Question

This question will deal with demand, supply, equilibrium and comparative statics in a specific market: the market for pork. We will use specific equations for Demand and Supply of pork which come from an academic paper: “Production Subsidy and Countervailing Duties in Vertically Related Markets: The Hog-Pork Case Between Canada and the United States” written by Giancarlo Moschini and Karl D. Meilke which appeared in American Journal of Agricultural Economics, Vol. 74, No. 4 (Nov., 1992), pp.951-961. The authors estimated demand and supply equations in the market for pork.

We will use parameters inspired by their estimates.

D (P, P_b, P_c, I) =171-20P+20P_b+3P_c+2I

Where

P= price of pork

P_b= price of beef

P_c= price of chicken

I= income

P_h= price of hogs an input in the production of pork

(a) Find the partial derivative: ∂D (P, P_b, P_c, I) /  ∂P_b

(b)In words, explain what your answer in part (a) means.

(c) Using the demand equation above, how are beef and pork related to each other

(substitutes or complements)? Clearly explain how you reached your answer.

(d) With your answer in (c) in mind, what do you expect to happen to equilibrium price (p*) and equilibrium quantity (Q*) if the price of beef increases, all else

remaining the same. (Do not want specific number answers, just generally do you expect the equilibrium variables to increase or decrease). Briefly explain

how you reached your answer.

e) Using these Demand and Supply equations, solve for ∂p*/∂P_b (the effect of a change in the price of beef on equilibrium price).

(f)Using these Demand and Supply equations, solve for ∂Q*/∂P_b (the effect of a change in

the price of beef on equilibrium quantity).

(g) Generally (no specific numbers) what do you expect to happen to equilibrium price (p*) and equilibrium quantity (Q*) if the price of hogs were to increase?

Explain how you reached your answer.

(h)Solve for ∂p*/∂P_h (the effect of a change in the price of hogs on equilibrium price).

Answer 1

D (P, P_b, P_c, I) = 171 - 20P + 20P_b + 3P_c + 2I

(a)

D(P, P_b, P_c, I)/P_b = 20

(b)

It means that as price of beef increases (decreases) by 1 unit, demand for pork increases (decreases) by 20 units.

(c)

Since coefficient of price of beef is positive, it means that increase (decrease) in price of beef will increase (decrease) the demand for pork, so cross-price elasticity is positive, signifying that they are substitutes.

(d)

If price of beef increases, demand for pork will increase. Its demand curve will shift rightward, which will increase both price and quantity of pork, ceteris paribus.

NOTE: As per Chegg Answering Policy, 1st 4 parts have been answered.