8. Portland Fluid Control, Inc., (PFC) is a major supplier of reverse osmosis an

Question

8. Portland Fluid Control, Inc., (PFC) is a major supplier of reverse osmosis and ultrafiltration 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. Relevant cost and revenue relations for this product are as follows: TR = $300Q-$0.001 Q2 MR = OTR/OQ = $300-$0.0020 TC $9,000,000 + $200 + $0·0004Q2 MC = OTC/OQ = $20 + $0.00080 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. i.Compute PFC's optimal monopoly price/output combination ii. Compute monopoly profits at this profit-maximizing activity leve.

Explanation / Answer

1.

For a monopoly firm, profit is maximized when marginal revenue (MR) equals marginal cost (MC).

For profit maximizing output,

MR = MC

300-.002Q = 20+.0008Q

280 = (.002+.008)*Q

Q = 280/.0028

Q = 100000

TR = 300Q - .001*Q^2 ------------- (1)

Dividing equation 1 by Q on both sides, will give price (P).

TR/Q = P = 300 - .001Q

For Q = 100000

P = 300 - .001*100000

P = 300 - 100 = $200

So, profit maximizing output is 100000 and price is $200.

2.

Profit = Total revenue – total cost

Profit = P*Q – (9000000 + 20*Q + .0004*Q^2)

Profit = 200*100000 - (9000000 + 20*100000 + .0004*100000^2)

Profit = $5000000

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