Question

1. Potato growers have a mandatory demand expansion program where all growers pay a certain amount to fund a promotion program for tomatoes. You have estimated the following market supply and demand functions for potatoes, which include a demand shifter for generic potato promotion:

Qd = 15 - P + 0.1PROM

Qs = 5 + 2.5P TC = 0.2Qs

where: Qd = quantity demanded of potatoes, measured in million pounds, P = price of potatoes measured in $ per pound, PROM = total generic promotion in million dollars, Qs= quantity supplied, measured in million pounds, TC = total production costs, but does not include the promotion costs.

(a) Assume that in 2019, PROM = 2.5. Calculate the equilibrium price, quantity, total industry net revenue (total revenue minus TC).

Answer 1

(a) Qd = 15 - P + 0.1PROM = 15 - P + 0.1*(2.5) = 15 - P + 0.25 = 15.25 - P

At equilibrium, Qd = Qs.
So, 15.25 - P = 5 + 2.5P
So, 2.5P + P = 15.25 - 5
So, 3.5P = 10.25
So, P = 10.25/3.5
So, P = 2.93

Q = 15.25 - P = 15.25 - 2.93 = 12.32
So, Q = 12.32

Total Revenue, TR = P*Q = (2.93)*(12.32) = 36.0976
TC = 0.2Q = 0.2*(12.32) = 2.464

Net revenue = TR - TC = 36.0976 - 2.464 = 33.63
Thus, net revenue = 33.63