Suppose that a price-searcher monopolist had a total cost function given by: TC = 10 + Q + 0.1Q2. The demand for the price searcher's product is given by: QD = 50-10P. Calculate the monopolist's producer surplus. (Do not include a dollar sign in your response. Round to the nearest two decimals.)

The monopolist's producer surplus is $20.

Explanation:

TC = 10 + Q + 0.1Q^2

MC = 1 + 0.2Q

Q = 50 - 10P

10P = 50 - Q

P = 5 - 0.1Q

TR = PQ

= 5Q - 0.1Q^2

MR = 5 - 0.2Q

for:

MR = MC

5 - 0.2Q = 1 + 0.2Q

4 = 0.4Q

Q = 10

P = 5 - 0.1 (10) = 4

at Q = 10,

MC = 1 + 0.2*10

= 3

P. S = (4 - 3) * 10 + 1/2*10 * (3 - 1)

= 10 + 10

= $20

Therefore, The monopolist's producer surplus is $20.