Appunti Economic policy

First Theorem of Welfare Economics

In a Walrasian Equilibrium, the allocation is Pareto efficient.

Competitive Prices and Decentralization

If, in an allocation, the two agents have different Marginal Rate of Substitution (MRS), there is scope for improving the allocation, while if these are equal, there is no scope for improvements.

The equality of MRS A and MRS B in a Walrasian equilibrium is not achieved by any central planner, but via competitive markets, where each of the agents just takes into account the prices and his endowments, when deciding what to consume. In doing so, both the agents equate their MRS with the prices, giving rise to efficiency.

If, for instance, there is a decrease in the available resources of commodity 1, this is likely to lead to an increase in the relative price of that good, which in turn leads to a lower consumption of that good in equilibrium by other agents. In essence, prices work to coordinate the actions of individuals.

The first welfare theorem formalizes the idea of Adam Smith that an

“Invisible hand” guides the economy towards efficiency. Even though every individual in the economy only acts selfishly, the end result is efficiency for the economy. It is based on the assumptions of:

1. perfect competition i.e. that all agents are price takers
2. the consumption of one agent does not directly affect the utility of any other agent
3. agents know the quality of what they are buying

We have discussed the trade-off between equality and efficiency. We shall now argue that such a trade-off is absent in the Edgeworth economy. If the government wants to redistribute between the two agents, it would prefer to reach the Pareto Efficiency.

SECOND THEOREM OF WELFARE ECONOMICS: Any Pareto efficient allocation can, after a suitable reallocation of resources, be implemented as a Walrasian Equilibrium.

The market economy described in Edgeworth box can be both efficient and achieve equality if there’s a government that pursues this objective by reallocating resources, through a

A lump-sum tax. The government will then leave to the market the task of reaching the Walrasian Equilibrium, hence efficiency. The result of the second theorem is in line with the Tinbergen's rule: for an economy to achieve a desired number of objectives, it is required an equal number of independent instruments: in this case, we have the perfect competition to reach efficiency, and a lump sum tax to reach equality.

ENVY FREE AND FAIR ALLOCATIONS: Is there an allocation in the Edgeworth Box that is both Pareto efficient and has the property that no agent prefers the consumption of the other agent over his own? A feasible allocation is said to be Envy Free if agent A prefers his consumption bundle over the one of agent B and agent B prefers his consumption bundle over that of agent A. We say that an allocation is fair if it's both Pareto Efficient and Envy Free (the allocation (wa1; wa2)= (wb1; wb2) is envy free but usually not Pareto Efficient). It shows that equality of consumption or

income is not the best criteria for equality. This argument shows, among other things, that fair allocations exist, whenever Walrasian equilibria exist.

MARKET POWER AND REGULATION:

In this chapter we explain what happens in a market without price taking behaviour by the firm, i.e when the firm is a monopoly. The outcome is inefficient, which according to our established approach to the role of government intervention leads to the next question: can the government improve such outcome? The answer is a conditional "yes": there are forms of regulations that lead to improvements.

NATURAL MONOPOLY:

Typically, by a natural monopoly we mean a firm with high fixed cost and more or less constant marginal costs. Examples are railway companies or water utility companies where laying the water pipes constitute a fixed cost and the marginal costs include the cost of the water provided to the consumer. Since average cost is decreasing with output, it is more efficient to only have one firm.

supplying the good in question. Also, in a situation where initially there is competition between firms, is it to be expected that one firm will end up dominating the market since by expanding its output, a firm lowers its average costs and hence is able to offer a lower price than other firms. If there is only one firm offering a product, it will become a price maker, dictating to its customers the price it finds optimal.

In the figure below we depict average and marginal costs for a natural monopoly:

Where AC = (F/Q) + c, that means average costs are equal to fixed costs per unit plus marginal costs. The natural monopoly takes into account the demand curve for its product, as described by the function D(p), to maximize its profit. The demand curve is downward sloping. The monopolist can look at the inverse, p(Q), to determine, for any quantity offered by the monopoly, the price at which consumers are willing to buy that quantity.

We assume that, given the inverse demand curve, the natural

monopoly chooses the quantity and the price that maximize its profit, i.e. revenue, p*Q, minus its costs, F + cQ. Formally the problem is:

max p*Q - (F + cQ)

to find the solution, we use the first order condition, FOC, by taking the derivative with respect to Q and setting it equal to zero:

p'Q + p - c = 0

where p'Q + p is the marginal revenue, MR.

Given that p' is negative (if the quantity supplied to the market increases, then the price must decrease; hence, the slope is negative; hence, the first derivative is negative), the MR is always lower than the price alone. It means there's always a solution that is below the one we would have had with perfect competition.

The FOC states that MR = MC;

The solution is the following:

At Q* we have MR = MC, so Q* is the quantity supplied by the monopoly when it maximizes its profit. To find the price that the monopoly charges its customers, we use the demand curve, and we see that that price is p*. The rectangle that goes

From p* to Q* is the total revenues. Using the average cost curve, AC we can also find the average costs when it produces Q*, and since these costs are lower than the price, it has a positive profit = Q × [p* − AC(Q*)] > 0, that is, the quantity times the difference between price per unit and cost per unit. This describes the equilibrium in the monopoly’s market. Note however, that this is not an equilibrium between demand and supply, simply because there is no supply curve. A supply curve describes how firms react to the price, but in the model of the monopoly, the firm does not react but, on the contrary, sets the price.

A monopoly leads to inefficiency. We now proceed to show that the equilibrium in the monopoly’s market is inefficient, i.e. that it is possible to find a Pareto improvement. The basic insight is that in the equilibrium, marginal costs are lower than the price as can be seen from the figure.

If we ask the monopolist to produce one additional unit of

good at price between p* and MC, both the additional consumer and the monopolist are better off, and the other consumers won't be worse off, hence it's a Pareto improvement. Actually, as long as the price of the additional unit is above the marginal cost and below the demand curve, it's a Pareto improvement (even though it would be discriminatory, because every consumer is getting a different price).

HOW CAN THE GOVERNMENT IMPROVE THE SITUATION OF INEFFICIENCY?

One idea would be to set price equal to marginal cost, as we do in perfect competition. This wouldn't be profitable for the monopolist, because the point where p=MC is below the AC curve, hence he would be making a loss.

Otherwise, we could ask the monopolist to produce where the demand curve and the average cost curve intersect: the monopolist would be earning 0, but the situation has improved, because more quantity is produced, but there's still room for improvement.

In reality government regulation of

Monopolies is complicated by the fact that neither the cost structure, nor the demand is perfectly known by governments.

One important issue is that technology evolves over time and a regulated monopoly needs incentives to develop or adopt new technologies. If it knows that no matter its choice of technology, its profit will be zero, it may stick to an old and inefficient one.

To further competition and thus the drive towards better products and more efficient technologies, the government may also make sure that there are more than one firm in the industry, thus creating an oligopoly structure, even if the firms will then not operate at an efficient scale.

The EU is entrusted with powers to limit anti-competitive behaviour. European antitrust policy was developed from the two central rules set out in the Treaty on the Functioning of the European Union.

The EU also acts to prevent the creation of monopolies (whether natural or not) through mergers or acquisitions.

A useful measure of the market

The power of firms, or a measure of the degree of competition among firms in a market, is given by the Herfindahl-Hirschman index. In a given market there are N firms, labelled with i= 1,2, 3, 4, … the HHI is the sum of the square market shares of each firm. When the market structure is close to perfect competition, HHI is close to 0. In case of monopoly, HHI is equal to 1.

MONOPOLY IN THE HEDGEWORTH BOX:

Suppose that A and B have their own preferences, but A has the power to set the prices, hence, to decide the inclination of the slope of the budget constraint.

Suppose A considers three budget lines:

For A, the best allocation is x’.

For each price vector, there’s an optimal consumption for agent B. The set of all these points is called offer curve:

It goes below the endowment.

It has the same role as the demand curve in a partial equilibrium model of a monopoly we saw before.

The problem of agent A is to choose a point on the offer curve (hence a price ratio) to maximise its

utility, which means he is going to choose the point where his indifference curves are tangent to the offer curve: Notice that it isn’t a Pareto Efficient point! It’s the same answer we found in the partial equilibrium.

EXTERNALITIES:

We say that there is an externality in consumption when the wellbeing of a consumer is directly influenced by the consumption of another consumer or the production of a firm.

We say there is an externality in production when the production possibilities of a firm are directly influenced by the consumption of a consumer or the production of another firm.

The externality may be positive or negative. For instance, painting a house in a nice colour creates a positive externality for people seeing the house, while burning car tires in the backyard of a house is likely to create a negative externality for those living nearby.

Externalities can also be multilateral, when many individuals are involved, or bilateral, when only two individuals are involved.

The effect of externalities is direct, and not transmitted via the market.