Question

Consider a classical model of large-open economy described by the following equations:

Y = C + I + G + NX

Y = 8,000

G = 2,500

T = 2,000

C = 500 + 2/3 (Y − T)

I = 1,000 − 50r

CF = 500 − 50r

NX = 1,000 − 250ε

where Y is output, C is consumption, I is investment, G is government purchases, NX is net exports, T is taxes, r is the real interest rate, CF is the net capital outflow, and ε is the real exchange rate.

1. In this economy, show the demand function of loanable funds (the sum of investment and the net capital outflow) and the supply (function) of loanable funds (national saving).

2. Solve for the real interest rate, investment, the net capital outflow, the trade balance, and the real exchange rate.

3. Suppose now that G is cut to 2,000. Solve for national saving, the real interest rate, investment, the net capital outflow, the trade balance, and the real exchange rate.

Answer 1

a).

Here the demand function of loanable fund is the sum of “Investment” and “net capital outflow=NCO”.

=> D = I+NCO = (1000 – 50*r) + (500 – 50*r) = 1,500 – 100*r, => D = 1,500 – 100*r.

The supply of loanable fund is given the following expression.

=> S = Y- C – G = 8,000 – [500 + 2/3*(8,000 – 2,000)] – 2,500 = 8,000 – 4,500 – 2,500 = 1,000.

=> S = 1,000.

b).

At the equilibrium the demand for loanable fund must be equal to supply of loanable fund.

=> D = S, =>1,500 – 100*r = 1,000, => r = 500/100 = 5, => r = 5.

So, the real interest rate is “r=5%”.

Now, the level of investment is “I = 1000 – 50*r = 1000 – 750, => I = 750”. The NCO is “500 – 50*r = 500 – 250 = 250”, => NCO = 250. Here at the equilibrium the NX must be equal to NCO.

=> NX = NCO, => 1,000 – 250*e = 250, => 250*e = 750, => e = 750/250 = 3, => e = 3 = real exchange rate.

The NX is given by, “NX = 1,000 – 250*e = 1,000 – 250*3 = 250”.

c).

Let’s assume the government spending cut to 2,000, => the new national savings function is given by.

=> S = Y – C – G = 8000 – 4500 – 2000 = 1,500, => S = 1,500.

At the equilibrium the demand for loanable fund must be equal to supply of loanable fund.

=> D = S, =>1,500 – 100*r = 1,500, => r = 0.

So, the real interest rate decreases to “r=0%”.

Now, the level of investment is “I = 1000 – 50*r = 1000 - 0, => I = 1,000”. The NCO is “500 – 50*r = 500 – 0 = 500”, => NCO = 500. Here at the equilibrium the NX must be equal to NCO.

=> NX = NCO, => 1,000 – 250*e = 500, => 250*e = 500, => e = 500/250 = 2, => e = 2 = real exchange rate.

The NX is given by, “NX = 1,000 – 250*e = 1,000 – 250*2 = 500”.

So, as the government spending decreases the real interest rate and real exchange rate both decreases on the other hand investment, NCO and NX increases.