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HETERODOX MICRO SECTION (2 ½ hours total) This section has
two parts A and B; you must answer both parts and there is some choice
in each part.
Part A - Problems. Choose one (1). [1 hour and 15 minutes]
1) Two fishers, Eye (i) and Jay (j), fish in the same lake, using their labor and
their nets. They consume their catch and do not engage in exchange. They
do not make agreements about their actions, yet each one’s action affects the
other. Specifically:
yi = αi (1-Bej)ei , where yi = amount of fish caught by Eye over some period
αi>0 = constant which varies with the size of Eye’s nets
ei and ej = respectively the share of the 24-hour day each spends fishing,
B> 0 is the impact of one agent’s actions on the other.
Fishers have analogous production functions, yi, and utility functions such that:
Ui = yi –ei2, Ue<0, Uy>0
a. Solve for the best response functions of the two actors and graph them.
b. Indicate any Nash equilibria. Are they/is it Pareto Optimal? What
accounts for this?
c. Suppose the state wishes to determine the Pareto Optimal outcome. Write
down the state’s optimization problem and find the new FOCs for
determining the optimal levels of ei and ej. Compare these to the FOCs
from the individual decisions. Explain the difference.
d. If the state wants to use a tax to get individuals to choose the joint
maximization outcome, what should the tax rate be?
e. Returning to b., how does the outcome change if we assume the fishers to
be altruistic? Is altruism a viable alternative to the state? Explain why or
why not?
PLAYER 2
Cooperate
Defect
Cooperate
b,b
d,a
Defect
a,d
c,c
2) Contract Enforcement: A population of individuals faces a prisoners’ dilemma-type
situation, with payoffs as in the box above and a>b>c>d. One possible solution to this
dilemma is to “inspect” the possible trading partner and use local information on player
reputation to decide how to play.
Players who inspect are called “Inspectors.” They pay a cost of δ to inspect and find a
cooperator. The behavior is to play defect. There are α Inspectors in the population.
a. Write down the expected payoffs for each type of individual (Inspectors and nonInspectors).
b. Find the equilibrium share of Inspectors in the population.
c. Is this equilibrium stable? How many total equilibria are there? If there is more than
one, explain which is more likely to occur.
d. What can you say about the pareto efficiency of this equilibrium?
e. What happens to the equilibrium if δ increases? What does this imply for which
equilibrium is likely to be achieved and Pareto efficiency?
f. Drawing on this model and the work of Avner Grief, explain the relationship between
local institutions and histories of market development.
3) A worker in a capitalist firm has a utility function U=U(w,e), so that expected utility is
V = U(w,e) + f(e)V + (1-t(e)) Z
1+i
where
w = wage rate
e= effort per hour by the worker
t= probability of retaining one’s job, i.e. the level of supervision in the firm
i = interest rate
Z= worker’s fall back position, i.e. what s/he would earn if fired
The firm maximizes Π = y(he(m,w,z)) - (w+m)h
Write down and explain the firm’s first order conditions. What is the problem the
firm must solve to maximize profit?
b. Let the worker’s utility function be u=aw-b/(1-e). Let b=1, a=2. Let p = 1, t=1-e;
m=0, i=0 and z=0. Find w* and e*. Explain the conditions which must hold at
h*. Graph the worker’s best response function and the solution w*, e*.
c. Using the worker’s BRF and also the FOCs from the full equation (before all the
simplifications in b., outline two ways that the firm could reduce unit labor costs
(labor costs per unit of output) without reducing the wage (given that Qe > 0), linking
these directly to variables in the BRF. Graph the new labor extraction functions with
new w*, e*. Explain
d. Carefully explain three ways that this problem (objective functions, outcomes)
would change if the firm were worker-owned. Compare the expected outcomes using
your graphs.
a.
Part B - Essay. Choose one (1) of the following. [1 hour and 15 minutes]
1) Explain the importance of the “Constitutional Conundrum” to economic analysis.
Explain the implications for this for neo-classical microeconomics. Under which
conditions would the neo-classical model be expected to accurately predict outcomes?
Under which conditions not? Make explicit reference to models and evidence in the area
of heterodox microeconomics.
2) Explain the connection between incomplete contracts and economic inequality using a
model of credit markets. Explain the relationship between redistribution and the
contracting problem. How might redistribution affect efficiency?