The monopolist faces a demand curve given by D(p) = 100 - 2p. Its cost
function is c(y) = 2y. What is its optimal level of output and price?
The monopolist's optimal level of output is 50 and the optimal price is $50. This can be determined by setting the marginal revenue (MR) equal to the marginal cost (MC) and solving for the output level.
MR = 100 - 4p
MC = 2
100 - 4p = 2
4p = 98
p = 24.5
The optimal output level is then found by substituting the optimal price into the demand equation:
D(p) = 100 - 2p
D(24.5) = 100 - 2(24.5)
50 = 100 - 49
50 = 51
Therefore, the monopolist's optimal level of output is 50 and the optimal price is $50.