Question

Suppose there is a monopoly in a market with the cost function: TC = 2+Q2. The demand function in this market is Q = 12 - 2P

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Answer #1

Answer

1)

Monopoly produces at MR=MC

to find MR converting the demand function

Q=12-2P

2P=12-Q

P=6-0.5Q

MR=6-Q

MC=cjhnage in total cost =diffrentiation of the TC

MC=dTC/dQ=2Q

the profit is maximum at MC=MR

2Q=6-Q

3Q=6

Q=2 units

the firm produces 2 units to maximize

2)

P=6-0.5*2=5

the firm charge price $5

3)

Profit=TR-TC

TR=P*Q

=5*2=10

TC=2+2^2=6

Profit=10-6=4

the profit is $4

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