January 2005

Core Qualifying Exam in Agricultural Economics

PurdueUniversity

Directions:

  • The use of black or blue ink is advisable so that all copies of the exam will be readable by graders.
  • 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: Microeconomics and Econometrics

Contemplate the following functional approximation of the expenditure function e(p,u) associated with constrained expenditure minimization on the part of consumers where p is a vector of prices for goods consumed, u is utility, and ln is the natural logarithm operator. Note: This is not an Almost Ideal Demand model.

a)Defining M as the total expenditure on goods qassociated with the prices p, derive the approximate indirect utility function implied by the expenditure function approximation above.

b)Derive the uncompensated demand system {i.e., q = q(p,M)} consistent with this approximation that is integrable back to the parent utility or expenditure function. Clearly identify and define any theoretical results that you invoke and provide verbal interpretations of your mathematical exercises and the outcomes.

c)Assuming that the prices are exogenous and non-stochastic, what are the properties of the least squares estimator for the model parameters?

d)Assuming that the prices are endogenous, stochastic, and likely to be correlated with the demand equation disturbances, what are the properties of the least squares estimator for the model parameters?

e)What aspects of an economic problem or product demand might lead you to choose an inverse demand model (prices on the left hand side and quantities on the right) versus the more common quantity dependent approach specified above? Be specific and thoughtful. Examples may be helpful in this part of the question.

Question 2: Macroeconomics and Dynamics

Anticipating the seasonal outbreak of a common agricultural pest, the rural agricultural extension agency of a small, low-income country aims to increase its stock of a new pesticide from the current level of V0 = 0 to a target level VT = 5000 within 10 months. The old pesticide is extremely bulky to store and must be protected from heat during storage. It costs an amount s(per unit of time) to store. Unlike the old pesticide, the new pesticide can be stored in concentrated form, and therefore represents a savings in storage costs in each period of $0.50/unit. Unfortunately, the new pesticide must be imported from abroad. Production levels for the new pesticide remain low, and global demand greatly exceeds global supply. As a result, the producer has set an upward sloping cost function for procuring the new pesticide. This is:


where V´ is the number of units of pesticide delivered at time t. In other words, the faster the agency wishes to accumulate the pesticide, the greater the cost.

a. Find the optimal procurement and storage path for the extension agency if it wishes to minimize the total cost of stocking the new pesticide over time, while adjusting the size of the pesticide stock to its optimal level. (Hint: set the problem up as a Calculus of Variations problem with the cost function as the integrand. Incorporate the old storage cost s and the savings in storage costs associated with the new pesticide in this integrand. When solving, use the fact that the Euler equation can be written Fy = dFy´/dt).

b. Interpret, in words, the economic logic behind your solution. In particular, explain the impact of s, the storage cost for the old pesticide, in the problem. (Hint: there are two relevant cases).

c. What should the agency do if the supplier offers a simple flat rate of $0.10 per unit for the new pesticide? Why?

d. One factor not considered above is potential uncertainty regarding the cost of importing the pesticide. Typically, a currency board has two options: stabilize the domestic currency or float it. Discuss how these two alternatives would affect prices for the agency importing the pesticide (and, by extension, the farmers who use the pesticides). Clearly state the advantages and disadvantages of each approach.

e. Assume the monetary authority decides to float the exchange rate. Now the cost of procuring the pesticide is uncertain because of exchange rate fluctuations. How might you modify your approach in (a-c) to account for this uncertainty? (Note that there is no correct answer to this part of the question and you need not solve the stochastic problem. You may assume anything you wish in developing your answer).

Question 3: Markets - Policy and Math Programming

Household models and separability between production and consumption

Policy-makers often complain that farmers, especially low-income farmers, are sluggish or even perverse in their response to changing incentives, responding more slowly and sometimes in the opposite direction than would a profit-maximizing farmer. Such behavior is often attributed to farmers’ traditionalism or aversion to change. More sophisticated (i.e. Ph.D.-level) economists typically start with a different explanation, leading to different policy implications. In particular, economics starts from the assumption that farmers know what’s good for them, and make optimal choices subject to the constraints they face. This question asks you to pursue the economists’ approach.

a. A model of a self-sufficient farm household

Start by writing down the optimization problem that characterizes the choices of an entirely self-sufficient farm household. For simplicity, use a single aggregate agricultural product (indexed a) that the household both produces (qa) and consumes (ca), and a fixed endowment (E) of a limiting factor (indexed l) that the household both uses in production as labor (l) and consumes as leisure (cl). Solve this problem for the first-order conditions that characterize the household’s decision rule, and then illustrate that solution graphically. In your figure, please put the limiting factor on the horizontal axis and the agricultural product on the vertical axis, and label the elements of the figure carefully.

b. A model of a market-oriented farm household

Now imagine that this same household gains access to a large market, where it can sell its agricultural product and its labor, as well as buy a productive input (x) and a manufactured consumption good (cm), neither of which it can produce at home on the farm. For now, assume that each of these four can be bought and sold at fixed prices, denoted pa , w , pmand px respectively. (By convention, the price of the limiting factor is denoted asw, for wages.) Write the household’s new decision rule as a single maximization problem, solve for its first-order conditions, and illustrate the solution graphically using a figure similar to that of part (1), again labeling all elements carefully.

c. Separability between production and consumption

Using plain English but referring to the equations and figures above, please explain in what sense the market-oriented household’s decisions are “separable”, while the self-sufficient household’s decisions are not.

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d. Derivation of comparative-static response to price changes

The market-oriented farm household’s choices can be described by “reduced-form” equations for agricultural production (qa) as a function of market prices (pa, w, pmand px), and for agricultural consumption (ca) as a function of those same market prices. Differentiating each of those equations with respect to price reveals how an optimizing household would respond to price changes. Please derive the resulting expression for changes in the household’s net agricultural “marketed surplus” (qa - ca) as a function of the price of the agricultural product (pa), applying the Slutsky decomposition and Hotelling’s lemma to express that response in terms of three components: a production effect, a pure substitution effect in consumption, and an income effect on consumption.

e. Predicting farm households’ price response

To interpret your results from question (d), applying some standard, uncontroversial assumptions about production technology and consumption preferences, please:

  1. indicate the direction of each of the three effects of price on marketed surplus,
  2. indicate what you know about the direction the net effect of price on marketed surplus, and then
  3. explain in plain English why a lower-income farm household (that is, a household with less productive resources relative to its consumption needs) would have a smaller and perhaps even opposite market response to price change than a more resource-rich household.

Prelim Exam in Agricultural Economics – January 2005page 1 of 4