10. Consider an 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=900-50r NX=1,500-250epsilon r=rast =8 a. In this economy,solve for private saving, public saving, national saving , investment, the trade balance, and the equilibrium exchange rate. b. Suppose now that G is cut to 2 ,000. Solve for private saving, public saving, national saving, investment, the trade balance, and the equilibrium exchange rate. Explain what you find. c. Now suppose that the world interest rate falls from 8 percent to 3 percent. (G is again 2,500 ) Solve for private saving public saving, national saving , investment, the trade balance, and the equilibrium exchange rate. Explain what you find.

a. In this economy, we can solve for the variables as follows:<br /><br />Private saving: $S_{p} = Y - T - C = 8,000 - 2,000 - (500 + 2/3(8,000 - 2,000)) = 5,000$<br /><br />Public saving: $S_{p} = T - G = 2,000 - 2,500 = -500$<br /><br />National saving: $S = S_{p} + S_{g} = 5,000 - 500 = 4,500$<br /><br />Investment: $I = 900 - 50r = 900 - 50(8) = 400$<br /><br />Trade balance: $NX = 1,500 - 250\epsilon = 1,500 - 250(8) = -1,000$<br /><br />Equilibrium exchange rate: $\epsilon = 1,500 / 250 = 6$<br /><br />b. If G is cut to 2,000, we can solve for the variables as follows:<br /><br />Private saving: $S_{p} = Y - T - C = 8,000 - 2,000 - (500 + 2/3(8,000 - 2,000)) = 5,000$<br /><br />Public saving: $S_{p} = T - G = 2,000 - 2,000 = 0$<br /><br />National saving: $S = S_{p} + S_{g} = 5,000 + 0 = 5,000$<br /><br />Investment: $I = 900 - 50r = 900 - 50(8) = 400$<br /><br />Trade balance: $NX = 1,500 - 250\epsilon = 1,500 - 250(8) = -1,000$<br /><br />Equilibrium exchange rate: $\epsilon = 1,500 / 250 = 6$<br /><br />In this scenario, public saving is zero because government spending is equal to taxes. National saving is equal to private saving, and the trade balance remains unchanged. The equilibrium exchange rate also remains unchanged.<br /><br />c. If the world interest rate falls from 8 percent to 3 percent, we can solve for the variables as follows:<br /><br />Private saving: $S_{p} = Y - T - C = 8,000 - 2,000 - (500 + 2/3(8,000 - 2,000)) = 5,000$<br /><br />Public saving: $S_{p} = T - G = 2,000 - 2,500 = -500$<br /><br />National saving: $S = S_{p} + S_{g} = 5,000 - 500 = 4,500$<br /><br />Investment: $I = 900 - 50r = 900 - 50(3) = 750$<br /><br />Trade balance: $NX = 1,500 - 250\epsilon = 1,500 - 250(3) = 750$<br /><br />Equilibrium exchange rate: $\epsilon = 1,500 / 250 = 6$<br /><br />In this scenario, the trade balance improves because the world interest rate falls, leading to an increase in net exports. The equilibrium exchange rate remains unchanged because the trade balance remains unchanged.