# Monopoly regulation

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Cable co: Demand curve for monthly service:

P=$37.50 -$0.0005Q.This implies annual demand and marginal revenue curves of:

P=$450 -$0.006Q

MR=$450-$0.012Q

where P is service in dollars and Q is no. of customers served.Total and marginal costs per year(before investment return) are described by the function:

TC=$4,275,000+$75Q+$0.0015Q^(squared)

MC=$75+$0.003Q

The co.has assets of $1.5 million and the utility commission has authorized a 15% return on investment.

A. Calculate profit-max price(monthly and annually), output, and rate of return levels.

B. What monthly price should commission grant to limit cable co. to a 15% rate of return? (please explain all steps used in calculation)

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A. calculate profit-max price(monthly and annually), output, and rate of return levels

To max profit, the first order condition of the firm is:

MR=MC, or

450-0.012Q=75+0.003Q, or

0.015 Q = 375

solve for Q= 25,000

then from the demand curve, ...

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