Question

Suppose there are two firms, Boors and Cudweiser, each selling identical-tasting nonalcoholic beer. Consumers of this beer have no brand loyalty so market demand can be expressed as P = 5 − .001(Qb + Qc). Boors’ marginal revenue function can be written MR = 5 − .001(2Qb + Qc) and symmetrically for Cudweiser. Boors operates with out-of-date technology and has constant cost of $2 per unit (MC = AC = 2), whereas Cudweiser has constant cost of $1 per unit Consider the same market for nonalcoholic beer as in the previous question. Cudweiser’s response function is a.

QB = 2,000 − .5QC

b. QB = 1,500 − .5QC

c. QC = 2,000 − .5QB

d. QC = 1,500 − .5QB

Answer 1

c. QC = 2,000 − .5QB

Explanation:
Cudweiser's marginal revenue function is symmetric to Boors. So, Cudweiser's marginal revenue function is given by:
MR = 5 − .001(2Qc + Qb)

Cudweiser has constant cost of $1 per unit. So, MC = $1

Cudweiser maximizes profit according to the rule MR = MC. So,
5 − .001(2Qc + Qb) = 1
So, 5 - 1 = .001(2Qc + Qb)
So, .001(2Qc + Qb) = 4
So, 2Qc + Qb = 4/.001 = 4000
So, 2Qc = 4000 - Qb
So, Qc = (4000/2) - (Qb/2)
So, Qc = 2,000 - 0.5Qb
This is  Cudweiser’s response function.