 1200 in equation 2

C = 100 + (2/3)(1200 - T)

Also, set C = 780

780 = 100 + (2/3)(1200 - T)

Simplifying,

T = 1200 - 680*3/2 = 180

Now substituting, Y = 1200, C = 780, I = 200, NX = 0 into equation 1

1200 = 780 + 200 + G

G = 220

1. G = 220

2. T = 180

3. E = 2