Eco 304L, Introduction to Macroeconomics
Fall 1998
Professor Harry Cleaver

Second Test


Part I: The Basic Keynesian Macro Model

(Answer 1 of the following questions for 20% of total grade.)

1. Explain how the centrality of the wage --which we studied in the section on the Keynesian solution to the Great Depression-- shows up in the Keynesian cross model that we have been working with. How does the model demonstrate that rising wages can be a good thing for the economy and for business?

The centrality of the wage shows up in the consumption function which dominates the aggregate expenditure/demand function Y = C + I + G. C is presented as a function of disposable income, e.g., C = a + b(Y - T), but we know that the primary form of that income which finances consumption is wages/after-tax-wages. There are other forms of income (interest income on savings accounts, stock dividends, rents, transfer payments, even profit) but for the vast majority of people --as we see on individual tax returns-- wages & salaries are the basic source. This centrality is also seen in the positive view of the Consumption function. A rise in consumption (upward shift in the Consumption function) stimulates the economy by raising aggregate demand, inducing more output and perhaps more investment and growth in productive capacity. Thus, indirectly we have an expression of rising wages as demand and stimulus rather than as cost and drag. Since rising output and investment are considered "good" increases in wages/consumption which stimulate those rises are "good" for the economy & business.

2. In our earlier discussion of growth we examined a model in which the more that was saved and invested, the faster the rate of growth. But in the Keynesian cross model an upward shift in the savings function will reduce the level of Y. Are these two approaches contradictory? If so, why? If not, why not?

The two models are not entirely contradictory. The growth model assumes that everything which is saved will be invested, so increasing savings automatically increases investment and produces growth. But in the Keynesian model there is this distinction between ex-ante & ex-post, between planned and actual savings and investment. Ex-post savings and investment are always equal (via inventory adjustment) but ex-ante they may not be. In the Keynesian model an upward shift in the savings function means at every level of income planned savings rises. But because investment is a separate function, determined by separate decision makers it may remain the same. If it does then the increases in savings will not only not be translated into more investment but the only way that level of savings can be realized in equilibrium will be for output to fall. Because the Keynesian model is a short-run model we can get growth (up to full employment) through expanding aggregate demand. But in the long run, the only way to shift the full employment level of Y to the right is to expand the productive base of the economy through investment --the same as the earlier growth model. Because it naturally takes more and more investment to keep growth going as the economy expands, an upward sloping investment function is more realistic than a flat one. An upward sloping function not only captures the Keynesian notion of "induced' investment but allows investment to expand with the growing economy.

Part II: Keynesian Theory and Policy

(Answer 1 of the following questions for 20% of total grade.)

3. Given a simple model of the sort: Y = C + I + G, C = a + bYd, Yd = Y - T, T = To + tY, I = g + hY and G = G, show how to derive the government expenditure and autonomous tax multipliers. What are these "multipliers", what do they tell us and why are they important for the calculation of fiscal policy?

Show work. The following is simple derivation, the multipliers can also be derived algebraically in the manner shown in the text book.
Y = a + b(Y - To - tY) + g + hY + G
Y = a + bY - bTo - btY + g + hY + G
Y - bY + btY - hY = a - bTo + g + G
(1 - b + bt - h)Y = a - bTo + g + G
dY/dG = 1/(1 - b + bt - h)
dY/dTo = -b/(1 - b + bt - h)

These multipliers are measures of the cumulative indirect effects of changes in G or T on the level of economic activity. Because several of the functions in our model include Y, then changes in Y brought on by changes in G or T will effect the other variables which will, in turn, effect Y. They are important for fiscal policy because if we don't know all these indirect effects we might underestimate the effect of any given policy change.

4. Using words and graphs explain how the Keynesian model provided a policy guide for getting the economy out of a deep recession. Discuss the ways fiscal and monetary policy could be used separately or conjointly to achieve this result. In our earlier discussion of the Keynesian solution to the Great Depression "productivity" figured prominently. Here it seems to be missing. How might monetary or fiscal policy be organized to have an impact on productivity?

Answer can involve either the Keynesian cross diagram or the IS-LM diagram. In the former case and increase in aggregate demand brought on by an expansion of G, a cut in T or both will raise AE, similarly an increase in I brought on by an expansionary monetary policy which lowers the rate of interest would also increase AE. In the latter case, expansionary fiscal policy shifts the IS curve to the right, expansionary monetary policy shifts LM to the right. The graphs used should illustrate these changes and be properly labeled and explained

Productivity is NOT explicit in this model but we can easily imagine the relationship between monetary and fiscal policy and productivity, e.g., G may be structured to support R& D public and/or private to encourage the growth of productivity. Similarly Taxes might be structured to do the same, lower on productivity raising investments. More generally one might argue that the Keynesian general desire to keep interest rates low to encourage investment is also a stimulus to the growth of productivity. On the other hand, the centrality of wage increases discussed in question one above also acted as a goad to business to raise productivity. Finally, clearly increases in productivity that had the effect of lowering labor costs and raising profits would show up as an upward shift in the MEC curve as expected rates of return rose.

5. Not long after the Keynesian model appeared it was reworked into what came to be called the IS-LM model. Show graphically how to derive such a model. What are the advantages of this model over the other, Keynesian cross model?

The graphical demonstration was included in class lectures and slides. The graphs should be accompanied by an explanation that makes clear that the students know what they are doing.

Advantages? If, as many Keynesians were, you are preoccupied with keeping interest rates low to encourage investmeent, then the IS-LM diagram has the advantage of keeping the interest rate in plain view where you can study the effects of monetary and fiscal policy on this variable as well as on Y. Another advantage is that you don't have to worry about "feed back effects", say between changes in Ms, I, Y and then Md because all of the points of the IS and of the LM are equilibrium points.

Part III: Policy Problem w/model

(Answer all the following questions for 40% of total grade)

The 1960s Inflation

It is the late 1960s. An extended period of steady growth --fueled by Great Society expenditures at home and defense expenditures for the Vietnam War-- is beginning to show signs of a troublesome, accelerating inflation. Over the last few years the inflation rate has moved up from 4% to 8% and seems likely to get worse. As policy advisor, you are called upon to recommend ways to deal with this problem.

Assume you have constructed the following model of the macro economy based on existing data:

C = 40 + 0.75Yd
Moreover, for the present period, you expect:
T = -10 + 0.1Y
government expenditures to = 80,
exports to = 13
and the Fed to expand the money supply to 100.
I = 110 + 0.1Y - 400i (Note: 0 < i < 1, e.g., ten percent interest appears as 0.10)
i = 5.1 - 0.05Md
M = - 37 + 0.05Y (M = imports)

Given this model and information answer the following questions:

6. Solve for the equilibrium level of income. Solve for the amount of taxes that will be forthcoming at that level of income and calculate the state of the government's budget (G - T). Solve for the level of expected imports and calculate the trade balance.

Ans: Begin with Y = C + I + G + X - M Y = 40 + 0.75(Y - {- 10 + 0.1Y}) +110 + 0.1Y - 400(5.1 - 0.05 {100}) + 80 + 13 - (- 37 + 0.05Y)
Y = 40 + 0.75(Y + 10 - 0.1Y) +110 + 0.1Y - 400(.1) + 80 +13 + 37 - 0.05Y
Y = 40 + 0.75Y + 7.5 - 0.075Y +110 + 0.1Y - 40 + 80 +13 + 37 - 0.05Y
Y - 0.75Y + 0.075Y - 0.1Y + 0.05Y = 40 + 7.5. + 110 - 40 + 80 + 13 + 37
Y(1 - 0.75 + 0.075 - 0.1 + 0.05) = 247.5
.275 Y = 247.5
Y = 1/.275(247.5) = 247.5/.275
Y = 900 = equilibrium level of income T = -10 + 0.1Y = - 10 + 0-.1(900) = - 10 + 90 = 80, so G - T = 0, the budget is balanced.
M = - 37 + 0.05(Y) = - 37 + 0.05(900) = - 37 + 45 = 8, so X - M = 13 - 8 = 5, so the trade balance is in surplus.

7. Suppose that you estimate that an equilibrium level of 880 would slow the rise in prices to a more acceptable level. Therefore, your problem is to recommend policies that would achieve this level of national income.

a) By how much would you have to change government expenditures to accomplish this by fiscal policy alone? By how much would you have to change autonomous taxes to achieve the same thing, with no change in government expenditures? What political problems might you foresee resulting from each of these two approaches?

Ans: one approach is to use the multiplier.
dY/dG = 3.6 [from Y = (1/.275)247.5, we see that the multiplier (e.g., dY/dG) = 1/.275 or + 3.636363636 or 3.6]
Then dY = 3.6 dG. Because Y = 900, the desired dY = - 20 to achieve Y = 880.
So, (- 20) = 3.6 dG or (- 20)/3.6 = dG = -5.6 so G would have to be lowered from 80 to 74.4.<

Another approach would be to solve for G.
You can avoid starting from the beginning by remembering that in the expression .275Y = 247.5, the 247.5 included a G of 80. So, if we take out 80 and add an unknown G, and substitute the desired 880 for Y, we can solve for the G necessary to produce a Y of 880:
.275(880) = 247.5 - 80 + G
242 = 167.5 + G
74.5 = G, which is within one decimel point of the 74.4 answer obtained in the previous method.

To find out how much autonomous taxes would have to be raised to lower Y to 880, you could also use the multiplier
The tax multiplier (dY/dTo) is - 0.75/.275 or - 2.72727 or - 2.727 (from above)
So, if dY/dTo = - 2.727, then dY = - 2.727 dT, but dY = - 20, so - 20 = - 2.727 dT
Therefore, - 20/-2.727 = dT = 7.33
Thus, to lower Y to 880, autonomous taxes would have to be raised 7.5 and T = -10 + 0.1Y would become
T = - 2.67 + 0.1Y.

A second approach would be to solve for To
Instead of 0.75(10) = 7.5
let 0.75(x) = x*
then, following the procedure used before
.275Y = 247.5 - 7.5 + x*
.275Y = 240 + x*
.275(880) = 240 + x*
242 = 240 + x*
x* = 2
So, if x* = 0.75(x) = 2, then
2/0.75 = x = -2.67, and T = -10 + 0.1Y would become
T = - 2.67 + 0.1Y, as in the other approach.

Political Problems: by raising taxes, you might incur the wrath of the middle class which might become less supportive of either the Great Society programs, or of the Vietnam War or both; by decreasing government expenditures you would have fewer resources to deal with problems both at home and abroad.

b) By how much would you have to change the money supply to achieve a national income of 880 by monetary policy alone?

Ans: If you want to lower Y (from 900 to 880), then you will want to reduce the money supply (Ms) to produce a higher interest rate which will tend to result in less investment and thus less Y. To find out by how much you need to reduce Ms you can work backward. First, find the i necessary to produce the level of I that will give Y = 880, then find the Ms that will give that i. Or, you can do it all at once in the following fashion, following the short cut method used in the answers to the previous questions.

In .275Y = 247.5, you know that - 40 of 247.5 came from that part of Investment accounted for by the interest rate, i.e., - 400(5.1 - 0.05(100) = - 40. Now what you want to know is what 100 should be raised to. So, ADD 40 to 247.5 along with an unknown x:
.275Y = 247.5 + 40 + x
.275(880) = 287.5 + x
242 - 287.5 = x
-45.5 = x
but x must = - 400(5.1 - 0.05Md), and Md must = Ms, so...
- 45.5 = - 2040 + 20Ms
1994.5 = 20Ms
99.725 = Ms, which is the level to which Ms must be lowered in order to generate an Investment which will in turn generate an equilibrium level of Y = 880. In other words, Ms must be lowered from 100 to 99.725 to achieve the desired policy goal.

Part IV: The Crisis of the Keynesian Era

(Answer 1 of the following questions for 20% of total grade.)

8. The breakdown of the Keynesian era was signaled at the international level by Nixon's abandonment of the Bretton Woods system of fixed exchange rates on August 15, 1971. What growing international economic problems led Nixon to this decision? In what ways had the American government tried and failed to deal with these problems at the domestic level in 1970? So, how did the shift to flexible exchange rates signal a breakdown in the domestic foundations assumed in the Bretton Woods agreements?

The most immediate problem was the emergence of a run on the dollar, preceeded by that of a foreign trade deficit, the first in a very long time. Behind these problems were others, such as the falling competitiveness of US exports with accelerating inflation. The attempt to stem inflation was the engineered recession of 1970 which by raising unemployment was expected to reduce inflationary pressures. But it failed to do so. Unemployment did rise but so did the price level. The shift to flexible exchange rates came because ŇadjustmentÓ could no longer be achieved within the country using Keynesian techniques. Most immediately if the trade deficit was due to inflation and a Keynesian recession didnŐt lower inflation then it didnŐt help the deficit in that manner. (It may have helped a bit by lowering M if M = f(Y)). The deficit together with the run on the dollar was putting downward pressure on the latter. Letting the dollar depreciate would, in principle, stimulate exports and depress imports thus bringing about adjustment with no direct Keynesian intervention.

9. At the core of the rise of the Keynesian era was the "productivity deal" embedded in union contracts and the welfare state. At the core of the fall of the Keynesian era was the collapse of that deal and the failure of the state to either renew it or find a substitute. Discuss that collapse both within the economy and within the larger society in as many dimensions as you can think of.

Collapse within the economy involved the rupture of the deal as workers pushed up wages and benefits faster than the rise in productivity, while in many cases slowing the growth in productivity or even pushing it down. This crisis in productivity involved an unwillingness to continue to accept the basic Keynesian deal that promised more money for continued work. People wanted more free time to complement their rising real wage. This was true in the larger society as well. E.g., students wanted to study what they wanted, or more time off for personal pursuits, women wanted less housework, welfare mothers wanted more income but used it to fight for still more, and so on and on. The basic points are: one: these developments followed from rising income which lead to more diverse desires and two: they were interrelated,e.g., what happened in the streets circulated into the factories, what happened in homes circulated into the schools.