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 Boors operates with out-of-date technology and has constant cost of $2 per unit , whereas Cudweiser has constant cost of $1 per unit. How many “units” of beer will Cudweiser produce in the Nash equilibrium?

Answer 1

Boors’ marginal revenue function is MR (B) = 5−.001(2QB+ QC) and

symmetrically for Cudweiser it is MR (C) = 5 −.001(QB+ 2QC)

Use MR = MC for both firms as they set their quantities simultaneously

5−.001(2QB+ QC) = 2 and 5 −.001(QB+ 2QC) = 1

3 - 0.001QC = 0.002QB and 4 - 0.001QB = 0.002QC

QB = 1500 - 0.5QC and QC = 2000 - 0.5QB

This gives QC = 2000 - 0.5*(1500 - 0.5QC)

QC = 1350 + 0.25QC

QC = 1666.67 and QB = 1500 - 0.5*1666.67 = 666.67

Hence  Cudweiser produce 1666.67 units in the Nash equilibrium.