Question

V. Consider an open economy in which the real exchange rate is fixed and equal to one. Consumption, investment, government spending, and taxes are given by С 10 + 0.8(Y-T), l 10, G-, 10, and T-10 Imports and exports are given by IM 0.3Y and X 0.3Y where Y" denotes foreign output. ECON 10SB Solve for equilibrium output in the domestic economy, given Y. What is the multiplier in this economy? If we were to close the economy-so exports and imports were identically equal to zero-what would the multiplier be? Why would the multiplier be different in a closed economy? a. b. Assume that the foreign economy is characterized by the same cquations as the domestic cconomy (with asterisks reversed). Use the two sets of equations to solve for the equilibrium output of each country. [Hint: Use the equations for the foreign economy to solve for Y as a function of Y and substitute this solution for Y in part (a).] What is the multiplier for each country now? Why is it different from the open cconomy multiplier in part (a)? Explain.

Answer 1

Given, C = 0 + 0.8 (y - T) I = 10, G = 10, T = 10 Imports and exports are given by 1M = 0.3y and x = 0.3 y^* y^* denotes foreign output. y = C + I + G [X - H] Y = 10 + 0.8 [X - 10] + 10 + 10 + [0.3Y^* - 0.3 Y] Y = 10 + 0.8 Y - 8 + 20 + 0.3 Y^* - 0.3 Y Y = 10 + 0.5 Y + 12 + 0.3 Y^* Y - 0.5Y = 10 + 12 + 0.3 Y^* Y [1 - 0.5] = 22 + 0.3 Y^* Y (0.5) = 22 + 0.3 Y^* Y = 1/.05 (22 + 0.3 Y^*) (1) Multiplier = 1/0.5 = 10/5 = 2 \r\n Now in closed economy, Y = C + I + G Y = 10 + 0.8 [Y - T] + I + G