San José State University
Department of Economics

applet-magic.com
Thayer Watkins
Silicon Valley
USA

The Pricing Decision by a Monopoly
and the Effects of Subsidization and
Other Measures to Reduce
Consumer Sensitivity to Price

Monopoly pricing is standard fare in microeconomic analysis, but that analysis takes output as the operative variable rather than price. The use of either price or output leads to the same result but using price as the operative variable gives more a more vivid depiction of what is involved and lends itself more readily to understanding the consequences of the subsidization of one part of the market. A monopoly raises price to the point where the negative effect on the quantity sold counterbalances the positive effect of the higher price per unit. Thus a monopoly does not stop raising price until it reaches the point where some or all of the consumers are restricting their consumption due to that price. A relevant case is the granting of monopolies for pharmaceuticals through the patent system. For this case the effect on the quantity demanded may be some consumers dropping out of the market rather than many consumers marginally reducing their purchases. If the government takes steps to keep price from affecting the purchases of one group of consumers through some subsidization program then the monopoly just moves the price up to the point where some other consumers diminish their consumption of the product due to the higher price.

## Analysis

Let P denote the price charged by the monopoly and p the price paid by consumers. The connection between P and p may involve some form of subsidy. Let Q be the quantity that the monopoly produces and sells. The demand function is of the form Q=f(p). The cost function for the monopolist is C(Q). Thus the profit Π of the monopolist, in the absence of taxes, is

#### Π = PQ(p) − C(Q(p))

The effect of a unit increase in price is given by

#### dΠ/dP = Q(p) + P(dQ/dp)(dp/dP) − (dC/dQ)(dQ/dp)(dp/dP) or, equivalently dΠ/dP = Q(p) + [P − (dC/dQ)](dQ/dp)(dp/dP)

Let the marginal cost (dC/dQ) be denoted by c. Since the focus of attention is elsewhere it is assumed to simplify the analysis that marginal cost is constant.

The monopolist will raise price if

#### dΠ/dP > 0 which is equivalent to [P − c](−(dQ/dp)(dp/dP) < Q(p) or −(1/Q)(dQ/dp) < 1/[(P−c)(dp/dP)]

The price that the monopolist chooses is the one such that dΠ/dP is equal to zero and hence profit is at a maximum. This is where

## Conclusions

The analysis may proceed further but this enough to make the essential point. That point is that any measure to reduce consumer sensitivy to price will result in the monopolist increasing the price. A subsidization of consumers by the government is one such measure. The government grants a subsidy, the monopolist raises the price and thus a portion of the subsidy goes to the benefit of the monopolist. The consumers, as tax payers, then have to pay for the subsidy through taxes. The net result is then that the consumers have to pay for the monopolist's share of the subsidy.

Another measure that would reduce consumer sensitivity to the price set by the monopolist is insurance. The payment for the product is spread over an extended period of time. Thus insurance leads to a higher monopoly price.

## Further Analysis

The condition for maximum profit found above is

#### −(1/Q)(dQ/dp) < 1/[(P−c)(dp/dP)] multiplication of both sides by p gives −(p/Q)(dQ/dp) = p/[(P−c)(dp/dP)]

The left side is simply the elasticity of demand, which will be denoted as ε(p).

Thus in the absence of any subsidization of consumers and p=P

#### ε(p) = p/(p−c) = 1/(1−c/p)

It is assumed that the demand function is of the following form:  The relationship between elasticity and price is then as follows. The elasticity continues to rise as the price rises.

The quantity on the right-hand side of the condition for profit maximization p/[(P−c)(dp/dP)] is always greater than one in value.

The price which maximizes profit is determined below for the case in which there is no subsidization. If this achieved and then any action which reduces the price elasticity of demand, such as a subsidy of consumers, will result in an increase in price. Suppose a subsidy of consumers is introduced in the form of p=αP where α<1 then the monopolist will find it advantageous to raise the price. The greater the subsidy the greater the price rise.

(To be continued.)