Consider the following demand equations for two differentiated products produced
ID: 1250459 • Letter: C
Question
Consider the following demand equations for two differentiated products produced by independent firms.q1(p1, p2, A) = 0.6A – 2p1 + p2
q2(p1, p2, A) = -0.4A + p1 – 3p2
For simplicity assume that costs are zero for both firms. Price reaction functions for the two firms can be derived as
p1 = (10 + .6A)/4 + (1/4)p2
p2 = (10 - .4A)/6 + (1/6)p1
a) Is advertising predatory or cooperative in this example?
b) Suppose that A = 10. Solve for p1 and p2.
c) Now suppose that firm 1 increases A to 20. Solve for p1 and p2. Briefly discuss.
Explanation / Answer
a. I'm fairly confident that advertising (A) is predatory in this example because q2 and p2 are decresing in A and q1 and p1 are increasing in A, so firm one wants to set a high level of advertising and firm two benefits from a low level of advertising.
b.if A=10
p1=(10+.6*10)/4+(1/4)p2
p1=4+(1/4)p2
p2=(10-.4*10)/6+(1/6)p1
p2=1+(1/6)p1
substitute equation for p1 into p2
p2=1+(1/6)(4+(1/4)p2)
p2=1+(2/3)+(1/24)p2
(23/24)p2=(5/3)
p2=(40/23)
then just substitute into p1=4+(1/4)p2 to get p1
c.now A=20
p1=(10+.6*20)/4+(1/4)p2
p1=(11/2)+(1/4)p2
p2=(10-.4*20)/6+(1/6)p1
p2=(1/3)+(1/6)p1
substiute p1 into p2 again
p2=(1/3)+(1/6)((11/2)+(1/4)p2)
p2=(1/3)+(11/12)+(1/24)p2
p2=(5/4)+(1/24)p2
(23/24)p2=(5/4)
p2=(30/23)
then just substitue into p1=(11/2)+(1/4)p2 to get p1
firm one sets a higher price when A increases, and firm two sets a lower price when A increases