Econ 305: Midterm1
Answer Key
October 5, 2005
D. Andolfatto Name
Instructions. Please write neatly and label all diagrams clearly. Limit your
answers to the space provided below each question—do not write your an-
swers on the back of the exam or in the exam booklets (which are to
be used for rough work only).
1. [10 marks]. Provide two reasons why it is important for any macroeco-
nomic theory to model individual preferences.
• Since preferences measure the willingness of individuals so substitute
across activities, we can use preferences to help make predictions;
• Since preferences measure individual well-being, we can use prefer-
ences to evaluate the welfare consequences of policy.
2. [10 marks]. Should government policy be designed to maximize an econ-
omy’s GDP? Explain why or why not.
• If people wanted to maximize GDP, they would presumably choose to
do so without government coercion. People clearly value things other
than GDP (like home production, leisure and schooling). Maximizing
GDP would mean foregoing all of these things. It is not obvious that
this would make people better off.
3. [25 marks]. Consider a model economy consisting of a representative agent
with preferences u(c, l) such that M RS(c, l) = (c/l)1/2 . The agent is en-
dowed with one unit of divisible time that can be allocated either to work
(n) or non-work (l) activities; i.e., n + l = 1. Consumption (c) is gener-
ated by a technology c = y = zn, where z is an exogenous productivity
parameter.
(a) Write down (mathematically) the choice problem faced by a benev-
olent social planner (do not solve—just state the problem).
• Choose (c, l, n) to maximize u(c, l) subject to: c = zn and n+l =
1.
(b) Write down the mathematical conditions that characterize (i.e., that
would allow you to solve) the optimal allocation (c∗ , l∗ , n∗ ) (again,
do not solve the problem).
µ ¶1/2
c∗
= z;
l∗
c∗ = zn∗ ;
∗
n + l∗ = 1.
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(c) Solve for the optimal allocation as a function of z.
z
n∗ (z) = ;
1+z
1
l∗ (z) = ;
1+z
z2
c∗ (z) = y ∗ (z) = .
1+z
(d) Imagine that this economy experienced exogenous fluctuations in pro-
ductivity (z). Using a diagram, show how it would be feasible for the
planner to stabilize both output and employment. Would it make
sense for the planner to stabilize the economy in this way? Explain.
c
A
B
C
l
Efficiency requires that output and employment fluctuate in response
to changes in z (say, from A to B in the above diagram). It is feasible
for the planner to stabilize both output and employment by choosing
an allocation like C. While this stabilizes the business cycle, it obvi-
ously reduces economic welfare.
(e) Using a diagram depicting labor supply and demand, explain how a
competitive economy would react in exactly the same way to exoge-
nous changes in productivity.
• [Draw diagram with upward sloping labor supply function and
downward sloping labor demand function]. An increase in z
would increase labor productivity and increase the demand for la-
bor. Higher labor demand would put upward pressure on the real
wage and induce households to substitute out of non-market time
into market time (employment). Output would expand because
more time is spent working, and because labor is more produc-
tive. This is precisely how a planner would react to the same
increase in labor productivity.
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4. [15 marks]. Imagine instead that each firm in a competitive economy
faced a production technology of the following form: y = z(N )n, where N
denotes aggregate (or average) employment (beyond the control of any in-
dividual firm). Assume further that productivity is an increasing function
of N, so that higher aggregate levels of employment make all firms more
productive. One way to model this (as explained in class) is to assume:
z(N ) = zL if N ≤ NC and z(N ) = zH if N > NC ,
for some number NC and where zL < zH . Of course, in equilibrium it must
be the case that z reflects the real wage, with employment determined
entirely by labor supply (i.e., labor demand is indeterminate). Explain (a
diagram would be helpful) how this economy can display two equilibria,
with each equilibrium determined by a self-fulfilling prophesy. Explain
further how such an economy can display business cycles that are driven
by exogenous changes in expectations. Finally, why any such fluctuations
would not be Pareto optimal (suggesting a potential role for government
stabilization policy).
• Draw a diagram similar to the one in the textbook. Suppose that peo-
ple expect a high level of employment (beyond the level NC ). Then it
is rational to expect that labor productivity (real wage) will be high;
i.e., zH . Given this expectation, it is rational to supply a lot of labor;
i.e., beyond level NC . But if everyone behaves in this way, then zH
will be the true level of productivity, which confirms the initial ex-
pectation. The reverse holds true if—for some reason—people initially
expected employment to be low (fall short of NC ). In this case, it is
rational to forecast a low level of productivity zL . Given this expec-
tation, it is rational to supply a low level of labor. But if everyone
behaves in this way, then the level of productivity will turn out to be
low, confirming the initial expectation. Either equilibrium may oc-
cur, and depending on the initial expectation, become a self-fulfilling
prophesy.
• This economy could display business cycles if people, for some rea-
son, coordinated their behavior on one and then the other equilibrium
over time. Such events could conceivably be triggered by ‘sunspots,’
i.e., random variables that have no direct effect on fundamentals, but
simply serve to coordinate peoples’ expectations toward ‘optimistic’
and ‘pessimistic’ states of the world (animal spirits).
• Fluctuations would not be Pareto optimal because (according to the
diagram), people are made best off by remaining at the ‘high-level’ (or
optimistic) equilibrium. Coordinating on the bad equilibrium leads to
lower economic welfare (a lower indifference curve). Government
fiscal policy may be of value here, by (for example) increasing the
demand for labor when expectations become pessimistic.
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