# Principles of Economics: Imperfect Competition

Monopoly

Barriers to entry are the fundamental cause for the rise of monopoly. Barriers appear in three forms: ownership of key resources, exclusive production rights and an efficient (return-to-)scale.

A firm’s ability to influence the market price is called market power. It entails that a firm can raise the price above some competitive level in a profitable way. The lowest possible price a firm can profitably charge is equal to the marginal cost of production. The market power can be expressed as the difference between the price it charges and the marginal cost. A firm is considered a price maker it exercises its market power; formally defined as $P'(Q) \neq 0$.

Given a price function $P(Q)$ and a monopoly that sets its profit as $\pi(P(Q),Q) = P(Q)Q-C(Q)$ and has the the derivative $\frac{d\pi}{dQ}=P + P'(Q)Q-C'(Q)$.

In perfect competition marginal costs is equal to the price. In the monopoly it is marginal costs plus the derivative of the demand. Monopolies make us of the fact that increased output decreases price and and therefore the marginal revenue is $P(Q)+P'(Q)Q < P(Q)$ and therefore the optimal production of the monopoly is $P(Q)+P'(Q)Q = C'(Q)$. Reformulated $P-C’ = P'(Q)Q$ and then $\frac{P-C'(Q)}{P} = – \frac{1}{\epsilon}$ where $\epsilon$ is the price elasticity. Consequently, the relative difference between the price and the marginal cost is inversely proportional to the price-elasticity of demand. The more sensitive demand is to the price the lower the relative difference between price and marginal cost. Close substitutes to a monopoly product induce high demand sensitivity and prices will not rise much above the marginal costs.

The market power of monopoly has two consequences: There is a redistributive effect as the profits of the firm increase at the expense of the consumers. There is also a loss of efficiency as the deadweight loss increases (i.e. the difference between the surplus in the competitive and monopolistic case). The allocative inefficiency is not judging whether consumers or producers are more deserving of the surplus, but criticising the deadweight loss. Market power causes market inefficiency as the reduction of output induces a welfare loss.

Rent-seeking behaviour

The existence of a potential rent may entice companies into rent-seeking behaviour. Acquiring a monopoly is of a major advantage and therefore highly sought after. Firms increase spending on monopoly-generating activities such as strategic and administrative expenses (lobbying, bribing, etc.) that do not generate social welfare.

Side note:

Competition laws sometimes prohibit market power above some minimum market power threshold. However, below the threshold the rules do not apply. Those thresholds may also differ for different practices.

Liebenstein 1966 X-inefficiency, Hart 1983 manager under competition, Nickell 1996 uk manifactoring 1972-1986

Natural Monopoly

Efficient scales leave only room for one company and therefore cause natural monopolies in network industries (water, electricity, internet, social networks, etc.). Usually, natural monopolies can produce at lower average costs than multiple firms.

If a monopoly prices at average cost, profits are zero. However, if we price at marginal cost the profits are negative and welfare is maximal. There exists a trade-off between allocative efficiency and productive efficiency. The Ramsey-Boiteux pricing is a policy rule setting out how a monopolist should set prices in order to maximise social welfare under the constraint of profits.

Price Discrimination

Restrictively formulated, price discrimination occurs when the “same good” is sold at different prices. A broader definition expands this to differences in prices that cannot be entirely explained by variation in marginal costs. Price discrimination is only feasible if consumers cannot resale the good to each other.

Price discrinomation has been categorised by Pigou (1932):

• 1st degree (complete discrimination): Each unit is sold at a different price. The producer captures the whole surplus and no deadweight loss occurs. Production is optimal, but it is never fully realised.
• 2nd degree (indirect segmentation): a proxy for a group is used (e.g. package size).
• 3rd degree (direct segmentation): general attributes of a buyer (e.g. age or gender) is considered.

Double marginalisation

Assuming we have two firms with monopolies: upstream firm  $P$ with a production cost $c$ and downstream firm $D$ with a distribution cost $d$. The Marginal revenue of the downstream firm is going to be the demand function for the upstream firm. However, the upstream firm will use its marginal revenue to calculate the quantity produced. Each monopoly in a chain of marginalisation will reduce the total quantity. For consumers (and welfare) a single monopoly controlling the whole production chain (vertical integration) is better (larger consumer surplus and less deadweight loss.)

Oligopoly

Situated between monopoly and perfect competition, an oligopoly is characterised by few producers with market power (albeit less than monopolies).

In 1838 Cournot introduced the first model of oligopoly.

Cournot assumes that the firms take into account the best response of the other firms. The aggregate production is between the competitive and monopoly outcome. Consumers are better off than with a monopoly. The sum of the profit of all firms is lower than the monopoly profit. With each additional firms

• the individual production decreases, total production increases
• consumers are better off
• the profit of each firm and of the industry decreases
• welfare increases tending towards the optimum (i.e. perfect competition)

The model was challenged by Bertrand in 1883. Without cooperation, the price will settle at the marginal cost. However, several assumptions can be relaxed:

• Goods are perfect substitutes
• Consumers can identify the cheapest producer without cost and switch
• Firms compete and do not collude
• Firms interact once and not repeatedly
• The marginal costs of firs are constant and there is no capacity constraint
• The actions available to firms are limited to price changes.

In 1925 Bertrand was critisised by Edgeworth for not considering productive capacities. In 1983 Edgeworth’s critique was limited by Kreps and Scheinkman who showed that if firms choose capacity first and set prices then, the results are equal to Bertrand’s stipulation.

There is no general model of oligopoly.

Entry

Oligopolies arise due to barriers to entry. In contrast to monopolies the barriers to entry are not completely prohibitive, but high enough to keep out a large number of producers. Barriers are constituted by: