Question

Assume that a firm in monopolistic competition facing the following demand and cost function P= 100 -30+4a1/2 and TC=4q+10q+a where P=price, Q=Quantity and A= Advertisement 

A find the equilibrium of quantity and Advertisement  

Answer 1

The equilibrium of quantity occurs at MR = MC.

$MR = TR'(q) = 100 - 6q + 4a^{0.5},$

MC = TC'(q) = 8q + 10,

$100 - 6q + 4a^{0.5} = 8q + 10,$

$q = (45 + 2a^{0.5})/7.$