Intermediate Macroeconomics-ECO 3203

Transcription

1 Intermediate Macroeconomics-ECO 3203 Homework 2 Solution Sample, Summer 2018 Instructor, Yun Wang Instructions: The full points of this homework exercise is 100. Show all your works (necessary steps to get the ) for every question. When drawing your graph, label all curves, axes, initial and final equilibrium values, and the direction of the change in any curve. Due Date: Tuesday, July 17th, at the beginning of the class. 1. Consider a closed economy to which the Keynesian-cross analysis applies. Consumption is given by the equation C = /3(Y T ). Planned investment is 300, as are government spending and taxes. a. If Y is 1500, what is planned spending? What is inventory accumulation or decumulation? Should equilibrium Y be higher or lower than 1500? (Note: decumulation just means negative accumulation) (8 ) b. What is equilibrium Y? (Hint: Substitute the values of equations for planned consumption, investment, and government spending into the equation Y = C + I + G and then solve for Y.) (6 ) c. What is the multiplier for government spending? (5 ) a. We know that P E = C + I + G Using the formulas given, and since I = 300 and G = 300 and T = 300 (as per the data in the prompt) we have P E = /3(Y T )

2 using Y = 1500: P E = 1600 This amount of planned expenditures is clearly above the level of output produced by firms (Y=1500), therefore firms will have to decumulate inventories (this is the only way that in a closed economy expenditures can occur above the level of output, i.e. by consuming goods from inventories). In general, inventories are accumulated by: Inventoriesaccumulation = OutputP lannedexpenditures Therefore inventory decumulation in our economy would be: Inventoriesaccumulation = = 100 b. Equilibrium Y is given by the equilibrium condition: Y = P E.So we will have: Y = P E = C + I + G It means: we finally have Y = /3(Y T ) Y = 1800 c. Recall that the government purchases multiplier Y/ G is given by: Y G = 1 1 MP C Since the MPC= 2/3 for us (look at the consumption function) the government purchases multiplier is Y G = 1 1 2/3 = 3 2. Suppose Congress decides to reduce the budget deficit by cutting government spending. a. Use the Keynesian-cross model to illustrate graphically the impact of a reduction in 2

3 government purchases on the equilibrium level of income. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values. (10 ) b. Use the IS-LM model to show the impact of a reduction in government purchases on the equilibrium level of income and Real interest rate. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values. (10 ) c. Explain in words what happens to equilibrium income and real interest rate as a result of the cut in government spending and the time horizon appropriate for this analysis. (5 ) a.cutting government spending means that G goes down. Graphically b. c. A contraction fiscal policy is going to lower the planned expenditure E immediately, which is going to bring down the output level Y by G 1 1 MP C. That is a right shift for IS curve. And the output Y dropping down to Y 2 first. But it is not the end yet! The increasing output Y will increase the money demand ( M P )d the decreasing of the interest rate. While the decreasing interest rate will increase investment I and bring down the output level Y until it hit the new equilibrium point, where output reached level Y 1 3

4 3. a. Graphically illustrate the impact of an open-market sale by the Federal Reserve on the equilibrium interest rate using the theory of liquidity preference and the market for real money balances. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v.the terminal equilibrium values. (10 ) b. Use the IS-LM model to show this impact on the equilibrium level of income and Real interest rate. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values. (10 ) c. Explain in words what happens to the equilibrium interest rate as a result of the openmarket purchase. An open-market operation consisting of sales of government bonds decreases the money supply in the economy. So M goes down. (5 ) a. An open-market operation consisting of sales of government bonds decreases the money supply in the economy. So M goes down b. c. A contraction monetary policy will bring down the real money supply, which leads to ( M P )d. That is, when you keep the national output Y fixed, interest needs to go up to meet the money demand increase LM curve shifts left or up. But this is not the end yet Now the interest rate r rising too high, causes the I Y 4

5 while Y ( M P )d which causes r to drop to level r 2 at new equilibrium point. 4. Suppose that the jobs report is strong enough, and provides conclusive evidence that the economy is at or might be soon above potential. This means that in the Long-run the economy would overheat. Given this conclusion the central bank decides that it is time to engage in contractionary monetary policy. To do so the Fed will sell government bonds in an open-market operation conducted by trading desk of the New York Fed. When they do this: a. Will the money supply increase or decrease? (2 ) b. Given your from part a, what will be the effect on the IS-LM model? (Hint: you may want to think what happens in the liquidity preferences model first.) (12 ) 5

6 c. Explain in words what happens to the interest rate and to income in equilibrium. Does income fall or increase? Why? (5 ) d. In the Aggregate Demand Aggregate Supply (AS-AS) model the current economic environment (the one in which actual output might already be above its potential level) is characterized by a short-run equilibrium that is above the long-run equilibrium. Draw an AD-AS graph of a short-run equilibrium that is above potential and graphically represent how the contractionary actions of the Fed would affect the economy. (12 ) a. Selling government bonds will decrease the money supply (which is the point of contractionary monetary policy). b. In the liquidity preferences model money supply shifts to the left, driving up interest rates at any given income level. In the IS-LM model this is represented by a shift to the left of the LM curve c. See Question #3. c d. A short-run equilibrium that is above potential is graphically represented by an intersection of the AD and SRAS curves that is to the right of potential (point A in the graph). Furthermore, the contractionary actions of the Fed wound cause the AD curve to shift to the left (bringing the economy to equilibrium B) since the higher interest rates lower investment spending (one of the components of the AD curve). 6

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