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Monoply Profit

Pavati Fluid Controls, Inc, (PDC) is a major supplier of reverse osmosis and ultra-filtration equipment, which helps industrial and commercial customers achieve improved production processes and a cleaner work environment. The company has recently introduced a new line of ceramic filters that enjoy patent protection. Are relevant cost and revenue relations for this product are as follows:

TR = $300Q - $0.001Q2
MR = ΔTR/ΔQ = $300-$0.002Q
TC = $9,000,000 + $20Q + $0.0004Q2
MC = ΔTC/ΔQ = $20 + $0.0008Q

Where TR is total revenue, Q is output , MR is marginal revenue, TC is total cost, including a risk-adjusted normal rate of return on investment, and MC is marginal cost.

A. As a monopoly, calculate PFC's optimal price/output combination.
B. Calculate monopoly profits and the optimal profit margin at this profit-maximizing activity level.

Solution Preview

Answer A:
Optimal price/output combination is where MR = MC. So
300 - .002Q = 20 + .0008Q
=> 280 = .0028Q
=> Q = 100,000
Because TR = PXQ
P = ...

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