15 May WHAT IS THE EFFECT OF THIS FISCAL EXPANSION ON Y AND R?
Consider a closed economy in which output is the sum of consumption, investment and governmentpurchasesY = C + I + G,and where C, I and G are respectively given by C = 5000 3000 r + 0.8Y,I = 2500 5000 r,and G = 2500.(a) (5 points) Recalling that national savings equals S = Y C G, find an equation relatingsavings S to Y and r.(b) (5 points) Find an analytical formula for the IS curve. To do this, set savings (which dependson Y and r) equal to investment (which depends on r), and solve for Y as a function of r.Depict the IS curve graphically. In your graph, where the IS curve intersect the Y axis? Andthe r axis?(c) (5 points) Suppose that money market equilibrium is given byM/P = 3,000 + 0.1 Y 16,000i, where the nominal interest rate i is the real interest rate r plus expected inflation. Assume forthe sake of this exercise that expected inflation is zero, so that the nominal and real interestrates are the same. Further, let M = 15,000 and P = 3. Solve for the LM curve and show itgraphically on your diagram from part(b). Where does the LM curve intersect the Y axis?(d) (5 points) At what point do your IS and LM curves intersect? What is the resulting level ofincome Y and real interest rate r?(e) (7 points) Suppose that the government wants to stimulate GDP using fiscal policy, forexample by raising G from 2,500 to 3,000. How does this affect your IS and LM curves?Where is the new intersection point? Show this in a new graph.(f) (7 points) Suppose that instead of using fiscal policy, G remains constant at 2,500, but themoney supply M increases from 15,000 to 18,000. How does this change your IS and LMgraphs and where is the new intersection point? Draw a new IS-LM graph to answer thisquestion. (Assume that P remains constant at 3.)(g) (8 points) Suppose that monetary policy continues to expand beyond the M=18,000 level. Atwhat level of M would interest rates reach 0? At this point, it is said that the economyreaches a liquidity trap. For values of M higher than this critical value, the IS and LM graphsintersect at a negative level of r. Since interest rates cannot be negative, however, output isno longer determined by the intersection point of the IS and LM curves. Instead, it isdetermined by the intersection of the IS curve with the horizontal axis, i.e., the r=0 axis.(h) (8 points) Now suppose that M is 30,000 and that the government increases G from 2500 to3000. What is the effect of this fiscal expansion on Y and r? In this case, is the increase in Gmore or less effective (as a stimulant of output) than in part e? What is the key differencebetween the two cases? In addition to your calculations, show your results graphically.Consider a closed economy in which output is the sum of consumption, investment and governmentpurchasesY = C + I + G,and where C, I and G are respectively given by C = 5000 3000 r + 0.8Y,I = 2500 5000 r,and G = 2500.(a) (5 points) Recalling that national savings equals S = Y C G, find an equation relatingsavings S to Y and r.(b) (5 points) Find an analytical formula for the IS curve. To do this, set savings (which dependson Y and r) equal to investment (which depends on r), and solve for Y as a function of r.Depict the IS curve graphically. In your graph, where the IS curve intersect the Y axis? Andthe r axis?(c) (5 points) Suppose that money market equilibrium is given byM/P = 3,000 + 0.1 Y 16,000i, where the nominal interest rate i is the real interest rate r plus expected inflation. Assume forthe sake of this exercise that expected inflation is zero, so that the nominal and real interestrates are the same. Further, let M = 15,000 and P = 3. Solve for the LM curve and show itgraphically on your diagram from part(b). Where does the LM curve intersect the Y axis?(d) (5 points) At what point do your IS and LM curves intersect? What is the resulting level ofincome Y and real interest rate r?(e) (7 points) Suppose that the government wants to stimulate GDP using fiscal policy, forexample by raising G from 2,500 to 3,000. How does this affect your IS and LM curves?Where is the new intersection point? Show this in a new graph.(f) (7 points) Suppose that instead of using fiscal policy, G remains constant at 2,500, but themoney supply M increases from 15,000 to 18,000. How does this change your IS and LMgraphs and where is the new intersection point? Draw a new IS-LM graph to answer thisquestion. (Assume that P remains constant at 3.)(g) (8 points) Suppose that monetary policy continues to expand beyond the M=18,000 level. Atwhat level of M would interest rates reach 0? At this point, it is said that the economyreaches a liquidity trap. For values of M higher than this critical value, the IS and LM graphsintersect at a negative level of r. Since interest rates cannot be negative, however, output isno longer determined by the intersection point of the IS and LM curves. Instead, it isdetermined by the intersection of the IS curve with the horizontal axis, i.e., the r=0 axis.(h) (8 points) Now suppose that M is 30,000 and that the government increases G from 2500 to3000. What is the effect of this fiscal expansion on Y and r? In this case, is the increase in Gmore or less effective (as a stimulant of output) than in part e? What is the key differencebetween the two cases? In addition to your calculations, show your results graphically.
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