How do you measure the social welfare of a market outcome under Pareto efficiency?

1 Social welfare functions

One way to measure the social welfare of a market outcome under Pareto efficiency is to use a social welfare function (SWF). A SWF is a mathematical function that assigns a numerical value to every possible allocation of resources, based on some criteria or preferences. For example, a utilitarian SWF would add up the utilities of all the agents, while a Rawlsian SWF would maximize the utility of the worst-off agent. A SWF can capture different notions of fairness, equity, and efficiency in a society.

2 Pareto optimality and trade-offs

However, using a SWF to measure the social welfare of a market outcome under Pareto efficiency is not straightforward. First, you need to specify the SWF, which may involve making some normative judgments or assumptions about the social preferences. Second, you need to compare the SWF values of different allocations, which may not be unique or well-defined. Third, you need to account for the possibility of Pareto improvements or trade-offs, which are changes in the allocation that make some agents better off and no one worse off. A Pareto optimal allocation is one that cannot be improved by any Pareto improvement.

3 Edgeworth box and contract curve

One way to illustrate the Pareto optimality and trade-offs of a market outcome under Pareto efficiency is to use an Edgeworth box and a contract curve. An Edgeworth box is a graphical representation of the feasible set of allocations for two agents who exchange two goods. The contract curve is the locus of points in the Edgeworth box that are Pareto optimal. The contract curve shows the potential gains from trade and the trade-offs between the agents' utilities. The market outcome under Pareto efficiency is one point on the contract curve that depends on the initial endowments and the prices of the goods.

4 Social indifference curves and social optimum

Another way to illustrate the Pareto optimality and trade-offs of a market outcome under Pareto efficiency is to use social indifference curves and a social optimum. A social indifference curve is a curve that represents the combinations of utilities of two agents that yield the same SWF value. A social optimum is a point on the contract curve that maximizes the SWF value. The social optimum shows the best possible allocation for a given SWF. The market outcome under Pareto efficiency may or may not coincide with the social optimum, depending on the shape and position of the social indifference curves.

5 Efficiency and equity

The main challenge of measuring the social welfare of a market outcome under Pareto efficiency is to balance the trade-offs between efficiency and equity. Efficiency refers to the maximization of the total output or utility from a given set of resources. Equity refers to the fairness or justice of the distribution of the output or utility among the agents. A Pareto efficient allocation is not necessarily equitable, and an equitable allocation is not necessarily Pareto efficient. Therefore, measuring the social welfare of a market outcome under Pareto efficiency requires making some value judgments or trade-offs between efficiency and equity.

6 Applications and limitations

Measuring the social welfare of a market outcome under Pareto efficiency has some applications and limitations in economics. On one hand, it can help evaluate the efficiency and equity of different market structures, policies, or interventions. It can also provide some insights into the role of incentives, information, and institutions in shaping the market outcomes. On the other hand, it can be unrealistic, incomplete, or controversial in some cases. It can ignore some important factors, such as externalities, public goods, or behavioral biases, that affect the social welfare. It can also face some ethical, political, or practical challenges in defining and implementing the SWF.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?