Question

Consider a firm facing a downward-sloping demand curve for its product given by: ?(?)=10−?
where 0≤?≤10 denotes the price of the firm’s output. The firm produces its output under a constant marginal cost of ?=1.

a) Write down the firm’s profit-maximization problem assuming the firm’s choice variable is quantity. Find the firm’s profit-maximizing price and quantity.
b) Based on your answers to part (a), find the firm’s equilibrium profits. sketch the firm’s demand, marginal revenue, and marginal cost functions.

Answer 1

A) Profit maximizing probably:

Max profit={p-1)(10-p)

Profit maximizing quantity is where ,

MR=MC

Q=10-p

P=10-q

MR=10-2q

MR= MC

10-2q=1

Q*=9/2=4.5

P*=10-4.5=5.5

B) Equilibrium profit=(p-1)*(10-p)

Profit=(5.5-1)*(10-5.5)=4.5*4.5=20.25