Question

The demand curve facing a firm operating under a monopoly is given by,
P = 85 - 2.5Q; The cost function is given by
TC = 20 + 25Q + 2.5Q²
What is the maximum profit?
What is the profit maximizing price elasticity of demand?
What is the revenue maximizing price elasticity of demand?

Answer 1

$TR=P\times Q=(85-2.5Q)\times Q=85Q-2.5Q^2$

MR=TR'=85-5Q

MC=TC'=25+5Q

85-5Q=25+5Q

q=6

$P-85-2.5\times Q=85-15=70$

Profit=TR-TC

$Profit max=6\times70-(20+25\times Q+2.5Q^2)=20-20-150-90=200$

The condition for maximizing profit is the equality: MR = MC.

Marginal revenue maximizes price elasticity of demand.

When MR> 0, then TP increases (total revenue), MR <0, then TR decreases. Total revenue peaks when MR = 0. When MR> 0, demand is elastic, when MR <0, demand is inelastic. Demand has unit elasticity when MR = 0, and the total

income at this point reaches a maximum