Price and quantity determination

In the textbook model of monopoly there is a single firm/seller in the market. Hence, the market demand curve (which reflects consumer preferences and incomes) is also the demand curve facing the firm.

In addition, if we assume that the firm maximizes profit, then the price and quantity is that which maximizes the firm's profit given this market demand and the firm's costs.

Example: Given market demand and cost of a monopoly firm, find the market price and quantity?

Price and output in a monopoly: Graphical example

Effect of a price ceiling (Perfect Competition)

Let us revisit the supply demand model. According to this model, equilibrium price is where demand curve intersects the supply curve (denote by \(p_{e}\) the figure below).

What is the effect of price ceiling on social surplus?

Effect of a price ceiling (Perfect Competition)

Price ceiling causes the social surplus to decrease by the area denoted ABE in the figure.

In general, a price ceiling in perfect competition always decreases social surplus.

Effect of a price ceiling (Monopoly)

Find the effect of price ceiling at \(p_{ceil}\) in the figure below.

Inefficiency of the monopoly outcome

Monopoly outcome is not Pareto efficient. The inefficiency is represented by the area BEM in the figure below. This inefficiency or loss of surplus relative to the efficient outcome is also called the deadweight loss of monopoly.

What is Pareto efficiency?

Define an allocation as a specification of the following:

An allocation \(A\) is said to be pareto efficient if no reallocation is possible that makes at least one person better off without making anyone worse off.

In other words, suppose there is an allocation \(X\). If resources can be reallocated such that at least one person can be made better off without making any one worse off, then \(X\) is not pareto efficient.

Inefficiency in the monopoly

Why is the outcome \( (p_{m}, Q_{m}) \) in the figure below pareto inefficient?

Consider the following reallocation: Everyone who is consuming the \(Q_{m}\) units continue to do so at price \(p_{m}\). However, in addition the firm is made to produce output between \(Q_{m}\) and \(Q_{E}\) and required to sell each of these additional units at price \(p_{E}\).

What is the pareto efficient output in the example below?

Condition for Pareto efficiency

In terms of the level of output produced, an alloction is pareto efficient if and only if the level of output produced is one at which \( WTP = MC \).

For discrete data this conditions translates to: an alloction is pareto efficient if and only if the level of output produced is the largest output for which \( WTP \geq MC \).

Efficiency for a price discriminating monopolist

Inefficiency of monopoly also requires that monopolist cannot price discriminate.