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.

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