Assume that a large open economy with a floating exchange rate is described in t

Question

Assume that a large open economy with a floating exchange rate is described in the short run by the equations: C = 0.5(Y- T) T= 1,000 I= 1,500-250r G - 1,500 NX- 1,000 The last two equations specify that CF net capital outflow, decreases with r, the interest rate, and that NX., the net exports, is equal to net capital outflow. NX is also related to the exchange rate, and falls when e appreciates. The price level (P) is fixed at 1.0. Calculate short-run equilibrium values of K, r, C, CP, NXt e, private saving, public saving, and foreign saving. Foreign saving is defined here as minus NX. Check your work by ensuring that C+1 + G = Kand private saving plus public saving plus foreign saving equals domestic investment.

Explanation / Answer

(1) Equation of IS curve:

Y = C + I + G + NX

Y = 0.5(Y - T) + 1,500 - 250r + 1,500 + 500 - 250r

Y = 3,500 + 0.5(Y - 1,000) - 500r

Y = 3,500 + 0.5Y - 500 - 500r

0.5Y = 3,000 - 500r

Y = 6,000 - 1,000r

Equation of LM curve:

0.5Y - 500r = 1,000

0.5Y = 500r + 1,000

Y = 1,000r + 2,000

In equilibrium, IS = LM

6,000 - 1,000r = 1,000r + 2,000

2,000r = 4,000

r = 2

Y = 1,000 x 2 + 2,000 = 2,000 + 2,000 = 4,000

C = 0.5 x (4,000 - 1,000) = 0.5 x 3,000 = 1,500

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

CF = 500 - (250 x 2) = 500 - 500 = 0

Private saving (S) = Y - C = 4,000 - 1,500 = 2,500

Public saving = T - G = 1,000 - 1,500 = - 500 (Implying dissaving)

Since NX = CF, we get: 1,000 - 250e = 0, or e = 1,000 / 250 = 4

Foreign saving = - NX = 0

Validation:

Y = C + I + G = 1,500 + 1,000 + 1,500 = 4,000

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