Welfare Analysis - Just Do It (Part 1: The Normative Representative Consumer)

In a previous post, I pondered some questions related to using market demand functions to make welfare statements, following broadly Microeconomic Theory by Andreu Mas-Colell, Michael D. Whinston, and Jerry R. Green (MWG).

Making welfare statements about aggregate demand revolves around a few key concepts including a positive representative consumer, a wealth distribution rule, and a social welfare function. At a high level, these concepts seem to represent the technical assumptions and characteristics that need to hold in order to make most of the basic normative theory of an intermediate microeconomics course mathematically sound or tractable for applied work. Here is a shot at some high level explanations:

positive representative consumer- at a high level, a hypothetical consumer who's utility maximization problem (UMP) facing society's budget constraint generates a market or economy's aggregate demand function.

wealth distribution rule - for every level of aggregate wealth, assigns individual wealth.

This rule or function is what allows us to write aggregate demand as a function of prices and wealth in order to move forward with the rest of our discussion about welfare analysis.

Examples given in MWG include wealth distribution rules that are a function of shareholdings of stocks and commodities which make wealth a function of the market's price vector.

social welfare function (SWF) - this assigns utility to all consumers in an economy or market. Represented below by W(.)

Maximizing Social Welfare and Defining the Normative Representative Consumer

The wealth distribution rule is assumed to maximize society's social welfare function subject to a given level of aggregate wealth. The optimal solution indicates a particular indirect utility function represented by v(p,w). A positive representative consumer whose indirect utility function is the optimal v(p,w) is a Normative Representative Consumer.

For v(p,w) to exist, we are assuming a SWF, and assuming it is maximized by an optimal distribution of wealth according to some specified wealth distribution rule.

 In the previous article I noted that some of the key assumptions required for making welfare statements based on aggregate demand (the symmetry and negative semi-definiteness of the slutsky substitution matrix) were likely not to hold in real world situations. Now it seems we are adding even more implausible assumptions? So how do economists actually 'do' welfare analysis? Stay tuned.....