Monopoly

Perloff 11.1-6; WB 15 and 16.
As with competitive firms, a monopolist must decide whether or not to produce, and if so how much. We examine monopoly behavior and compare it to the competitive outcome using welfare analysis.

We will talk about monopoly behavior further when we get to pricing and strategy.

# Context

The field of industrial organization studies one industry at three different levels:

• Market structure — which firms are active1
• Firm behavior — how firms produce, price and iteract
• Market performance — the outcome, especially welfare

We will study firm behavior and market performance for three market structures:

• Perfect competition
• Monopoly
• Oligopoly with identical firms

# Monopoly behavior

The monopolist must decide whether or not to enter the market; and if it does, how much to produce.

The monopolist's technology and the input prices it faces are captured by its cost function; while demand conditions are captured by the Demand function (or the inverse Demand function).

We can think of the monopolist as choosing how much to produce OR as setting the price. These are equivalent.

### Shut down rule

The monopolist will enter only if its expected profit is non-negative. We can work backwards: solving the pricing problem, and then checking if the profit is non-negative.

### Pricing rule

Like any firm, if the monopolist enters it will produce where MC = MR (marginal cost is equal to marginal revenue).

The monopolist's MR curve has the same P-intercept as the Demand curve, but twice the slope, so that its Q-intercept is half that of the Demand curve (the reason for this is explained in class; and Perloff, 11.3). The MR at a given price can be expressed in terms of the elasticity of Demand at that price (eq'n 11.4 in Perloff):

(1)
\begin{align} MR=P\left(1-\frac{1}{|\varepsilon|}\right) \end{align}

There is also an easy rule for finding the monopolist's MR curve when facing a linear inverse Demand curve.

• Given Demand and the cost function, solve the monopolist's problem for PM and QM.
• Solve the monopolist's entire problem (buying inputs, choosing output, deciding whether or not to enter), as seen in WB 16.

### Zero-cost case

In the special case of zero cost, we can solve the monopolist's problem using Demand alone. Because there are no costs, profit maximization is the same as revenue maximization.

• Given Demand, find the monopolist's optimal price and quantity, PM and QM.
• Given Demand and a price, should the monopolist raise or lower it?

# Evaluating monopoly

We can compare monopoly to the competitive outcome by looking at the welfare effects and the firm's market power.

### Welfare effects

• Calculate the change in PS, CS and W from a monopoly. Also, calculate the DWL.

### Market power

We can measure the monopolist's market power, or ability to price above marginal cost, using the Lerner index (LI),

(2)
\begin{align} LI^M=\frac{P^M-MC}{P^M}. \end{align}

Using the fact that MR = MC at PM and our expression for MR above, we find that $LI^M=1/|\varepsilon|$, so that the monopolist has greater market power when consumers are less elastic.

• Calculate the LI at monopolist's optimal price and quantity.
• When consumers are more elastic, is the monopoly's market power greater or less?
• When there are more substitutes for the good, is the monopoly's market power greater or less?

# Why is it a monopoly?

A monopoly can defend itself from competitors with (i) a cost advantage (ii) a government mandate or (iii) anti-competitive practices. We will discuss some of the details later (strategy and externalities).

### Natural monopolies

With economies of scale, it may be “natural” for only one firm to operate, the natural monopoly. See Perloff 11.5 and 14.2.

Also, the first firm to enter a market may get a head start on rivals because of network effects. See Perloff 11.8. It's like having "economies of market share."

### Government

The government sets up and defends monopolies in many industries. Some examples are given below. See Perloff 11.6.

Intellectual property. The government supports those who create new ideas by granting monopolies. The production of ideas creates positive externalities if they are spread freely; we will see later that this means ideas will be inefficiently under-supplied in this case. A patent gives an innovator a short-term monopoly on its innovation. A trademark gives a brand-holder an indefinite monopoly on its name and logo as long as it continue to use them. A copyright is an automatic, short-term monopoly covering any creative work (writing, music, art).

Public utilities. The government grants monopolies to important firms, mostly to keep them closely watched and regulated. These firms may already be natural monopolies. Bloggers enjoy debating whether or not “Wall Street,” Google and Facebook qualify as public utilities.

### Anti-competitive behavior

The monopoly might commit to start a price war — by producing more than the optimal quantity and flooding the market — if a second firm enters.

# Short-run behavior

In the short-run, the monopolist may operate even when its profits are negative. We should instead look at its operating profit, which nets out the cost of capital (which is fixed in the short-run).

• Solve the monopolist's short-run problem.