University of Wisconsin-Madison
Department of Agricultural and Applied Economics
Development Economics Preliminary Examination
28 August-1 September 2006
Answer any three of the following five questions. All questions have equal weight. Please type
your answers. Your answers must be submitted to Michael Carter, Development Prelim Chair,
421 Taylor Hall no later than 5 pm on Friday, 1 September
1. Consider a household i that lives in a valley v and has W0 units of wealth that it can allocate
to either a stochastic production process or save. Assume that households have access to a
risk-free savings instrument, but that they can neither borrow nor obtain formal insurance. In
this setting, a household's expected utility maximization problem is:
Max
Ws ,W p
E[u (ci )]
subject to
ci  (1  r )Ws  y  p H H
y   i f (W p | H )
W s  W p  W0
where u() is the household's utility function, c is consumption; r is the non-stochastic rate of
return on wealth allocated to savings, Ws; f() is a net-revenue (production) function which,
for a given amount of land, H, exhibits positive but diminishing returns to wealth invested in
production, Wp; and, i is a random variable for which E(i) = 1. Finally, pH is the market
value of land.
a. Analytically characterize the behavior of this household—i.e., how will the household
divide its wealth between safe savings and investment in the risky production
process? For purposes of later analysis, denote the solutions to this autarchy problem
as W sA* and W pA* .
b. The random variable, , can be decomposed as follows:
i  v   i
where v, is a common rainfall shock received by all households in valley v, and i is
an idiosyncratic random variable with mean zero, variance  2 and is independent of
valley-level rainfall measure. Suppose that actuarially fair rainfall insurance
contracts become available that payoff as follows:
  f (WpA* | H )  max[ 0,1   ])
and the premium for the insurance, , is set such that:
  E( )
Taking the stochastic structure as given, show how household resource allocation,
income, etc. will change once the rainfall insurance is available.
2
c. Finally, how are the effects of the rainfall insurance change as the stochastic structure
changes (e.g., as  2 changes). More speculatively (i.e., without further formal
analysis), how do you think the value of the insurance will change as H changes?
2. Following the lead of the Mexican Progresa program, a number of countries have begun to
initiate conditional cash transfer (CCT) programs designed to combat poverty while
encouraging poor families to achieve higher rates of schooling and child health investments.
Under these CCT programs, the cash payments are only made if children attend school fulltime. One criticism of CCT programs is that they do little for improving well-being of the
current generation. This question asks you to think about this aspect of CCT programs.
Consider the following two-period model of a household confronting a CCT program:
Max
s , k ,c ,e
u (c1 )   E[u (c 2 )]   (e)
subject to
c1  s  k  y1
c2  y 2
y 2   i f (, k )  I (e  1)  (1  r ) s
   A  (1  e)
s, k , ct  0
where e is the binary education variable, and  is the payment the family receives conditional
on school attendance (e=1). To keep things relatively simple, we assume that the family’s
first period income is pre-determined ( y1 ) and that the family can divide that income
between current consumption, productive investment (k) and safe savings (s). Adult labor
supply to the production process that generates second period income is fixed at  A . The
production function f has the usual properties and i is a random weather variable with
expectation equal to one. The function u is a standard utility function, and the family is
assumed to enjoy additional positive utility when their child attends school ().
a. Using this model, please analyze the family’s decision to participate in the CCT
program. Be sure to consider the impact of the CCT program on the investment and
production decisions of the family. Under what circumstances will the CCT have
additivity in the sense that it boosts productive investment and expected income for
the family?
b. From the perspective of the economic theory of poverty traps, how would you modify
the structure of this model in order to more fully explore the implications of a CCT on
the economic well-being of the current generation? You do not need to fully analyze
your modified model (which may be dynamic), but drawing on the relevant literature,
please discuss the additional considerations your poverty trap model might bring to
the analysis of CCTs. Be sure to discuss implications your model might have for the
design of cash transfer program that meets both human capital (next generation) as
well as current generation poverty reduction goals.
3
3. Development economists have given considerable attention to the ways in which inequality
among decentralized agents can impact cooperative behavior in common property - common
pool situations. In the context of a capital-complementing input like an irrigation project,
develop a simple model that explores the role of inequality.
a. First analyze the model under the assumption of symmetric access to exit options
among the economic agents.
b. Second, repeat the analysis under the assumption of asymmetric access to exit
options.
c. Comment on the policy implications of your model and explain how those
implications change with economy-wide conditions that alter agents’ exit options.
4. Economic models of agricultural technology adoption in developing countries focus on how
farmer choices related to distinctive products (e.g., pineapples in Ghana – Conley and Udry)
or “technology packages” (e.g., high-yielding varieties of the Green Revolution – Feder, Just,
and Zilberman, 1985) are shaped by farm and farmer characteristics as well as social
networks. The first wave of agricultural biotechnology innovation of the past decade has
given rise to seeds that add and often stack “traits” like weed or insect (or drought) resistance
to existing high-yielding varieties. Other than soybeans in Argentina and Brazil and cotton
in China, adoption of agricultural biotechnology innovations in the developing world has
been very limited. Please answer the following two sub-questions and then as possible relate
the two answers in a closing statement.
a. What are some of the key factors limiting the application of agricultural
biotechnology innovations to developing country contexts where they could
potentially be of high value?
b. What are the main strengths and weaknesses in terms of methodology of applying
recent economic models of technology adoption in developing countries to the case of
agricultural biotechnology? Be explicit in your discussion about the basic theoretical
assumptions and econometric methods used in these modeling efforts.
4
5. Neoclassical economic theory asserts that international migration together with remittance
‘backflows’ must improve welfare in both sending and receiving countries, but that result is
of course conditional on many assumptions. This question asks you to focus on the welfare
effects of migration in a typical sending country, which you should think of as a low or
middle-income developing economy.
a. Assume the economy is a price-taker in international markets, is free of distortions
and policies, and that all aggregate factor endowments are exogenously determined.
Use a simple real general equilibrium model to investigate the static effects of an
exogenous outmigration “shock”, in which aggregate remittances from outmigrants
are some fraction   0 of their earnings in the pre-migration equilibrium. Evaluate
changes in the structure of production and trade, aggregate income, and the welfare of
a representative consumer. Do this first for the simplest case of two traded goods,
and then for the extension to three goods—importables, exportables and nontradables. Briefly discuss and compare the results.
b. To confirm the logic of your trade-related results, reconcile the effects of
outmigration and remittances in a simple statement of the current and capital accounts
of the balance of payments.
c. It is well known that outmigrants from poor countries are not taken randomly from
the labor force, but are disproportionately drawn from the upper tails of the
educational, skills and entrepreneurship distributions. Extend the supply side of your
model to identify the expected impact of outmigration by relatively more productive
workers on prospects for long-run growth. Establish a baseline result using standard
neoclassical assumptions, then extend the supply-side model or relax its assumptions
in ways that might generate endogenous growth outcomes and recomputed the effects
of the outmigration/remittance experiment. Provide brief but convincing empirical
explanations for any amendments you make to the neoclassical model. What are the
key parameters governing the long-run results?
d. How do the results in part (c) differ from those from the short-run model in part (a)?
Discuss structural aspects of the results and supply a brief normative (i.e. policyoriented) discussion.
5