Development Field Exam
January 12, 2011
This exam has two parts: A section of four long questions and a section of four short
questions. You should answer only three of the four longer questions. However, please answer
all four short questions.
Longer Questions
Complete three of these longer questions. Each is worth 30 points. These may require a
more sustained argument than the short questions, but clarity and concision are still very
desirable. We would prefer that you do not use a blue book, but instead use letter-sized
notepaper, written on one side. Please also begin each long question you complete on a new
sheet of paper.
1. Insurance and Inequality Consider a village of nfarmers who live over Tperiods.
Each person has a time-separable von Neumann-Morgenstern utility function, and
derives utility from consumption. Each farmer iharvests a quantity of the consumption
good ei∈ {1,2}in every period, with the probability of a good harvest varying by
person (but not over time), so that Pr(ei= 2) = πi.
(a) Supposing that n= 2, sketch a state-date tree for the economy described above.
(b) Relaxing the assumption that n= 2, assume that the momentary utility func-
tions of farmers iand j(i.e., the functions governing the utility they receive from
consumption at a particular date-state) are both increasing, concave, and con-
tinuously differentiable. Show that in an efficient allocation these two farmers’
marginal utilities will be perfectly correlated.
(c) Now suppose that with probability ψ > 0 known to the farmers, a government
program is introduced at time tthat will give eligible farmers (say just farmer 1
in this village) an additional unit of the consumption good in every period from t
on. How does this additional source of risk affect the date-state tree you sketched
above?
(d) If in fact the program is introduced, then how do you expect the announcement of
this program to affect the allocation of consumption between eligible and ineligible
farmers at t? At t+ 1? At t−1?
(e) It turns out that this village is merely one in a population of villages which are
being randomly assigned to “treatment” and “control” groups, with the “treat-
ment” being the introduction of the program. A “baseline” survey of consumption
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