Homeworks and answers will be posted here. Each Tuesday evening, a new homework assignment will be posted here, and it will be due in the Econ 311 box in the Economics Department Office by the following Teusday. The first homework will be posted here January 4.
First homework: questions 2, 3 and 4 at end of Chapter 3. Due January 11.
Answers to homework #1.
Homework #2, due January 18.
1. Consider the model in question 2, page 62. Suppose G rises permanently from 150 to 160.
(a) derive what happens to equilibrium income.
(b) describe the transition from the old equilibrium to the new equilibrium in detail. To do this, you will need some additional assumptions about disequilibrium dynamics in the goods market. Suppose each day is divided into a morning and an afternoon. The production of goods by factories occurs in the morning and sales occur in the afternoon. Suppose firms set production in the morning equal to the previous day’s sales. For example, if production was 1000 in the previous period and there was unplanned inventory decumulation in the amount 10, then we can infer that sales in the previous afternoon were 1010. Under our assumption about disequilibrium dynamics, production in the current morning would be 1010.
Suppose that the economy was in the old equilibrium in day 0. Record the values in day 0 of: total income, household saving, the government deficit, production, sales, unanticipated inventory accumulation, consumption and investment. Do the same for period 1, 2, and 3. You should report these results in a table.
2. Consider our Keynesian Cross model with the planned investment equation replaced by I (planned) = I(bar) – b*i.
Suppose money demand is M/P=a0*Y – a1*i. Suppose the supply of M/P is an exogenously given number, say MM. Derive a formula for equilibrium output in the IS-LM model.
3. Do question 4, page 85 in the textbook. Do question 2, with 0.35 replaced by 0.50 in the money demand equation.
Answers to homework #2.
Homework #3, due January 25.
1. Questions 5, 7, 8 at the end of chapter 5.
2. Consider the model in question 4, end of chapter 5. (i) Compute the equilibrium level of consumption, saving, output, investment and the interest rate for the model. Now compute the equilibrium values of these variables when taxes are cut from 200 to 150. (ii) Repeat (i), except do so for the version of the model without the investment accelerator, i.e., the version in which the coefficient on Y in the investment equation is zero. (iii) Compare the magnitude of the increase in equilibrium output between (i) and (ii). Provide the intuition for the difference in the results. In which case does the cut of taxes generate less crowding out? Give intuition for your answer.
Answers to homework #3.
Homework #4, due February 2
Questions 1, 6, 7, page 131 in the book.
Answers to homework #4.
Homework #5, due February 9, answers.
1. Questions 6 and 7, page 159 in the book.
2. Using the AS-AD model, show the effects of an increase in I(bar): (i) begin by drawing the AD-AS model in medium run equilibrium, before the shock to I(bar); (ii) show how the increase in I(bar) moves the AD curve (make your argument taking into account the fact that the AD curve is constructed from the IS-LM diagram); (iii) point out the short run and medium run equilibria; (iv) describe in detail what happens to the interest rate, investment, consumption, employment, unemployment and output as you move from the old medium run equilibrium to the short run equilibrium, to the new medium run equilibrium (illustrate your argument by using the various graphs that go into constructing the AD and AS curves); (v) how does the size of the multiplier effect in the short run compare with the multiplier in the Keynesian Cross model and the multiplier in the IS-LM model? Why are the multipliers different? What is the multiplier in medium run in the AD-AS model? (vi) what happens to the composition of spending, between investment, consumption and government spending, differ across the old and the new medium run equilibria?
Homework #6, due Thursday, February 17. Answers.
Using the AS-AD model,
1. Consider a rise in labor productivity: (i) explain in detail how this shifts the AS curve, but does not change the natural rate of unemployment. (ii) Work out the implications in the short run and the medium run, for the interest rate, C, P, I, employment and unemployment of the rise in labor productivity. Establish your results using graphs, and then provide intuition. (iii) Why might globalization produce a rise in the economy’s labor productivity?
2. Suppose that the size of the labor force increases. What happens to the natural rate of unemployment in the medium run? What happens to the natural rate of output?
3. Suppose there is a rise in the quality of unemployment insurance. Explain why this increases the natural rate of unemployment. What is the impact on output, interest rates, the price level, investment, consumption in the short run and the medium run. Establish your results using graphs, and also provide the intuition.
4. Explain why globalization may lead to a fall in the natural rate of unemployment in the medium run. Work out the implications, in the short and medium run, for interest rates, the price level, the unemployment rate and consumption, of increased globalization. Make your argument using graphs, and then provide the economic intuition.
Homework #7, due Thursday, February 24. Answers
1. Suppose there is a decrease in the money supply.
(a) Work through the short run impact of this change on output, employment, the price level, the interest rate and unemployment. What happens in the medium run? How much does the expected price level move in the medium run? First show what is going on in the AD-AS and the IS-LM diagrams. Then, provide a journalistic discussion.
(b) Reconsider the experiment in (a). This time, suppose that when the money supply falls, the expected price level falls at the same time, by the amount it changed in the medium run in (a). Redo the analysis in (a).
(c) What can you infer from your analysis in (a) and (b) about the importance of slow adjustment in expectations for the transmission of money supply changes to economic variables?
2. Consider an economy that begins in medium run equilibrium, and is then hit by two shocks: there is a drop in government spending, and a substantial improvement in the quality of the unemployment insurance system. Suppose the initial medium run price level is above the level that is consistent with the Gold Standard. In addition to the above two shocks, the government wants to manipulate the money supply to restore the Gold Standard.
(a) In the AD-AS diagram, illustrate what the G and unemployment system shocks do to the AD and AS curves. Where are the short run and medium run equilibria in the absence of a monetary policy response?
(b) Suppose the monetary authorities simply want to reach the Gold standard in the medium run. How much do they need to move the AD curve to accomplish this? Explain why this requires a decrease in the money supply.
(c) Suppose the monetary authorities want to reach the Gold Standard in the short run. Show how much they need to move the AS curve to accomplish this. Which generates a greater recession, (b) or (c)? What does the monetary authority need to do to the money supply as the economy moves to its medium run equilibrium, if it wants to remain on the Gold Standard all the time?
3. Suppose you observe P and Y going in the opposite direction, but no change in the real wage, W/P. What is the shock driving the economy? Explain using graphs.
4. Suppose that in 3 you instead observe W/P rising. How does this change what you infer about the source of the shocks? Use graphs.
Homework #8, Due March 3.
1. Suppose there is a rise in Pe, the expected price level.
a. Explain, in full detail (i.e., describe the movements of all the endogenous variables, and motivate your conclusions using graphs), where the economy goes in the short run and where it goes in the medium run.
b. Discuss the dilemma faced by a central bank, which sees the rise in Pe (it sees the strong wage demands) and correctly understands that the scenario in (a) will unfold if it does nothing (i.e., if the central bank chooses ‘non-accommodation’). Describe in detail the ‘accommodation scenario’, the one in which the central bank uses its control of the money supply to prevent any rise in unemployment. Discuss the advantages and disadvantages of accommodation versus non-accommodation.
c. Suppose the central bank is known to be inclined towards increasing the money supply in the event that it observes unemployment rising. What does this do to the likelihood that Pe may rise sometime in the future?
d. Use your analysis in the previous parts of this question to explain why it is that the European Central Bank was made independent of national or euro area-wide government organizations (hint: independence means they will be less subject to political pressure to keep unemployment low), and was given a mandate to place a very high priority on achieving low inflation. Does it not seem to be a waste, to give up the possibility to use monetary policy to help stabilize the economy?
2. Up to now, we modeled an increase in productivity as showing up only in the equation relating unemployment to output: u=1-Y/(aL), where the production function is given by Y=aN. This gave rise to the following AS curve: P=(1+ µ )F(1-Y/(aL),z). Now, we’ll take a slightly more sophisticated approach, one that does not change the AS curve, but which does change its parts. Let the productivity parameter, a, enter the price equation like this: P=(1+µ)W/a. To understand why this is, recall that P is the price for one good. Under our theory this is equated to a markup over the marginal labor cost of labor in producing the good. W measures the marginal cost of one hour of labor. So, if a=1 then the marginal labor cost of one good is W. But, if a jumps to, say, 2, then the marginal labor cost of one good is W/2, because it now takes the worker only 1/2 hour to make the good, at a labor cost of W/2. Now consider the bargaining equation. I suppose that a shows up in this expression as follows: W=aPeF(u,z). The idea behind this is that when a rises, the amount produced by a given worker goes up. The nature of the bargaining is that what the worker gets for his/her labors goes up in the same proportion as a.
a. Suppose a goes up. Explain carefully why the natural rate of unemployment does not change, but the natural rate of output does. Also, explain why the real wage, W/P, rises. These are sensible properties for our model to have, since over long periods of time a does rise, while W/P and output both rise too, but unemployment does not rise.
b. Suppose a goes up. Explain in detail what happens as the economy moves to the short run equilibrium. Then, explain how it moves to the medium run equilibrium.