Assume the firms cost function is: C(Q) = 100 + 10Q + Q^2 Determine whether this

Question

Assume the firms cost function is: C(Q) = 100 + 10Q + Q^2 Determine whether this industry is a natural monopoly when the demand function is: (1) D(P) = 100

Explanation / Answer

Hi, If you like my answer rate me first...that way only I can earn points. Thanks 1) demand Q = 100 - 3P P = (100 -Q)/3 TR = P*Q = Q*(100-Q)/3 MR = 100/3 - 2Q/3 MC = 10 + 2Q MR = MC => Q = 8.75 TC = 264.0625 TR = 266.15 Since there is supernormal profit(TR>TC), so this is a natural monopoly 2) Similiarly TR = Q*(90-Q)/3 MR = 30 - 2Q/3 MC = 10 + 2Q MR = MC => Q =15 TR = 375 TC = 355 Since there is supernormal profit(TR>TC), so this is a natural monopoly 3) Similarly TR = Q*(100-Q)/2 MR = 50 - Q MC = 10 + 2Q MR = MC => Q =13.33 TR = 577.78 TC = 411.11 Since there is supernormal profit(TR>TC), so this is a natural monopoly

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