15.1 Introduction

OK, so here’s our story in consumer theory thus far:

• We derived a consumer’s optimal choice $(x_1^\star, x_2^\star)$ by maximizing their utility function $u(x_1,x_2)$ subject to a specific budget constraint; e.g. $2x_1 + x_2 = 12$.
• We derived a consumer’s optimal choice as a function of prices an income by maximizing their utility function subject to a general budget line $p_1x_1 + p_2x_2 = m$.
• Holding $p_2$ and $m$ constant, we analyzed the response of that bundle to changes in $p_1$ (the demand curve for good 1).
• Holding $p_1$ and $m$ constant, we analyzed the response of that bundle to changes in $p_2$ (analyzing complements and substitutes).

Today, we round out our analysis of comparative statics by seeing how the consumer’s optimal bundle responds to changes in income, holding $p_1$ and $p_2$ constant.

In doing so, we will be able to ask two important economic questions:

• For a given utility function, how does your maximum possible utility depend on your income?
• If you want to achieve a certain level of utility, how much money do you need to do so?

These questions will allow us to analyze some important policy questions, which we’ll get to on Friday:

• How much does inflation “hurt”? Conversely, how much should we be willing to pay for lower prices?
• How much should senior citizens and others on Social Security get as a cost of living adjustment?
• Could we encourage less gasoline use (and thereby fight climate change) through a combination of a high gas tax and a “freedom dividend,” as proposed by conservative economist Greg Mankiw and others?
• Could we fund the U.S. Government through tariffs only, and abolish the income tax? (We might not have time to get to this one, so spoiler alert: no.)

But before we get to that juicy stuff, let’s introduce a new visualization technique that will help us with these analyses: offer curves.