16.1 Consumer Welfare

The presentation of any economic theory generally falls into several parts:

• In the first, the economist will lay out the kind of model they’re interested in. What are the exogenous and endogenous variables? What problems are the agents in the model faced with? If it’s a model with multiple agents, what characterizes equilibrium? For our consumer theory model, that meant writing down the consumer’s utility function and budget constraint.
• In the second, they “solve” the model, either for an agent’s optimal choice or an equilibrium outcome. In this model, that meant solving for the optimal bundle as a function of prices and income.
• In the third, they examine the comparative statics of the model: how do changes in the exogenous variables translate into changes in the endogenous variables? How responsive are the endogenous variables to changes in the exogenous variables? Is there a useful decomposition that breaks down the overall changes into their component parts? This is what we’ve done for the past several chapters, analyzing demand curves, and income and substitution effects.
• Lastly, and most importantly, they examine the welfare implications of the model. This is what we have come to now.

The welfare implications of the model posit the question: now that we know how economic agents will respond to changes, how good or bad is that for them? How much does a price increase hurt them, or conversely, how much would a price decrease help them?

This is an incredibly important aspect of economic analysis, especially because it factors in a lot of important policy decisions. Think of these two examples:

• Suppose you were in charge of determining the amount of social security support senior citizens receive. Fundamentally, your job would be to maintain the standard of living for people on fixed incomes. If the prices of some goods went up, but the prices of others stayed the same, by how much would you need to increase their income to ensure that their standard of living remained the same?
• Suppose you wanted to impose a gas tax to fight climate change. This would hurt people who depend on driving their cars, so you propose a “tax and rebate” system that both increases the price of gas and then rebates the tax as a lump sum. How much of a rebate would you need to give people in order to make them just as well off as they were before the tax?

To answer these questions, let’s return to the Hicks decomposition bundle we derived on Monday. Now that we’ve done the mathematics of cost minimization, we have everything we need to find its location.