University of Wisconsin-Madison
Department of Agricultural and Applied Economics
Development Economics Preliminary Examination
June 30 – July 4 2003
Answer any three questions. All questions have equal weight. Please type your answers. Your
answers must be submitted to Ian Coxhead, Development Prelim Chair, 413 Taylor Hall no later
than 5 pm on Friday, July 4.
1. A recent article in The Economist (December 19, 2002) highlights transport costs and
inadequate infrastructure as factors inhibiting development, illustrating the African
Development Bank’s finding of “a strong link between poverty and remoteness”. (The
article cites the rising cost of a bottle of Coca-Cola with distance from the bottling plant in
Yaoundé, Cameroon: 300 local currency units in Yaoundé; 315 in a town 125 km away, 350
in a village 100 km further yet, and so on). This question asks you to consider the spatial
incidence of some common developing-country tax policies, their consequences and cures.
Consider an agricultural economy in which all commercial farmers grow one crop, which is
exported through the port. The farm-gate price of the crop, k, depends on distance from the
port (x) and fuel costs (a* per kilometer); thus k(x) = p – ax defines the farm-gate price at
any distance x from the port, given price p and fuel cost a. Now assume that exports are
taxed at a rate t, such that the export price at the port is p = p* – t, where p* is the world price
in domestic currency terms. Assume that production uses only family labor and a locationspecific resource, land, which is uniform in every other respect.
a. Demonstrate that the incidence of the tax (as a percentage of the farm gate price) is
increasing with respect to distance from the port, and quantify its implications for
individual farm profits.
b. Clearly there is a distance from the port beyond which profit-maximizing producers
will not produce the export crop. Suppose that producers beyond this ‘boundary of
cultivation’ instead produce non-traded goods (such as a locally-consumed grain
crop), and that land used in production of either crop must be cleared from forest.
Develop a concise analysis quantifying the demand for land (i.e., the pressure for
deforestation) and its implied price as a function of trade policy and transport costs.
c. If property rights in forest to be cleared for agriculture less than fully enforced, and if
standing forest has positive social value, what implications do policy reform or
exogenous price changes have for the expansion of agriculture, and for aggregate
social welfare?
d. Based on your answer to parts b and c, provide a policy-oriented commentary on the
relationship between poverty, trade and infrastructure policies, and the use of natural
resources (here, forests) in poor agrarian economies. Build your analysis, either
formally or informally, on the supposition that poverty alleviation is an important
goal of development policy.
2. Poverty rates are disproportionately high in rural areas of most world regions. This
observation has led some to advocate policies that will improve the access of poor rural
households to land. Others argue that such policies will be ineffective. This question asks
you to consider the debate between these two positions both theoretically and empirically.
a. Define total income for a rural family as:
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Y  P.Q( LQ , A )  w( L f  LQf )  wLQh  r A ,
where the agricultural commodity, Q, is produced with a constant returns to scale
technology using labor ( LQ ) and land (A). Farm labor is the sum of family and hired
labor ( LQ  LQf  LQh ). To keep things simple, assume that the land to which the
family has access is fixed at A . The family has a total labor stock of labor ( L f ) that
can be allocated to farm and non-farm activities. Some of the labor allocated offfarm may be used up in searching for jobs, and the number of days employed as a
function of time allocated to off-farm activities is ( L f  LQF ) , where
0    1;   0;   0 . P is the price of the commodity Q, w is the wage rate, and r
is the land rental rate.
Assuming that families allocate resources in order to maximize income, under what
circumstances will a policy that enhances land access (i.e., increases A ) for a poor
family actually make them better off in income terms? When will improved land
access have no effect on family income? In answering this question, you should
define a poor family as one for whom LQH=0 and LQf< L f . You may find the
analysis easier if you note that under constant returns to scale, the income of a poor
family can be written as:


y  P Aq (lq )  w L f  lq A  r A ,
where the lower case letters denote values per-unit of land.
b. Suppose that you now want to use the model above to empirically determine whether
or not policies designed to improve land access are good anti-poverty measures.
Using the model, please explain what empirical proposition you would test.
c. Finally, assume that you had data on a random sample of rural households (rich and
poor, landed and landless). Econometrically, how would you undertake the task of
estimating the test statistic you identified in part (b) above.
3. T.J. Lybbert et al. (2001) report the following non-parametric estimates of the impact of herd
size in year t on herd size in year t+j among Ethiopian pastoralists:
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Expected Future Herd Size, Ht+j
E(Ht+10 | Ht )
30
E(Ht+1 | Ht )
Ht= Ht+j
20
10
0
0
10
20
30
Herd Size This Year, Ht
(Source: Lybbert T.J., C.B. Barrett, S. Desta, and D.L. Coppock. 2001. “Pastoral Risk and
Wealth-Differentiated Herd Accumulation Patterns in Southern Ethiopia.” Cornell University
mimeo.)
a. Briefly describe and interpret the results in the above graph. What are the primary
patterns and puzzles that you see?
b. How would you account for the patterns that you see? Drawing on relevant literature,
sketch out a theory that might account for these patterns.
c. Do the patterns in the graph (and your proposed explanation of them) justify a public
policy intervention? Explain why and what if any intervention you might
recommend.
4. In their article, “Does natural resource abundance increase Latin American income
inequality,” Journal of Development Economics, Volume 59 (1999): 3-42, Leamer, Maul,
Rodriguez, and Schott argue that natural resource abundance and export orientation are
fundamentally related to Latin America’s high levels of income inequality as well as to their
weak growth performance.
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a. Evaluate their empirical argument concerning the impacts of natural resource
booms on inequality and growth. Then, comment more broadly on the empirical
issue of whether specialization in natural-resource exports has proven to be
problematic for inequality and growth elsewhere in the world, emphasizing both
trends and potential explanations of these trends.
b. Develop or borrow an endogenous growth model that explicitly links inequality
and slow growth to natural resource specialization. Try to be clear about what
assumptions drive the inequality and the growth results and how they are linked.
Do the results depend on the ownership structure of the resource sector? If so,
how? If not, why not?
c. Choose a policy intervention that might be used to improve growth and inequality
outcomes associated with your model. Comment on the potential tradeoffs
associated with the policy intervention you choose.
2. Imagine a small open economy in which n goods are produced using m factors.
Production of each good also generates pollution. Vectors p, q, c, y and z, each of length
n, denote world and domestic prices, consumption of marketed commodities, domestic
supply, and pollution respectively. Factor endowments are given by a vector v, with
length m. World prices are determined outside the model by the small country
assumption, and domestic prices are related to them by q = p + t, where t is a vector of
tariffs or export taxes. Firms are also subject to pollution taxes at rates given by the nvector s. Choose the first good to be numéraire, so p = (1, p2, …, pn) and q = (1+t1, p2+t2,
…, pn+tn).
A representative consumer has a utility function u(c, z), with uc > 0 and uz < 0; by
assumption, this function is strictly quasiconcave in c. Aggregate expenditure is denoted
by the conditional expenditure function e(q,z,u)  min q' c | u, where a prime denotes
the transpose of a vector. This function is non-decreasing and concave in q, and nondecreasing in z and u. Aggregate income is given by a revenue (or GNP) function
g(q,s,v)  maxq' y  s' z | v. The revenue function is convex in (q, s) and concave in
v; its derivatives with respect to environmental taxes give the quantities of pollution
emitted, i.e. zi   g(q, s,v) si  0 .
Net imports, m, are the excess of domestic demands over supplies; given the properties of
the expenditure and revenue functions, mi = ei – gi for the ith sector, where ei and gi are
partial derivatives with respect to price. By this definition, mi< 0 if a good is a net export.
Assume that tariff and tax revenues are rebated to consumers in lump-sum form.
Equilibrium is described by the aggregate budget constraint (1), the market-clearing
condition for net imports (2), and the production of pollution (3):
e(q, z,u)  g(q,s,v)  s'z  t' m
(1)
m  eq (q, z,u)  gq (q,s,v)
(2)
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z  gs
(3)
These equations can be solved as a system for the three endogenous variables: aggregate
welfare (u), net imports, and the quantity of pollution produced.
a. Using total differentiation, find and characterize the first-best combination of
trade and environmental policies.
b. Consider a constrained case in which environmental policy cannot be used. Find
and characterize the second-best trade policy solution. Comment on economic
welfare relative to the first-best case.
c. This model illustrates the assertion that “every economic policy is a de facto
environmental policy by virtue of its effects on the allocation of resources and the
structure of production”. It can equally be said that every environmental policy is
a de facto economic policy. Using insights from the above model, consider
informally the case of an industrializing developing country in which the poor are
overwhelmingly employed in a highly polluting, protected, import-competing
industry, but pollution is consumed equally by rich and poor alike. Discuss the
dilemma of a social planner concerned both to alleviate poverty and maintain
environmental quality.
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