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Monopoly regulation

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)

Solution Preview

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, ...

Solution Summary

The solution answers the question(s) below.

$2.19