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).

(b) Simulate the equilibrium price, quantity, total industry net revenue if the industry spent zero on promotion, i.e., PROM=0. Compute the average net benefit-cost ratio for the potato industry for potato promotion.

(c) Now assume the new demand curve for tomatoes is: Qd = 15 - P + 0.5PROM Based on the new demand function, what is the average net BCR due to potato generic Promotion?

Answer 1

Potato growers have a mandatory demand expansion program where all growers pay a certain amount to fund a promotion program for tomatoes.

Qd = 15 - P + 0.1PROM

Qs = 5 + 2.5P TC = 0.2Qs

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

Ans.

Qd = 15 - P + 0.1PROM

Hence, QD =15-P +0.1(2.5)

=15 -P +0.25 = 5 + 2.5P (Equating Qs=Qd)

: 15.25-5 = 2.5P + P

: 7.25 =3.5 P

P = 2.07

Qs = 5 + 2.5P TC = 0.2Qs

Qs= 5+2.5(2.07)

= 5 + 5.175 = 10.175

TC= 0.2 (10.175) = 2.035

TR = Qs*P = 2.07*10.175 = 21.07

Net Revenue = 21.07 - 2.035 = 19.04

(b) Simulate the equilibrium price, quantity, total industry net revenue if the industry spent zero on promotion, i.e., PROM=0. Compute the average net benefit-cost ratio for the potato industry for potato promotion.

Qd = 15 - P + 0.1PROM

Qd = 15 - P + 0.1 (0)

Qd = 15 - P

Qs = 5 + 2.5P TC = 0.2Qs

Hence, 15-P = 5+2.5P (Equating Qs=Qd)

10=3.5P

P=2.86

Qs = 5 + 2.5P = 5+2.5(2.86) = 12.15

TR=Qs*P

TR = 2.86 * 12.15 = 34.75

TC = 0.2 (12.15) = 2.43

Benefit : Cost = 34.75 : 2.43 = 14.3

(c) Now assume the new demand curve for tomatoes is: Qd = 15 - P + 0.5PROM Based on the new demand function, what is the average net BCR due to potato generic Promotion?

Qd = 15 - P + 0.5 (2.5)

Qd= 15-P+1.25

Qs = 5 + 2.5P TC = 0.2Qs

Equating Qs=Qd,

15 - P +1.25 = 5 + 2.5 P

16.25 -5 = 2.5P +P

11.25 = 3.5 P

P = 3.214

Hence Qs = 5 + 2.5 (3.214) = 13.035

TC = 2.61 (0.2*Qs)

TR = 41.9 (P*Qs)

Benefit : Cost = 41.9: 2.61 = 16.07