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Firm Perfcomp is acquired by a bigger firm called MonopoCorp. Overtime, MonopoCo

ID: 1199379 • Letter: F

Question

Firm Perfcomp is acquired by a bigger firm called MonopoCorp. Overtime, MonopoCorp successfully acquires all other widget-producing firms and becomes the monopolist in the market. MonopoCorp's total cost function is TC(Q) = Fixed Costs + Variable Costs, Thus TC(Q) = 600 + 2Q The inverse market demand function for widgets is P(Q) = 10 - 0.01Q Thus TR(Q) = P(Q) * Q = 10 - 0.01Q^2 Determine the MonopoCorp's profit function. Determine the level of output at which Firm MonopoCorp should produce in order to maximize profits. Confirm that this quantity represents maximum profits for the firm by using the second-order condition. Determine the maximum profits Finn MonopoCorp can achieve.

Explanation / Answer

a) TR=10Q -0.01Q2 (given wrong in question)

total profit= total revenue- total cost

                  =10Q -0.01Q2 - (600+2Q)

                TP =8Q-0.01Q2 - 600

b)

maximize profit, first order derivative should be = 0

dTP/dQ = 8-0.02Q=0

                   Q= 8/0.02=400

at Q=400, profit will be maximum

c) 2 nd order condition

d2TP/dQ2 = -0.02<0 so maximum

d) maximum profit by inserting Q=400 in profit function

TP =8Q-0.01Q2 - 600

     = 8*(400) -0.01*(400)2 -600 = 3200-1600-600 = 1000