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 [latex] Q = D(p) [/latex] is the quantity that consumers want to buy at the price level [latex] p [/latex]. 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 [latex] p [/latex] for the good.

The integral [latex] S(Q) [/latex] of a specific price [latex] p [/latex] is the willingness to pay or (gross) surplus. The net profit [latex] pQ [/latex] 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.

[latex display=true]\epsilon = \frac{\Delta Q / Q}{\Delta p / p} = \frac{P}{Q}\frac{dP}{dQ} [/latex]

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% [latex display=true]\epsilon = -0.1 [/latex] whereas the short term it will decrease consumption by 7% [latex display=true]\epsilon = -0.7 [/latex]. Other long term effects are slower car growth [latex display=true]\epsilon = -0.1 [/latex], mileage [latex display=true]\epsilon = -0.2 [/latex], motorway usage [latex display=true]\epsilon = -0.4 [/latex]. The price is inelastic.

A carbon tax of 14 euros would translate to 4 cents per litre or 3.3%. It translates into  [latex display=true]\epsilon = -0.03 [/latex] in the short-term and [latex display=true]\epsilon = -2.3 [/latex] 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 [latex]c(q)[/latex] describes the cost of producing [latex]q[/latex] units expressed in $ / unit. We assume that supplier maximise their profit. The profit is defined as [latex]\pi(p,q) = p\cdot q – c(q)[/latex].

The average production cost is [latex]AC(q) = \frac{c(q)}{q}[/latex]. 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 [latex]MC(q) = c'(q) = \frac{dc(q)}{dq}[/latex] 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 [latex] MC(q) = AC(q) [/latex]. 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 [latex] \frac{\delta \pi}{\delta q} = p – c'(q)[/latex]. Based on the derivative it can decide whether to produce or not. It should produce the qunatity that equalises price with marginal cost [latex] p = c'(q) = MC(q)[/latex]. 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 [latex]p^*[/latex] clears the market such that [latex]O(p^*)=D(p^*)[/latex], 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 [latex] W(Q) = S(Q) – C(Q)[/latex]. If the price is [latex]p[/latex] then we can expand it to [latex] W(Q) = [S(Q)-pQ] + [pQ – C(Q)][/latex]. 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 [latex]S'(Q)[/latex] among consumers but also a cost [latex]C'(Q)[/latex] which has a resulting effect on welfare of [latex]S'(Q)-C'(Q)[/latex]. Therefore the optimal allocation is [latex]S'(Q)=C'(Q)[/latex]. 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.