## Tuesday, September 14, 2010

### Microeconomics: Chapter 12 General Equilibrium and Welfare Economics

Chapter 12: General Equilibrium and Welfare Economics
Partial equilibrium analysis is the study of equilibrium in one market in isolation. In contrast, general equilibrium analysis is the study of the equilibrium of all markets simultaneously.

12.1 General Equilibrium Analysis
Supply and Demand Curves
1. The markets for two goods are linked if the two items are “related” (substitutes or complements) or if one of them is an input into the production of the other. When markets are linked, a shift in the supply or demand curve in one market has consequences for the price and output in the second market. Thus, when policymakers consider intervention in one market (e.g. a tax or regulation), they should try to think about the effects in other markets as well.
2. Suppose that the commodities X and Y are related, and there is a shift in either the supply or demand curve of commodity X. A partial equilibrium analysis of the effect of the shift may be in error because of feedback effects from the market of Y. For example, if a tax raises the price of beer, then the demand for wine may increase (since it is a substitute), but this increase in demand causes the price of wine to increase, which in turn shifts the demand of beer up, and so on. Ultimately, the economy settles to a new general equilibrium.

General Equilibrium Analysis of the Minimum Wage
The partial equilibrium model shows that when a minimum wage is instituted, some workers gain and others lose. The winners are the workers who are lucky enough to get employment in the covered sector. Losers include workers who used to work in the covered sector and either become unemployed or take jobs with lower wages in the uncovered sector.

The general equilibrium model provides an important new insight. Just because a worker is initially employed in the uncovered sector does not mean that he or she is unaffected by the minimum wage. The losers from the minimum wage include workers in the uncovered sector, whose wages go down because of the influx of workers from the covered sector.

General Equilibrium in a Pure Exchange Economy
A pure exchange economy is an economy in which the quantities supplied of all goods are fixed; the only economic problem is to allocate amounts of the goods among consumers.

Edgeworth Box
An Edgeworth box can be used to depict the allocation of two goods between two people. The height of the box represents the total quantity available of Good 1, and the length of the box represents the total quantity available of Good 2. The amount of Good 1 allocated to Person 1 is measured by vertical distance from the bottom left corner to a designated point. The amount of Good 1 allocated to Person 2 is measured by the vertical distance from the top right corner to that same point. Any point in the Edgeworth box represents an allocation of commodities between two consumers.

In an Edgeworth box, for Person 1, higher levels of utility are represented by moves to the northeast; for Person 2, to the southwest.

Given an initial allocation, Person 1 and Person 2 can make mutually beneficial trades to maximize their respective utility. This occurs at a point where their indifference curves are tangent. (This occurs when both people set their MRSs equal to the price ratio.)

12.2 Welfare Economics
Welfare economics is the branch of economic theory concerned with the social desirability of alternative economic states.

Consumption Efficiency
An allocation is said to be consumption efficient if, given the total supplies of the commodities, the only way to make one person better off is to make another worse off.

The contract curve is the locus of all the consumption-efficient points in an Edgeworth box. (There can be many, depending on the starting point for allocations.) It is defined by the mutual tangencies between the two consumers' indifference curves.

Consumption Efficiency and Water Rationing
Water rationing can be examined using an Edgeworth box with sides representing water and a composite of all other goods. Allotting each person an equal share of water and forbidding its sale is inefficient if the allocation is not on the contract curve. A simple solution would be to provide tradable ration coupons, which would allow people to trade water for “all other goods” in order to reach the contract curve. This is not always done because officials feel it may be “unfair” for some people to end up with less water than others, particularly if those people were the poorest members of the community. Behind this position is the notion that people cannot be expected to make trades that are in their own interest, and hence must be protected by not allowing them to trade at all.

Production Efficiency
In an Edgeworth box for production, the length and width represent amounts of the respective inputs. Each point in the Edgeworth box shows the allocation of the inputs between the two outputs. Within the Edgeworth box, isoquants can be drawn for each commodity representing the various combinations of inputs that produce the same number of units of a particular commodity. (The equivalent of indifference curves for consumption.)

The allocation of inputs is production efficient if the only way to increase the output of one commodity is to decrease the output of another commodity. The locus of production-efficient points is defined by the mutual tangencies between the two sets of isoquants.

Production Possibilities Curve
The production possibilities curve is the locus of production-efficient points, which is defined as the mutual tangencies between the two sets of isoquants. It can also be drawn on a graph with axis representing the number of units of Commodity 1 produced per year on one axis and the number of units of Commodity 2 produced per year on the other axis.

The marginal rate of transformation is the rate at which the economy can transform one output into another by shifting its resources; the negative of the slope of the production possibilities curve. MRT12=MC1/MC2 (The marginal rate of transformation for commodity 1 and commodity 2 is the ratio of their marginal costs.)

Pareto Efficiency
Allocations of commodities and inputs such that the only way to make one individual better off is to make another worse off are referred to as Pareto efficient. A Pareto efficient allocation must be consumption efficient (on the contract curve) and production efficient (on the production possibilities curve). A Pareto efficient outcome must be allocation efficient: MRT12=MRS12, i.e. the marginal rate of transformation between any two goods is equal to consumers' common value of the marginal rate of substitution between the two goods.

The utility possibilities frontier is a graph that shows the maximum amount of utility that one individual can obtain, given another's level of utility.

A Pareto improvement is a reallocation of resources that makes at least one person better off without making anyone else worse off.

The First Fundamental Theorem of Welfare Economics
First Welfare Theorem: As long as producers and consumers act as price takers and there is a market for every commodity, the equilibrium allocation of resources is Pareto efficient. That is, the economy operates at some point on the utility possibilities frontier.

Intuition behind the First Welfare Theorem
1. Consumption efficiency: If all people pay the same prices, then every person’s marginal rate of substitution (MRS) is equal to the price ratio. Thus, their MRSs must also be equal to each other. This is the requirement for consumption efficiency.
2. Production efficiency: If firms are price-takers in factor markets and output markets, then they all face the same price of labor (w) and price of capital (c). To minimize costs, the firm must set its marginal rate of technical substitution (MRTS) equal to the ratio of the prices of labor and capital. The same is true for any commodity. Therefore, every firm must have the same MRTS, which is the necessary condition for production efficiency.
3. Allocation efficiency: Now we have to show that the marginal rate of transformation between two commodities equals the marginal rate of substitution. We know that a profit-maximizing competitive firm produces output up to the point at which marginal cost is equal to price. Thus the marginal cost ratio of the firms is equal to the price ratio. The MRS of every person is also equal to the price ratio, so the MRS of every person is also equal to the marginal cost ratio of the two firms. We showed earlier that MRT is also equal to the ratio of marginal cost. Therefore, the MRS for each person is equal to the MRT for the two commodities.

Prices and Decentralization
An important implication of the First Welfare Theorem is that the price system allows Pareto efficiency to be achieved in a totally decentralized setting. Relative prices convey to people all of the information they need to know.

Are Competitive Prices Fair?
The first welfare theorem doesn’t say anything about fairness – it only refers to efficiency. You may or may not believe that the efficient prices are just or fair.

The Theory of the Second Best
The Theory of the Second Best states that if a first-best allocation is impossible to obtain, then a second-best allocation may involve the introduction of additional wedges between price and marginal cost.

This theory means that when one change has already been made, so that the solution is no longer Pareto efficient, it may be most efficient to make a second change. For example, normally it would be inefficient to put a tax on videotapes. However, if there is already a tax on movie tickets that cannot be removed, then adding a tax on videotapes might move consumption back towards the efficient level.

The First Welfare Theory and Total Surplus Analysis
What relationship does surplus analysis have to Pareto efficiency? Surplus maximization is consistent with a multiplicity of efficient applications. Depending on market conditions, there are a large number of possible Pareto-efficient allocations, each corresponding to a different distribution of real income.

The Second Fundamental Theory of Welfare Economics
Second Welfare Theorem: Provided that all indifference curves and isoquants are convex to the origin, for each Pareto efficient allocation of resources there is a set of prices that can attain that allocation as a general competitive equilibrium.

12.3 The Welfare Economics of Time and Uncertainty
Efficiency and Intertemporal Resource Allocation
Why don’t consumers and producers who are interested in high levels of consumption and profits now squander society’s resources so there will not be “enough” for the future? The anticipation of higher prices in the future induces owners of these resources not to dump them on the market for a quick profit.

Efficiency and Uncertainty
Markets allow people to reduce risk, because given the chance, people will trade or make deals with each other in order to reduce (or smooth) the risk they face. Another way in which market markets allow people to reduce risk is by providing opportunities for diversification. The stock market is crucial in this respect – it divides the risk of investment over a large number of people. In this way, private market may be better able than government to take on risky projects.

12.4 Welfare Economics and the Real World
Market Failure
Market Power
If some individuals are price makers (rather than price takers) then results will generally be allocated inefficiently. This is because a firm with market power may be able to raise prices above marginal cost by supplying less output than a competitor would. This can happen in a monopoly or oligopoly. It can also occur in a market with many firms, but where the product is differentiated (Calvin Klein jeans).

Nonexistence of Markets
If a market for a commodity doesn’t exist, we can’t expect the market to allocate it efficiently. Markets may be missing because of asymmetric information (one party in a transaction has information that is not available to another). One type of inefficiency due to the non-existence of a market is an externality. In the case of externalities social cost is not the same as private cost.

Market Failure and a Role for Government Intervention
Government intervention may lead to greater efficiency if it can help to solve these market failure problems.

Equity
The social welfare function is a function or schedule that shows how the welfare of society depends upon the utilities of its members. A particular Pareto-efficient allocation of resources need not be socially desirable.

Even if the economy generates a Pareto-efficient allocation of resources, government intervention may be necessary to achieve a “fair” distribution of utility.