Help with problem regarding profit maximizing price/output combination and economic profits?

Question

During recent years, MBU, Inc. has enjoyed substantial economic profits derived from patents covering a wide range of inventions and innovations. A recent software product, QuickerBetter has proven especially profitable. Market demand and marginal revenues for this software product are:

P = $5,500 - $0.05*Q

MR = $5,500 - $0.10*Q

Where P is the product price, its quantity sold is Q and MR is the marginal revenue of the product. Fixed costs are zero since the research and development expenses have been fully amortized in previous periods. Average variable costs are constant at $4,500 per unit.

a. Calculate the profit maximizing price/output combination and economic profits if MBU enjoys an effective monopoly on QuickerBetter due to patent protection.

b. Calculate the price/output combination and the total economic profits that would result if competitors offer similar software that makes the QuickerBetter market competitive.

Answer 1

a) in a monopoly, marginal cost equals marginal revenue

marginal cost is 4500

4500=5500-.10Q

1000=.10Q

Q=10000

P=$5000

b)in a competitive market, P=MC

P=$4500

4500=5500-.05Q

1000=.05Q

Q=20000

Answer 2

a)

AVC=4500

AVC=TC/Q

TC=AVC*Q

TC=4500*Q

Profit maximization condition MR=MC

MC=(TC)'=(4500*Q)'=4500

MR=MC

5500-0.1*Q=4500

0.1Q=5500-4500=1000

Q=1000/0.1=10'000

P=5500-0.05*Q= 5500-0.05* 10000=5500-500=5'000

Profit=TR-TC

TR=P*Q=10'000* 5'000=50'000'000

TC=4500*Q=4500*10'000=45'000'000

Profit=50'000'000 - 45'000'000=$+5'000'000

Answer: for monopoly Profit=$+5'000'000 Q=10'000 P=5'000

b)

For perfect competition profit=0

Profit=TR-TC

TR-TC=0

TR=TC

P*Q=4500*Q

Q*(5500-0.05Q)=4500*Q

5500-0.05*Q=4500

0.05*Q=5500-4500=1000

Q=1000/0.05=20'000

P=5500-0.05*20'000=5500-1000=$4'500

Profit=0

Answer: for perfect competition Profit=0 Q=20'000 P=4'500