Question

Can you help me with the following Q.

a monopolist faces a demand curve p= a-Q.

The monopolist incurs average cost (AC) which equals to marginal cost (MC). Lets assume that AC=MC=c. if the monopolist's marginal revenue is given by the equation MR=a-2Q then:

a/ calculate the monopolist's TR and TC.
b/ if monopolist isnt allowed to discriminate the price, what will be its profit maximization output level? what will be the total profit and price at the profit maximization output level?

Answer 1

demand curve p= a-Q.
AC = MC = c
MR=a-2Q
a) calculate the monopolist's TR and TC.
MR = TR', so TR = 0.5a^2 - Q^2
MC = TC', so TC = 0.5c^2
b) if monopolist isn't allowed to discriminate the price, what will be its
profit maximization output level?
The monopolist needs for profit maximization the output level to be in the
point, where MR = MC
So, a - 2Q = c.
Q = (a - c)/2
what will be the total profit and price at the profit maximization output
level?
The price will be p = a - Q = a - a/2 +c/2 = (a + c)/2
The profit will be TR - TC = P*Q - TC = (a + c)*(a - c)/4 - 0.5c^2 = 0.25a^2 -
0.25c^2 - 0.5c^2 = 0.25a^2 - 0.75c^2