May 15th, 2006
Core Qualifying Exam in Agricultural Economics
Purdue University
Directions:
 To ensure that photocopies of your exam will be readable by
graders, please write clearly and leave a wide margin around the
edges of each page. Please use blue or black ink, or bear down if
you write in pencil so that the lines are dark.
 Write your identifying exam number on each page of your work
and number the pages.
 This exam consists of three questions each with multiple parts.
Please answer all parts of all three questions.
 You have four hours to complete the exam. Therefore, you should
use your time wisely and be sure to allocate time to optimize your
ability to display your knowledge to the examining committee.
 You may ask questions of the proctor aimed at clarifying the
meaning of the question, but questions related to concepts will not
be answered.
 You are welcome to disassemble the exam when questions run
over onto multiple pages so that you can view the question in its
entirety.
GOOD LUCK!
Question 1: Individual behavior and optimization
Consider the case of a consumer maximizing utility, U x f , xn  subject to a budget
constraint for two goods: food ( x f ) and non-food ( x n ). The cash budget available to be
spent on consumption is M. In addition to M, the consumer receives a coupon, S , which
can be exchanged for food but not non-food. This gives the consumer a total income of
M  S , but S can only be spent on food. Because M can be spent on either food or nonfood, it is referred to as discretionary income.
1.
Write the consumer’s optimization problem given price p f for food and p n for
non-food. Declare explicitly any assumptions made regarding consumer behavior.
(Hint: Your problem should have two budget constraints – one for total income
and one for discretionary income.)
2.
Write out the first-order conditions of the consumer’s optimization problem and
provide an economic interpretation of the relationships.
3.
Assume only the total budget constraint of the consumer binds (i.e., some
discretionary income is spent on food). Graphically depict the consumer’s
problem in x f , x n  space. Label all points of interest on the graph.
4.
Using your graphical depiction of the problem from question 3, sign the following
comparative statics, providing explanations for your determinations. If a
derivative can not be signed, explain why it can not.
a)
b)
5.
U *
U *
U *
i   f , n ,
,
pi
M
S
xi *
xi *
i, j   f , n,
  M , S 
p j

Now consider the case where both the total income and discretionary income
constraints bind. Depict this situation graphically.
6.
Assume that in the current situation, a subsidy is in place such that consumers are
not spending any discretionary income on food. The government decides that the value
of coupons distributed, S, is too high. The government wants at least 10 percent of
discretionary income to be spent on food purchases and assigns you the task of finding
the subsidy level that will achieve this. Write a math program that (assuming you have a
well-behaved, parameterized utility function) solves for the government’s ideal subsidy
level. Is the new food subsidy level guaranteed to be lower than the in the initial
equilibrium? Explain.
Prelim Exam in Agricultural Economics – May 2006
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Question 2: Market equilibrium and econometrics
Preliminaries: Since the late 1970’s, there has been a tremendous concentration of beef
slaughtering (i.e. beef processing or manufacturing) capacity and food retailing (e.g.,
grocery stores and supermarkets) in the United States. This, in turn, led to a large number
of studies aimed at measuring the degree of oligopsony market power exercised by this
concentrated beef processing sector over farmers and/or oligopoly power exercised by
retailers over consumers of beef. However, less attention has been paid to the interplay
between beef processors and retailers in the wholesale beef market. It is possible that
both retailers and manufacturers have some market power in the wholesale market. In this
question we will focus solely on the potential market power which processors exert in the
market for wholesale beef. You will be asked to contrast this oligopoly outcome with the
equilibrium when both processors and retailers are price takers. To keep things simple,
we will also assume throughout that retailers have no market power in their output market
and processors have no market power in their input market.
1. Graphical Analysis:
a. Bilateral Price Taking(BPT): Begin with the case of bilateral price taking. Here, both
retailers and processors of beef take the wholesale price of beef as given. Provide a
graphical analysis of this equilibrium, starting from a linear retail demand schedule, a
linear retailers’ marginal cost schedule and a linear manufacturers’ marginal cost
schedule. Show how these three fundamental economic relationships interact to
determine the equilibrium quantity of processed (wholesale) beef sold to retailers, as well
as the equilibrium wholesale and retail prices for beef. In addition, please provide a
verbal description of the graphical equilibrium and how it is determined.
b.Retailer Price Taking (RPT): Now allow the processors to exercise market power in
their merchandising of wholesale beef, while the retailers continue to take their input
price as given (hence the term Retailer Price Taking). Modify your figure in light of this
fact, by adding a perceived marginal revenue schedule for processed beef sold by the
processors. In addition, please provide a verbal description of the graphical equilibrium
and how it is determined. Compare the equilibrium price and quantity outcomes in this
RPT case to those under the BPT case. Discuss the efficiency and distributional
consequences of this change in market structure. Consider the implications for farmers,
beef manufacturers, retailers and consumers.
Prelim Exam in Agricultural Economics – May 2006
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2. Econometric Analysis:
Now, let us specify explicit functions for retail demand and marginal costs:
Let the inverse retail demand curve be described by
Pr  a0  a1Q  a2 Z  
(1)
where Pr is retail price; Q is wholesale quantity; Z is an exogenous demand shifter; ε is an
additive random error term; and a0, a1, and a2 are parameters. Retailers’ and
manufacturers’ marginal costs, MCr and MCm are given by
MC r  b0  b1Q  b2W  
MC m  c0  c1Q  c2V  
(2)
(3)
where W and V are exogenous factor prices; η and μ are random errors; and b0, b1, b2, c0,
c1, and c2 are parameters.
The BPT Equilibrium in this market may be obtained by deducting retailers’ marginal
cost from per unit retail revenue and equating this derived demand for processed beef to
the marginal cost of manufacturers’ supply. This yields equation (4), which, when
accompanied by equations for retail demand and wholesale supply, give us the following
three equations with which to determine the three unknowns: Pr, Q, and Pw, where Pw is
the wholesale price.
Pr  b1  c1 Q  b0  c0   b2W  c2V     
Pr  a0  a1Q  a2 Z  
Pw  c0  c1Q  c2V  
(4)
(5)
(6)
a. Show that the single equation ordinary least squares estimator of the parameters for
equation (6) is biased in small sample.
b. Discuss an alternative system estimator for these equations. Be sure to discuss the
reasons why a system estimator is appropriate and necessary. Show that all parameters in
the BPT model are identified in the system context.
c. Show whether or not your system estimator is unbiased in small sample and whether or
not it is consistent in large sample.
Prelim Exam in Agricultural Economics – May 2006
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d. Now consider the RPT model. In this case, perceived marginal revenue (PMRm) may
be written as follows:
PMRm  PNMRr   (a1  b1 )Q
(7)
where   0,1 measures the degree of market power that processors have in their sales
of boxed beef with 0 being price taking and 1 being fully monopolistic and PNMRr is the
perceived net marginal revenue. This additional complication gives rise to a new set of
equilibrium conditions, where equation (4) has now been replaced by (4’) and (6) has
been replaced by (6’):
Pr  a1  (1   )b1  c1 )Q  b0  c0   b2W  c2V     
(4’)
Pr  a0  a1Q  a2 Z  
(5)
(6’)
Pw  c0   (a1  b1 )  c1 Q  c2V  
Discuss how the addition of processor market power in the merchandising of wholesale
beef affects your identification strategy. What modification in the fundamental equations
of the model (marginal costs and/or retail demand) is needed to permit identification of
market power in this case? Explain intuitively why this is the case.
Prelim Exam in Agricultural Economics – May 2006
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Question 3: Macroeconomics and dynamics
Part A (30 minutes). One of the most basic questions in economics analysis is why
there are such large differences in per-capita income across countries. Robert Solow was
one of the first economists to provide a formal model to help answer this question. His
approach, first published in 1956, focuses on the accumulation of capital per worker, as
described by:
k  sy   n    k
where variables are defined as follows:
k = capital per worker, and k is its derivative with respect to time
y = output per worker
s = the rate of savings (assumed constant over time)
n = the rate of population growth (assumed constant over time)
 = the rate of capital depreciation (assumed constant over time).
In the simplest version of a Solow model, capital per worker is the only factor of

production, and the production function is Cobb-Douglas in form y  k , 0    1 .


i. To what does this simple two-equation model attribute the large differences in income
across countries?
ii. The following figure, taken from Jones (2002), illustrates a basic pattern exhibited by
cross-country data on rates of investment and real output per worker. Do these data
uphold or reject the predictions of a simple Solow model?
iii. What does the model, as upheld or rejected by these data, suggest governments can do
to help their country become richer?
Prelim Exam in Agricultural Economics – May 2006
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Part B (30 minutes). The figure shown in Part A of this question is suggestive of a
relationship between investment and GDP, but there appears to be substantial variance in
the data. One of the important factors omitted from the simple Solow model is the role of
human capital. Robert Lucas proposed a variant of the Solow model in which human
capital per person, denoted h, enters the production function as follows:
Y  K   hL 
1
.
i. How would you formally incorporate this idea of human capital formation into the
Solow model of Part A? In particular, how would you augment the fundamental
dynamics of the growth model to account for human capital?
ii. Discuss how this introduction of human capital might influence the predictions of the
model regarding economic output. Do you think the addition of human capital is
sufficient to reconcile the empirical growth rates in the figure above? If not, what
other factors might you want to consider and how would you incorporate them in the
model?
Prelim Exam in Agricultural Economics – May 2006
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