Monopoly Price Regulation: Optimal Price/Output Decision Making

Monopoly regulation imposes a price ceiling at P2 just sufficient to provide a fair return (area PnAECn) on investment. Under regulation, price falls from P1 to P2 and output expands from Q1 to Q2.

Price and cost

Price and cost

TC = $3,750,000 + $70Q + 0.00002Q2 MC = ATC/AQ = $70 + $0.00004Q

where cost is expressed in dollars.

To find the profit-maximizing level of output, demand and marginal revenue curves for annual service must be derived. This will give all revenue and cost relations a common annual basis. The demand curve for annual service is 12 times monthly demand:

Total and marginal revenue curves for this annual demand curve are

TR = $270Q - $0.00048Q2 MR = ATR/AQ = $270 - $0.00096Q

The profit-maximizing level of output is found by setting MC = MR (where Mn = 0) and solving for Q:

MC = MR $70 + $0.00004Q = $270 - $0.00096Q $0.001 Q = $200 Q = 200,000

The monthly service price is

This price/output combination generates annual total profits of n = $270Q - $0.00048Q2 - $3,750,000 - $70Q - $0.00002Q2 = -$0.0005Q2 + $200Q - $3,750,000 = -$0.0005(200,0002) + $200(200,000) - $3,750,000 = $16,250,000

If the company has $125 million invested in plant and equipment, the annual rate of return on investment is v u t ^ 4. $16,250,000 ni_ 1Q0, Return on Investment = = 0.13, or 13%

$125,000,000

Now assume that the State Public Utility Commission decides that a 12 percent rate of return is fair given the level of risk taken and conditions in the financial markets. With a 12 percent rate of return on total assets, Malibu Beach would earn business profits of n = Allowed Return X Total Assets = 0.12 X $125,000,000 = $15,000,000

To determine the level of output that would generate this level of total profits, total profit must be set equal to $15 million:

n = TR - TC $15,000,000 = -$0.0005Q2 + $200Q - $3,750,000

This implies that

which is a function of the form aQ2 + bQ - c = 0. Solving for the roots of this equation provides the target output level. We use the quadratic equation as follows:

_ -200 ± V 2002 - 4(-0.0005)(18,750,000) 2(-0.0005)

= 150,000 or 250,000

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