Student
Price Discrimination Notes
ISyE 6230 Economic Decision Analysis
Matt Drake
Spring 2005
1
Preliminaries
Before we begin our discussion of price discrimination and its economic motivations, we must first (re)introduce a few topics in microeconomics that will prove useful in our subsequent analysis.
1.1
Demand
In order to determine how economic agents should determine prices and quantities of production, we must specify how consumers in a market will react to various prices. The most common method of characterizing consumer behavior is by specifying a demand function that determines the quantity demanded at each price offered by the seller. We can also invert the demand function and characterize the price at which a certain quantity is demanded.
For the balance of this essay, we will consider deterministic demand functions which relate exactly what will be sold at a given price. Admittedly demand is generally stochastic, varying randomly from observation to observation, selling period to selling period. While we could introduce a stochastic demand element into the following discussions, deterministic demand allows us to concentrate on the economic insights from the models presented without the complications that accompany random demand.
The following1 are several common demand functions utilized in price discrimination analysis. Although these functions are only dependent on the price of the good itself, they can be generalized to include the prices of other goods and other variables as well such as income.
1. Linear demand
Q(p) = a − bp
In the linear demand model, both of the parameters (a and b) are positive. The parameter a can be thought of as the market potential for the good, since this is the amount that would be sold if the price was zero; b is a measure of the consumers’ price sensitivity.
2. Cobb-Douglas (Constant Elasticity) demand
Q(p) = ap−
In the Cobb-Douglas demand model, parameters a and are positive. Again the
ISyE 6230 Economic Decision Analysis
Matt Drake
Spring 2005
1
Preliminaries
Before we begin our discussion of price discrimination and its economic motivations, we must first (re)introduce a few topics in microeconomics that will prove useful in our subsequent analysis.
1.1
Demand
In order to determine how economic agents should determine prices and quantities of production, we must specify how consumers in a market will react to various prices. The most common method of characterizing consumer behavior is by specifying a demand function that determines the quantity demanded at each price offered by the seller. We can also invert the demand function and characterize the price at which a certain quantity is demanded.
For the balance of this essay, we will consider deterministic demand functions which relate exactly what will be sold at a given price. Admittedly demand is generally stochastic, varying randomly from observation to observation, selling period to selling period. While we could introduce a stochastic demand element into the following discussions, deterministic demand allows us to concentrate on the economic insights from the models presented without the complications that accompany random demand.
The following1 are several common demand functions utilized in price discrimination analysis. Although these functions are only dependent on the price of the good itself, they can be generalized to include the prices of other goods and other variables as well such as income.
1. Linear demand
Q(p) = a − bp
In the linear demand model, both of the parameters (a and b) are positive. The parameter a can be thought of as the market potential for the good, since this is the amount that would be sold if the price was zero; b is a measure of the consumers’ price sensitivity.
2. Cobb-Douglas (Constant Elasticity) demand
Q(p) = ap−
In the Cobb-Douglas demand model, parameters a and are positive. Again the
References: [1] K. Carroll and D. Coates (1999). Teaching price discrimination: Some clarification. Southern Economic Journal, 66(2), 466-480. [2] G. Debreu. Theory of Value. Wiley, New York, 1959. [3] S. Happel and M. Jennings (1995). Herd them together and scalp them. The Wall Street Journal, February 23, page A-14, column 4. [4] L. Phlips. The Economics of Price Discrimination. Cambridge University Press, New York, 1983. [5] A. Pigou. The Economics of Welfare. Macmillan, London, 1920. [6] J. Tirole. The Theory of Industrial Organization. MIT Press, Cambridge, MA, 1988. [7] H. Varian. Microeconomic Analysis. Third Edition. W.W. Norton & Company, New York, 1992. 12