# 5.1: Introduction to the Endowment Model


This chapter introduces a wrinkle to the standard consumer theory model that greatly enhances its applicability. Instead of treating income as a given cash amount, we model the consumer as having a given initial endowment of goods that can be traded for other goods. This transforms the consumer into a combined consumer and seller.

Although the power of this approach may not be immediately obvious, we will see that a wide variety of examples such as saving/borrowing, charitable giving, and much more can be handled with this modification.

#### The Budget Constraint in an Endowment Model

Instead of the usual income (m) variable, an Endowment Model is characterized by a budget constraint that equates expenditures and revenues from sales out of the initial endowment. $p_1x_1 + p_2x_2 = p_1 \omega _1 + p_2 \omega _2$ The term on the right-hand side says that the consumer has a given amount of each good, $$\omega _1$$ and $$\omega _2$$ (this is Greek letter omega so we have omega-one and omega-two). Because the initial amounts of each good are given, $$\omega _1$$ and $$\omega _2$$ are exogenous variables.

The starting amount of each good, the coordinate pair $$\omega _1$$, $$\omega _2$$, is called the initial endowment. If we multiply the initial amount of each good by the price of that good, as done in the right-hand side of the budget constraint equation, we get a dollar-valued amount that represents the total income that can be raised by selling the entire endowment.

Thus, the budget constraint says that spending (on the left-hand side) must equal the value of the consumer’s assets (on the right-hand side).

The classic example to illustrate someone operating with an endowment model constraint is a farmer who goes to market with his crop. He sells his produce and, with the revenue obtained by selling, buys other goods. The core idea is that the farmer is a buyer and a seller.

Perhaps a more modern example is eBay. People sell all kinds of products and turn around and buy different products. It is a massive online garage-sale community. Once again, the core idea is that eBayers sell and buy.

In an Endowment Model, what the agent can buy depends on how much revenue is generated by sales. High prices for goods to be sold are a good thing from the agent’s point of view because they generate a lot of revenue with which to buy other goods.

Because Endowment Models transform the consumer into a combined buying-selling agent, we can get different results than we saw in the Standard Model. One critical difference is that price increases lead to decreases in quantity demanded (assuming the good is normal), as usual, but as price keeps rising, we can cross the zero barrier and get negative quantity demanded! We will see that the agent switches from being a buyer to being a seller. This is a key idea.

Let’s put these abstract ideas into concrete examples so we can understand what is going on with the Endowment Model.

STEP Open the Excel workbook EndowmentIntro.xls, read the Intro sheet, then go to the MovingAround sheet. Follow the instructions on the sheet to learn how we can create a budget line from a single point.

Just like the Standard Model, the agent faces a consumption possibilities frontier, also known as the budget line, that shows the feasible combinations. Bundles beyond the line are unattainable.

STEP Proceed to the Properties sheet.

#### The Endowment Model Extends the Standard Model

The Endowment Model is the Standard Model of the Theory of Consumer Behavior with an initial endowment of goods instead of cash income. This transforms the consumer into the dual-role of seller and buyer of goods. The driving force in the agent’s decision making remains utility maximization. Many of the ideas behind the Standard Model (such as equating the MRS and price ratio) carry over to the Endowment Model. Of course, the framework for presenting and understanding the model, comparative statics analysis, remains the same.

It may seem that replacing income with an initial endowment is a minor twist, but we will see that the Endowment Model enables analysis of a wide range of choice problems.

## Exercises

1. Perform a comparative statics analysis of c, the exponent on $$x_1$$, using the Comparative Statics Wizard. Use increments in c of 0.1. State the effect of changing c on $$x_1 \mbox{*}$$. Describe your procedure and take screen shots of your results as needed.

2. Use your comparative statics results to find the c elasticity of $$x_1 \mbox{*}$$ from 1 to 1.1. Show your work.

3. Use the reduced form expression in this chapter to find the c elasticity of $$x_1 \mbox{*}$$. Show your work.

4. Compare your answers from questions 2 and 3. Explain why they are the same or differ.

#### References

The epigraph is from page 188 of David M. Kreps A Course in Microeconomic Theory (1990). If you are interested in graduate study in economics, this book is worth browsing. In the preface, Kreps says (p. xv),

The primary target for this book is a first-year graduate student who is looking for an introduction to microeconomic theory that goes beyond the traditional models of the consumer, the firm, and the market.

Kreps allows that it could be used for undergraduate majors taking an "advanced theory" course or "mathematically sophisticated students," but he warns that, "The book presumes, however, that the reader has survived the standard intermediate microeconomics course."

The Endowment Model is taking us close to the next level of microeconomic theory. Google "graduate micro theory" for more advanced micro books.