Department of Agricultural Economics

Department Core Prelim Exam

6 June 2003

Instructions:

This exam consists of three questions. Each question is of equal value. You should answer all three questions. Please start each question on a new sheet of paper and be sure to identify yourself by the ID number assigned to you. Do not write your name on any of the pages.

You have four hours to complete the exam. Don’t panic. Just think. Good luck.

Question 1

Agricultural economists recognize the exchange rate as one of the most important variables influencing prices and income in an agricultural sector. But some argue that the standard linkage between exchange rates and prices fails to hold as typically specified, and exchange rate pass through is incomplete, as a consequence.

  1. Define exchange rate pass through. How does exchange rate pass through differ from two very closely related concepts – the law of one price andpurchasing power parity?
  2. Under what circumstances might exchange rate pass through be incomplete? Why?

In China, soybeans are imported by a state trader at a zero tariff, who resells the soybeans on the domestic market. To measure the extent of exchange rate pass through for soybeans in China, we can estimate the following linear regression model:

where PSC is the nominal soybean price in China (Yuan per metric ton), EC is the Chinese exchange rate (Yuan/$), PSUS is the nominal U.S. soybean price ($ per metric ton), CPICUS is the ratio of the Chinese consumer price index to the U.S. CPI, andεt is an error term. The observed data are monthly prices and exchange rates from January, 1990, to December, 2002, and all variables in the equations are converted to natural logarithms.

  1. Assume the linear regression model is correctly specified and suppose you use the ordinary least squares (OLS) estimator to estimate the parameters. Briefly discuss the sampling properties of the OLS estimator and state any other required assumptions.

Using your model you derive the fitted linear regression model:

where the estimated standard errors appear in parentheses below the estimated parameters.

  1. Use these estimates and the attached table of critical values to explicitly test the null hypothesis that exchange rate pass through is complete in the short run (one month).
  2. According to these results would you agree that exchange rate pass through is complete
    in the long run? Why? According to these results, how long is the long run?
  3. How would you test the null hypothesis that the fitted model is consistent with the law of one price? What would you expect to find?
  4. Based on these limited estimation results, does it appear that purchasing power parity holds in the short run? Why or why not?

Critical Values for Question 1

Upper Tail Probability  / Standard Normal
Quantile z such that
/ Student T Quantile t
such that
(degrees of freedom
greater than 150)
0.100 / 1.28 / 1.29
0.050 / 1.64 / 1.66
0.025 / 1.96 / 1.98
0.010 / 2.33 / 2.35
0.005 / 2.58 / 2.61

Question 2

Mr. Jones owns a small lake containing fish that can be sold for human consumption. He has approached you to help him develop an optimal harvesting plan for these fish, which are a renewable resource. The fish sell for an exogenously determined price of p per kg. The production of fish (in kg) can best be characterized by a production function where x denotes the stock of fish, k denotes Jones’ capital stock (fishing equipment), v is the amount of labor employed in fishing (at a wage of w per unit of labor), and I is the investment rate for new capital. Note that capital depreciates at the rate of per year (0 ≤ ≤ 1) and can be purchased at a cost of q per unit of capital. The growth rate of fish biomass is . Jones’ current capital stock consists of k0 units of fishing gear; the current biomass of fish in his lake has been estimated to be x0. Capital follows an equation of motion defined as.

a. Mr. Jones would like you to formulate mathematically and interpret in words his dynamic optimization problem assuming a discounted infinite planning horizon. Be sure to define the objective function and all relevant equations and constraints.

b. Characterize Mr. Jones’ problem in an optimal control framework by defining the Hamiltonian and deriving all necessary conditions for optimality. Provide an accurate economic interpretation in words for these conditions.

A dual (indirect) function for this problem can be specified as where δ is a discount rate. According to the dynamic envelope theorem (Caputo, JEDC 1990) some of the more economically meaningful comparative dynamics of the problem can be stated as:

i) iv)

ii) v) , and
iii) vi)

where y*, v*, and I* are optimal pathsfor output, labor use, and investment conditional on exogenous variables. Propose an econometric model consistent with Mr. Jones’ comparative dynamics. In particular, answer the following questions:

c.What testable hypotheses are implied by the model?

d.What data and methods would you use to test these predictions?

Question 3

Background Information

In his classic 1975 article on this topic, Bruce Gardner introduced the notion of a perfectly competitive food industry that purchases agricultural products (a) and marketing inputs (b), combining them using a constant elasticity of substitution, constant returns to scale production function in order to produce retail food products (x):

where

x =retail food supplies,

a = agricultural products purchase by the food manufacturer,

b =non-agricultural marketing inputs,

α, δa, δb =constant parameters,

σ = 1/(1+ρ) =constant elasticity of substitution between a and b in the production of retail food, and

Px, Pa, Pb =the prices of retail food, agricultural inputs, and non-agricultural inputs.

Minimizing the cost of producing retail food using this technology, we obtain the optimal demands for the marketing inputs:

where c denotes the unit cost which equals Px under perfect competition with constant returns to scale.

Gardner works with the differential form of these demand equations (where ^ denotes proportional change):

where , with Sa and Sb denoting the cost shares for agricultural and nonagricultural inputs. He expresses demand in log-linear form: , where ηp is the own-price elasticity of retail demand, is the proportional change in income, and ηy is the elasticity of demand with respect to income.

Questions

a.Using this background information, lay out a partial equilibrium model of the food sector in which supply is predetermined, and the supply of non-agricultural marketing inputs is perfectly elastic.

b.Solve this model for the price of the agricultural input Paas a function of an exogenous shock to income. Interpret the resulting expression. In particular, discuss the role of the elasticity of substitution and the cost shares in determining the link between the retail demand shock and farm prices.

c.Now consider the impact of introducing imperfect competition in the food marketing sector – specifically consider market power in the retail market. Assume that there are n identical firms in this industry so that:

.

i.Use a general representation of the inverse demand function at the retail level to formulate the individual food marketing firm’s profit maximization problem and determine the first-order condition that determines the equilibrium output level, xi, assuming Cournot behavior (i.e., individual firms assume that other firms do not respond to their own output changes).

ii.Now assume the inverse demand schedule is linear. Graph the Cournot oligopoly outcome in this market and compare it to the case of perfect competition. Is food marketing output higher or lower? Explain your conclusion. Also compare this to the case where there is a single (monopolistic) food marketing firm.

iii.Finally, return to the problem of a retail demand shift associated with an increase in income. Discuss how the farm price will be affected by such a shift in the presence of imperfect competition versus perfectly competitive food marketing system analyzed previously.

.