3 Assume that longrun real GDP Y is 8000 in a small open eco

3. Assume that long-run real GDP (Y) is 8,000 in a small, open economy. Consumption (C) Is given by: C= 500 +0.667(Y-T). Investment (1) is given by I= 900 - 50r where \"r\" is the real interest rate in percent (i.e., 4% = 4 not 0.04). The world real interest rate (r*) = 8%. Net exports (NX) is given by NX = 1,500 - 250e (where e is the real exchange rate). Both taxes (T) are government spending (G) are exogenously determined and equal $2,000 and $2,500, respectively. a. What are the values of private sector saving (Sp), government saving (S,), and national saving (Sn)? b. What are the values of investment (I), the trade balance (NX), and the equilibrium real exchange rate (e)? c. Suppose that due to increased world savings, the world real interest rate (r*) falls from 8 to 3 percent. What are the new values for the 6 variables in a and b above? Explain your findings.

Solution

(a) When Y = 8,000

C = 500 + 0.667 x (8,000 - 2,000) = 500 + 0.667 x 6,000 = 500 + 4,000 = 4,500

Sp = Y - C = 8,000 - 4,500 = 3,500

Sg = T - G = 2,000 - 2,500 = - 500

Sn = Sp + Sg = 3,500 - 500 = 3,000

(b) In equilibrium, Y = C + I + G + NX

8,000 = 4,500 + 900 - 50r + 2,000 + 1,500 - 250e

8,000 = 8,900 - (50 x 8) - 250e

8,000 = 8,900 - 400 - 250e

8,000 = 8,500 - 250e

250e = 500

e = 2

I = 900 - (50 x 8) = 900 - 400 = 500

NX = 1,500 - (250 x 2) = 1,500 - 500 = 1,000

(c) When r = 3, the values of C, T and G are unchanged, being independent of interest rate.

Sp = Y - C = 8,000 - 4,500 = 3,500

Sg = T - G = 2,000 - 2,500 = - 500

Sn = Sp + Sg = 3,500 - 500 = 3,000

In equilibrium, Y = C + I + G + NX

8,000 = 4,500 + 900 - 50r + 2,000 + 1,500 - 250e

8,000 = 8,900 - (50 x 3) - 250e

8,000 = 8,900 - 150 - 250e

8,000 = 8,750 - 250e

250e = 750

e = 3 (Exchange rate increases by (3 - 2)% = 1%)

I = 900 - (50 x 3) = 900 - 150 = 750 (Investment increases by (750 - 500) = 250)

NX = 1,500 - (250 x 3) = 1,500 - 750 = 750 (NX decreases by (1,000 - 750) = 250).

Fall in interest rate has lowered the cost of borrowing, so investment has increased. Higher investment by 250 has lowered the savings-investment gap (= S - I) by 250, and by the twin deficit hypothesis, since savings-investment gap is equal to NX, a fall in savings-investment gap by 250 has led to a fall in NX by 250.