Question

C. (Blanchard and Johnson (2015), p. 142, question 3] Consider the following open economy. The real exchange rate is fixed and equal to one. Consumption, investment, government spending and taxes are given by: C = c + (Y -T), I=1, G = G, and T=T Imports and exports are given by: Q = my and X = 2Y* where asterisk denotes a foreign variable. 1. Solve for equilibrium income in the domestic economy, given Y*. What is the multiplier in this economy? If we were to close the economy (so that exports and imports were equal to zero), what would the multiplier be? Why are the two multipliers different? 2. Now, suppose you are given the following values for the exogenous variables and para- meters: co = 10, ci = 0.8, 1 = 10, G = 10, r=0.3 Find the numerical value for equilibrium income in the domestic economy, given Y* What is the numerical value of the multiplier in this economy? If we were to close the economy (so that exports and imports were equal to zero), what would the numerical value of the multiplier be?

Answer 1

1) Equilibrium income in the domestic economy:

Savings= Investment

or, Income- consumption = Investment

Multiplier in the economy = change in income/ change in investment =( change in consumption, investment, government expenditure, taxes, net imports)/ change in investment

For closed economy, multiplier would be= change in income/ change in investment =( change in consumption, investment, government expenditure, taxes)/ change in investment

Two multipliers will be different because: in open economy, change of net exports is taken as a component of income in open economy and whereas, change in net exports is not a component of income in closed economy.

2. Equilibrium income in the domestic economy: (0.5Y -12)/0.3

Solution:

Y= C+ I+ G -T +Exports - Imports

or, Y = 10 + 0.8(Y-10) +10+10-10+0.3Y*- 0.3Y

or, Y-0.8Y +0.3Y = 12 + 0.3Y*

or, Y* = (0.5Y -12)/0.3

Multiplier in the open economy = Change in Y / Change in I = ((0.5Y -12)/0.3)/10 =(0.5Y -12)/3

Multiplier in the close economy: Change in Y(CLOSED ECONOMY) / I = Change in Y / Change in I = 60/10 =6

Solution:

Y of the closed economy= C +I+G-T = 10 +0.8Y-8+10+10-10

or, Y = 12/0.2 = 60