Question

suppose that the demand for a monopolist's product is estimated to be q=50-P. This monopolist's total cost function is C=20Q and the marginal cost function is MC=20. Under the first price degree price discrimination the number of total units sold (Q), profit and consumer surplus are

Solve for Q, profit and consumer surplus

Answer 1

Answer
The inverse demand function
q=50-P
P=50-q
the first price degree price discrimination monopolist produces at MC=P
equating both
50-q=20
q=30
the monopolist produces 30 units
The monopolist's profit is equal to consumer surplus under perfect competition.
profit=0.5*(y-intercept of demand curve-MC)*quantity
=0.5*(50-20)*30
=450
The consumer surplus under perfect competition is zero because the price charged to each consumer is equal to its willingness to pay.