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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.

Readings

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:

  • Cost advantage (key resources)
  • Regulation
  • Economies of scale

In the long run the number of firms is endogenous. Incumbents will try to deter the entry of new competitors. Whether they succeed depends on whether a market is contestable. Baumol (1982) argued that the number of firms in the market does not matter, but whether a new firm can enter (and exit) the market for free.

A hit-and-run entry is a characteristic of contestable markets. Essentially, a firm enters a market, gets profits, and exits before the prices change.

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Principles of Economics: Public and Common Goods

To define Public Goods we need two concepts: Excludable goods and Rival goods.

  • Excludable goods can be prevented from use (food) in contrast to non-excludable goods that can always be consumed (radio or air).
  • Rival goods cannot be consumed without diminishing others’ use of it (food) in contrast to non-rival goods (mp3-files).

Based on the two properties four types of goods can be defined:

  • Private: Excludable & rival
  • Public: Non-excludable & non-rival
  • Common: Non-Excludable & rival
  • Club: Excludable & non-rival

As Public goods are non-excludable and non-rival goods, it is hard to provide public goods with private markets because of the free-rider problem. A free rider receives the benefits of a good, but avoids paying for it.

If the benefit of a public goods exceeds the cost of providing it, the government should provide the good by collecting tax to pay it. However, measuring the benefit is usually difficult. An approach to solve the problem is to perform cost-benefit analysis. Nonetheless, such cost-benefit analyses are imprecise and provide less efficiency than private markets.

In contrast Common Goods are non-excludable and rival. This causes the Tragedies of the Commons as free-riding is the best option for any rational, self-interested actor (i.e. consuming as much as possible without contributing). Several policies are used to restrict the tragedy:

  • Regulated resources
  • Corrective taxs
  • Auctioning of permits
  • Privatisation (e.g. make land private, sell in parcels)

Elinor Ostrom developed 8 principles to govern commons:

  • Clearly defined boundaries;
  • Rules regarding the appropriation and provision of common resources that are adapted to local conditions;
  • Collective-choice arrangements that allow most resource appropriators to participate in the decision-making process;
  • Effective monitoring by monitors who are part of or accountable to the appropriators;
  • A scale of graduated sanctions for resource appropriators who violate community rules;
  • Mechanisms of conflict resolution that are cheap and of easy access;
  • Self-determination of the community recognized by higher-level authorities;
  • In the case of larger common-pool resources (CPR), organization in the form of multiple layers of nested enterprises, with small local CPRs at the base level.

This illustrates that institutions are necessary to manage common goods and they require a high level of administration.

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Principles of Economics: Externalities

Externality

An uncompensated impact of one person’s action on the well-being of a bystander. It is a type of market failure as it reduces the efficiency of the market. In general, it is caused by self-interested buyers and sellers neglecting the external costs or benefits of their actions. However, public policy can reduce externalities and increase efficiency.

On the one hand, positive externalities include herd immunity by vaccination, R&D or higher education. On the other hand, negative externalities include air and water pollution.

Internalisation

The idea is to alter incentives such that people take into account the external effects of their actions. Negative externalities are usually larger than socially desirable, whereas positive externalities are usually smaller than socially desirable. Example remedies to internalise respectively are tax and subsidise food. A tax on production may make a firm’s costs equal to social costs.

Public policies can be roughly divided in two:

  • Command-and-control policies regulate behaviour directly;
  • Market-based policies provide incentives so that private decision-makers will choose to solve the problem on their own.

Taxes and Subsidies

A corrective tax designed to induce private decision-makers to take account of the social costs that arise from a negative externality.

Arthur Pigou (1877-1959) introduced the Pigovian tax which is equal to the external costs. Subsidies are therefore negative taxes to optimally compensate for the external benefit. Those taxes should align private incentives with society’s interests. An import fact is that Pigovian tax moves an economy toward a more efficient allocation of resources. This contrasts with other taxes and subsidies, which actually distort incentives and move an economy away from the social optimum.

The marginal damage is the increase of pollution per additionally produced unit. The marginal cost of abatement is the cost to reduce an additionally produced unit of pollution. Small (initial) reductions in pollution are cheap, however, the price to reduce pollution increases exponentially. The optimal pollution is defined as the equilibrium where the marginal abatement costs equals the marginal damage. A tax equal to the equilibrium point therefore forces companies to reduce the pollution to the equilibrium point (otherwise they pay taxes higher than the cost of abatement). For the abatement costs higher than the tax the company pays taxes as this is cheaper than abatement.

However, each company will have different costs of pollution abatement. Firms with the lowest abatement costs will reduce pollution most. Firms with high abatement costs have a greater willingness to pay the tax. This contrasts with a regulation to only emit a certain amount, as the reduction in pollution is obtained in the most efficient way.

Corrective taxes are better for the environment:

  • reduce pollution up to the level of tax
  • cleaner technology are quickly adopted to reduce tax load.

Tradable pollution permits

Tradable pollution permit systems reduce pollution at lower cost than regulation. Firms with low cost of reducing pollution do so and sell their unused permits. Firms with high cost of reducing pollution buy permits. Pollution reduction is concentrated among those firms with the lowest cost.

The permit price is set at the marginal cost of abatement. At the optimal pollution the marginal damage is gain equal to the marginal abatement cost. If the pollution is larger than the optimal pollution, additional permits need to be bought, on the other hand, if pollution is lower than the optimal pollution, permits can be sold.

However, in the example of the EU ETS, the profits of companies increased and the price for end-users as well. Pollution permits – while similar to Pigou taxes in design – are not a form of taxation.

There are limits as environmentalists argue no one should be able to buy the right to pollute and that pricing the environment is inherently impossible. However, without pricing it becomes difficult to judge the value of clean air and water. So far, market-based approaches have reduced the cost of environmental protection and therefore seem to be partially justified.

The Coase Theorem

Assuming everyone has perfect information, consumers and producers are price-takers, enforcing agreements in courts is costless, no transaction costs and no strategic behaviour. Based on those assumptions the initial assignment of property rights regarding externalities does not matter for efficiency. In this world it is a secondary issue who pays and all externalities are internalised. Property rights are merely used for gaining efficiency (not redistribution).

In reality, pollution causes potentially large transaction costs, which depend on the initial allocation of property rights. Free-riding also causes problems due to the asymmetric information on damages and costs. Lastly, no mention of any compensation for victims in conjunction with the previous points makes the Coase Theorem unrealistic.

To contain these problems (and get closer to the circumstances of the Coase Theorem) environmental damage is evaluated. Indirect methods compute affection by pollution on isolated markets, which revealed preferences. Direct methods (contingent valuation) are based survey on consumer willingness to pay for a better environment, which is based on stated preferences.

 

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Principles of Economics: Efficient Competitive Markets

The goal of the lesson is to understand how markets work. We need a benchmark to analyse a market and it will be perfect competition. It is an idealised world where nobody has sufficient market power to influence the market and therefore good prices are exogenous. Also producers are altruistic inasmuch they do not consider the influence that their selling of a good has on the market. In future lessons we will relax some assumption to understand the real world better.

Perfect competition occurs when:

  • Atomicity of agents (no agents overlap)
  • Perfect information (no information advantage for any agent)
  • Decreasing returns-to-sale (see later)
  • No barrier to entry (anybody can start selling)
  • Homogeneous goods (each instance of a good is equal)

The equilibrium price equates supply and demand. In the long-term profits are (almost) zero, since firms enter as long as a positive profit is possible. The situation is Pareto-optimal.

Consumers

The demand function  Q = D(p) is the quantity that consumers want to buy at the price level  p . It is also the aggregation of individual demand functions.

It can also be seen as representative people along the cost-spectrum and their willingness to pay the price  p for the good.

The integral  S(Q) of a specific price  p is the willingness to pay or (gross) surplus. The net profit  pQ must be subtracted to compute the consumer (net) surplus. The surplus is the difference between the price they are willing to pay and the price they actually pay. So consumers have money to spend elsewhere that they would otherwise spend on this product.

Elasticity

A measure of the sensitivity of demand to a change in price.

\epsilon = \frac{\Delta Q / Q}{\Delta p / p} = \frac{P}{Q}\frac{dP}{dQ}

Electricity is inelastic (0.5); changes in price barely influence consumption. Cement is still inelastic (0.8); changes in price weakly influence consumption.

Examples

Demand for fuel in France as a case study. If the price increases 10%. In the short term it will decrease consumption by 1% \epsilon = -0.1 whereas the short term it will decrease consumption by 7% \epsilon = -0.7 . Other long term effects are slower car growth \epsilon = -0.1 , mileage \epsilon = -0.2 , motorway usage \epsilon = -0.4 . The price is inelastic.

A carbon tax of 14 euros would translate to 4 cents per litre or 3.3%. It translates into  \epsilon = -0.03 in the short-term and \epsilon = -2.3 in the long term (based on a simulation). Currently the carbon tax is at 6 percent.

The Bonus-Malus program was introduced to punish heavy polluter and (promote less pollution) by transferring the fee from polluters to “non-polluters” and was supposed to be budget-balanced. However, it cost the state of France 200 million euro in 2008 as the sale of large cars slumped by 27% while the sale of small cars rose by 15%. The government had underestimated the demand elasticity.

Short-term predictions are easier compute, but long-term predictions are difficult as the change may also change the underlying system (e.g. behaviour patterns).

Supplier

The cost c(q) describes the cost of producing q units expressed in $ / unit. We assume that supplier maximise their profit. The profit is defined as \pi(p,q) = p\cdot q - c(q).

The average production cost is AC(q) = \frac{c(q)}{q}. The return-to-scale is characterised by the average cost per unit. In order to double the output:

  • Constant return-to-scale means to double all inputs levels and results in no change to the average cost.
  • Decreasing return-to-scale means  it requires more than doubling the input and results in an increase in the average cost.
  • Increasing return-to-scale means it requires less than doubling the inputs and results in an decrease in the average cost.

In terms of average production cost less firms are producing lower average costs and if the goal is to reduce costs a monopoly can be beneficial. This is especially common in productions with creasing return-to-scale. For instance, this applies often for public infrastructure such as rail networks, electricity grids and water supply.

The marginal cost is MC(q) = c'(q) = \frac{dc(q)}{dq} is mathematically speaking the derivative of the cost. Economically, it can be used to understand how costly it is to produce one additional unit or the cost to produce the last unit. If the marginal benefit is larger than the marginal cost, a supplier has an incentive to increase the production and vice versa if the marginal cost is higher than the marginal benefit, a supplier has an incentive to decrease the production.

Usually, we assume that marginal cost is increasing. It first decreases and then eventually increases. The low point of the cost-function is located where  MC(q) = AC(q) . This is called the minimum efficient scale.

Fixed and variable costs

Whether costs should be considered fixed or variable depends on the scale at which production is observed (specifically; small energy supplier have a fixed production cost, but large energy suppliers have a variable production cost. Generally; single companies may have fixed costs that nonetheless turn to variable costs observed on an industry level).

Supply function

The aforementioned profit has the derivative  \frac{\delta \pi}{\delta q} = p - c'(q). Based on the derivative it can decide whether to produce or not. It should produce the qunatity that equalises price with marginal cost  p = c'(q) = MC(q). Therefore the supply function is determined by the marginal cost.

The Market Equilibrium

Comparing the supply to the demand function shows allows to determine the Market Equilibrium. A price p^* clears the market such that O(p^*)=D(p^*), i.e. the intersection between the curves. An equilibrium is a price such that the supply equals the demand.

To evaluate the efficiency of the market we look at industry equilibrium. The welfare function can be defined as a function of the quantity produced. The welfare is the difference between the consumer gross surplus and the industry cost  W(Q) = S(Q) - C(Q). If the price is p then we can expand it to  W(Q) = [S(Q)-pQ] + [pQ - C(Q)]. The welfare is an indicator of the gain for the society by the production and consumption of Q units.

To analyse the efficiency of a market we find the condition that maximises the welfare. The Market Equilibrium will provide the maximal welfare. An additional unit of Q creates a gross utility S'(Q) among consumers but also a cost C'(Q) which has a resulting effect on welfare of S'(Q)-C'(Q). Therefore the optimal allocation is S'(Q)=C'(Q). This is obtained if the consumer surplus is equal to the marginal industry cost.

Therefore the perfectly competitive market outcome is efficient and the production is optimal. A competitive market is efficient from the point-of-view of the public interest. This is called Pareto-optimal, after the Italian economist and sociologist Vilfredo Pareto (1848-1923). It is a situation in which you cannot improve the condition of a single individual without deteriorating the condition of the second. However, this has implications for equity as it prohibits the redistribution from rich to poor. Pareto-efficiency is only about allocation, not equity.

Some (additional) Definitions

  • Market power is the ability to judge one’s impact on the market, for instance:
    • If only one firm is selling the good it is a Monopoly.
    • If there are few firms selling the good it is an Oligopoly.
    • If there is only one buyer it is a Monopsony.

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Principles of Economics: Introduction

The course’s objective is to introduce the study of economics, and the economic way of thinking about societal problems. It should provide basic understanding of a market economy and the potentials and limitations of economic policies.

Economics is the study of how society manages scares resources to use them in the most efficient way.

The textbook is Economics(Mankiw & Taylor, 2014).

References

Mankiw, N. G., & Taylor, M. P. (2014). Economics (3rd ed.). Cengage Learning.

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