Econ 305: Midterm 1
June 14, 2012
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: 80.
Methodology (15 points)
[1a] How is a theory defined? Explain how a theory can be used to make conditional forecasts.
We defined theory in class as a logical mapping from a set of exogenous variables to a set of endogenous
variables; the endogenous variables are a function of the exogenous variables. A conditional forecast is a
prediction of what happens conditional on some event happening. One can treat an event as an exogenous
variable. Conditional on the event occurring, the theory makes a prediction; in this sense, the theory can be
used to make a conditional forecast.
[1b] According to Karl Popper, a theory is scientific if and only if... (complete the statement).
...it makes predictions that can be falsified by emprical observation.
[1c] In his essay On the Methodology of Positive Economics, what distinction does Milton Friedman draw
between the concepts of positive and normative economics?
Positive economics pertains to “what is” whereas normative economics pertains to “what ought to be.”
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True/False/Uncertain and Explain (15 points)
[2a] The real wage is a price.
True. The real wage is the price of time (either labor or leisure time) measured in units of output.
(Alternatively: The real wage is the purchasing power of a unit of labor time.)
[2b] The real interest rate is a price.
True. The real interest rate is the price of current output measured in units of future output.
[2c] Labor supply is likely to respond more strongly to a permanent wage change relative to a transitory
wage change.
False. TAs, there are two ways to answer this and either way is fine.
First, any wage change will result in substitution and wealth effects. An increase in the wage makes
leisure more expensive, so the demand for leisure falls. On the other hand, an increase in the wage increases
wealth, which increases the demand for all normal goods, including leisure. The two effects move leisure
(and hence labor) in opposite directions. But the wealth effect is weaker for a transitory wage change, so
that the substitution effect is likely to dominate. For a permanent wage change, the wealth effect is likely
to offset the substitution effect completely.
Second, according to the intertemporal substitution of leisure hypothesis, individuals will want to reallocate their labor to the most productive periods. A permanent wage increase leaves all periods equally
productive, so there is little incentive to reallocate labor across time. A transitory wage increase, however,
makes the current period more productive relative to future periods. Hence, there is a strong incentive to
increase work effort today and postpone leisure for the future.
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Productivity Growth and Employment (20 points)
[3] 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.
(b) Provide a mathematical characterization of the solution. Provide a diagrammatic characterization of
the solution.
(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.)
(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)
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Redistribution Policy and Inequality (15 points)
[4] Many economists have advocated the Negative Income Tax (NIT) as a policy that simultaneously simplifies the tax code and redistributes income to those who need it the most.
(a) What is a NIT? Explain how it simplifies the tax code and redistributes income.
The NIT guarantees everyone a minimum income  and taxes everyone’s earnings at a flat rate   It
simplifies the tax code because all one has to do to calculate taxes owed is to compute   −  where 
represents gross earnings. The NIT redistributes income because those with high earnings   −   0 are
net contributors to the tax system and those with with low earnings   −   0 are net recipients of transfer
income.
(b) How is the NIT likely to change work incentives for low wage and high wage individuals?
The flat tax on earnings lowers the after-tax return to work, so all individuals are encouraged to substitute
out of work into leisure. Because low wage earners are net recipients of transfer income, a positive wealth
effect further encourages work effort (as they can now afford more leisure). Because high wage earners are
net contributors of tax revenue, a negative wealth effect encourages them to work harder (as they can now
affort less leisure). On balance then, one would expect the labor supply of low wage earners to decline (as
substitution and wealth effects move labor in the same direction); and the labor supply of high wage earners
to remain relatively stable (as substitution and wealth effects move labor in the opposite direction).
(c) Explain how the NIT is likely to reduce after-tax income inequality, but increase earnings (before-tax
income) inequality.
As explained in part (a), the NIT redistributes income from high earners to low earners—in this way, the
distribution of after-tax income is likely to display more equality. As explained in part (b), the NIT is likely
to cause labor supply to decline for low earners, but remain relatively stable for high earners. Therefore, the
distribution of earnings is likely to become more unequal.
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Rational Optimism and Pessimism (15 points)
[5] Consider the following model economy. There is a representative individual with preferences defined
over expected output   and labor  given by the expected utility function   − ()  where   1
For these preferences, we have  (   ) = −1  Output is generated with labor according to the
technology  =  where  is a random productivity parameter that takes on two values,     Let
  = (1 − ) +  denote the expected return to labor. That is, the parameter 0    1 denotes
the probability that the return to labor is low. Assume that the labor input  must be chosen before
individuals know the true value of 
(a) For this economy, the optimal labor input ∗ must satisfy   =    Solve for ∗ 
  =   ⇒ −1 =   ; so
∙

 =

∗
1
¸ −1
(b) Suppose that individuals in this economy suddenly receive information that leads them to revise downward their forecast over the expected return to their labor (i.e., imagine that some bad news arrives
that leads to an increase in ). What does the model predict will happen to employment and the
expected level of real GDP? Explain.
An increase in  lowers expected productivity    By part (a) above, this leads to a decline in employment
  The expected level of GDP is equal to   =   ∗  Consequently,   declines. Explanation: Bad news
means that the expected return to labor is lower. The lower expected return to labor leads people to
devote fewer resources to employoment activities. As a result, the expected level of GDP falls, first, because
employment declines and second, because the lower level of employment is expected to be less productive.
∗
(c) Suppose that after the bad news arrives, that the actual productivity turns out to be   If individuals
had known that this was to be the case, the model predicts that they would have worked harder.
Is it correct to say that individuals in this case made a “mistake,” or that their expectations were
“irrational?" Explain.
One might say that individuals made a mistake in an ex post sense, but not in an ex ante sense. The
question is whether individuals would make the same choices given the same information. In this model, the
answer is clearly yes. In this sense, the choices made are not usefully characterized as “irrational.” It’s just
that decisions have to be made with limited information. Limited information does not imply “irrationality.”
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