5. Consider an economy described as follows: Y=C+I+G Y=8,000 G=2,500 T=2,000 C=1000+2/3(Y-T) I=1,200-100r a) In this economy, compute private saving, public saving, and national saving. b) Find the equilibrium interest rate. c) Now suppose that G is reduced by 500. Compute private saving, public saving, and national saving. d) Find the new equilibrium interest rate.

a) To compute private saving, we need to subtract consumption (C) from disposable income (Y-T). Disposable income is calculated as Y - T.<br /><br />Private saving = (Y - T) - C<br />Private saving = (8000 - 2000) - (1000 + 2/3(8000 - 2000))<br />Private saving = 6000 - (1000 + 2/3(6000))<br />Private saving = 6000 - (1000 + 4000)<br />Private saving = 6000 - 5000<br />Private saving = 1000<br /><br />To compute public saving, we need to subtract government spending (G) from tax revenue (T).<br /><br />Public saving = T - G<br />Public saving = 2000 - 2500<br />Public saving = -500<br /><br />National saving is the sum of private saving and public saving.<br /><br />National saving = Private saving + Public saving<br />National saving = 1000 - 500<br />National saving = 500<br /><br />b) To find the equilibrium interest rate, we need to set the investment function (I) equal to national saving.<br /><br />I = National saving<br />1200 - 100r = 500<br />r = (1200 - 500) / 100<br />r = 7<br /><br />c) Now suppose that G is reduced by 500. We need to recalculate private saving, public saving, and national saving.<br /><br />Private saving = (Y - T) - C<br />Private saving = (8000 - 2000) - (1000 + 2/3(8000 - 2000))<br />Private saving = 6000 - (1000 + 2/3(6000))<br />Private saving = 6000 - (1000 + 4000)<br />Private saving = 6000 - 5000<br />Private saving = 1000<br /><br />Public saving = T - G<br />Public saving = 2000 - 2000<br />Public saving = 0<br /><br />National saving = Private saving + Public saving<br />National saving = 1000 + 0<br />National saving = 1000<br /><br />d) To find the new equilibrium interest rate, we need to set the investment function (I) equal to the new national saving.<br /><br />I = National saving<br />1200 - 100r = 1000<br />r = (1200 - 1000) / 100<br />r = 2<br /><br />Therefore, the new equilibrium interest rate is 2.