Econ 305: Midterm 1 (Answer Key)
June 09, 2011
D. Andolfatto
Name
Instructions. Use the scrap paper assigned to you for rough work only—do not hand it in. Write your final
answers on the exam paper itself and limit yourself to the space provided below each question. Do not write
on the back of the exam paper. For your own sake, write as neatly as possible and label all diagrams clearly.
If a question asks you to “explain,” you are expected to provide economic intuition in plain English (making
minimal use of economic jargon). Time limit: 90 minutes. Total points: 55.
True/False/Uncertain and Explain (15 points)
[1a] If a theory makes one or more unrealistic assumptions, it is necessarily useless. [Marker: there are several
ways in which one might answer this question, so be generous with your grading as long as the answer comes
close to below and/or otherwise makes sense.]
False. Most theories contain unrealistic assumptions in the sense that they abstract from forces that
are considered to be relatively less important for understanding a given phenomenon. Just because some
assumptions are unrealistic does not mean that a theory is useless either as a tool to form conditional
forecasts, or as a tool to help us organize our thinking about the way the world works.
[1b] Government policies should be designed to help maximize an economy’s GDP.
False. The GDP, which is a measure of aggregate income and production, is obviously important for
material living standards. But producing GDP comes at a cost. That is, people also value time spent in (or
output produced by) non-market activities, for example, leisure, education, and other home-related activities.
Maximizing one likely means minimizing the other. People likely want some balance in their lives.
[1c] The term rational expectations refers to the ability to forecast future events with perfect accuracy.
False. “Rational expectations” means that people utilize the information at their disposal to form their
expectations in a manner that is statistically consistent with the world in which they live.
Productivity Growth and Employment (20 points)
[2] Consider the following model economy. There is a representative individual with preferences for consumption and leisure ( ) given by  ( ) = ln() +  ln() where   0 Consequently, we have
 ( ) = () There is a time constraint  +  = 1 where  denotes time spent working. There
is also a resource constraint  =  where   0 indexes productivity (the rate of return on labor).
(a) Give a mathematical statement of the individual’s choice problem and explain what it means.
Choose (  ) to maximize  ( ) subject to  +  = 1 and  = 
(b) Provide a mathematical characterization of the solution. Provide a diagrammatic characterization of
the solution.
Mathematical:  ( ∗  ∗ ) =  and  ∗ = (1 − ∗ ) OR  (∗  1 − ∗ ) = 
Diagrammatic: Draw an indifference curve tangent to budget line.
(c) Using the mathematical characterization in (b), solve for the equilibrium level of output and employment
( ∗  ∗ ) as a function of parameters ( ) (Just report your answer—no need to show derivation.)
µ
¶
1
∗ =
1+
µ
¶

∗ =
1+
1
(d) Over the last century, productivity (the real wage) has increased significantly, while the amount of time
devoted to employment has remained relatively stable. Is the theory developed here consistent with
this observation? Explain the interpretation offered by the theory. (A diagram may be helpful)
Yes, the theory is consistent with this observation. In particular, from part (2c) we see that the level of
employment is independent of productivity, while the level of output is increasing in productivity.
The interpretation offered here is that an increase in productivity has roughly offsetting substitution and
wealth effects on labor supply. On the one hand, higher productivity increases the return to labor, which
increases labor supply. On the other hand, higher productivity means that people are wealthier—that is, they
can afford to consume more leisure—which reduces labor supply. These two effects work in opposite directions
on labor supply and may roughly cancel in reality.
The Business Cycle (20 points)
[3a] Suppose it is within the power of the government to stabilize output and employment perfectly. Should
it use these powers to stabilize the business cycle? Explain why (and under what circumstances) it
may not make sense to eliminate the business cycle. (Do not use math, but do use an appropriate
diagram. Explain using plain English).
Whether or not stabilization policies should be employed depends on the “shocks” that are causing the
business cycle, as well as whether the economy can be expected to respond efficiently to these shocks. Imagine, for example, that output and employment fluctuate because individuals respond efficiently to exogenous
changes in productivity; see diagram. While the economy fluctuates between A and B, these fluctuations
(while unfortunate) are efficient. One could, in principle, stabilize both output and employment at a point
like C (point lies on the interior of the lowest production possibilities frontier). Point C, however, corresponds to a relatively low level of economic welfare (indifference curve lies lower than the other two through
points A and B). What this demonstrates is that low and stable output is not necessarily preferred to high
and volatile output.
[3b] The following two figures are from David Altig’s article on actual and potential GDP. Explain in words
how these two pictures represent two very different views of the business cycle. Begin by defining the
terms “potential GDP” and the “output gap.” Then explain what problem we have in making the
concept of “potential GDP” operational (i.e., useful). Continue your essay from there.
Potential GDP is defined as the level of output that would be produced if markets worked perfectly. The
output gap is defined as the difference between actual GDP and potential GDP. The problem with operationalizing the concept of potential GDP is that it is not observable.
Because potential output is not observable, it must be estimated. But estimation is performed within the
context of a theory of what determines the business cycle.
One view is that potential output evolves in a stable manner (diagram on the left). Under this view, there
are large departures in actual GDP from potential. These departures are frequently viewed as being driven by
“animal spirits”—exogenous fluctuations in expectations. The implication is that the output gap is large and
that the business cycle is highly inefficient. This view suggests a role for government stabilization policies.
Another view is that potential output is itself subject to large fluctuations (diagram on the right). These
fluctuations are viewed as being caused by fundamental changes in productivity and/or expectations. Under
this view, the departures in actual GDP from potential are small or nonexistent. The implication is that the
output gap is small and that there is little, if any, role for government stabilization policies.
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