Consumer Theory

 

 

Consumer Theory Made Much Too Simple

 

 

00. Level Set

A set of points that have the same height. For example, all the locations on Mt. Rose that are 8,000 feet above mean high tide. For our purposes, consider the equation in 3 space x1 = 20 + 6.67 x2 + 10 x3 - .5 x32. Take x1 to be height. The model shows the surface in three space. The red lines on the model show points (x2,x3) that have the same height. The red lines are the level sets.

0. A bundle

is a collection of goods (e.g., 2 apples, 3 green beans). In an economy with n goods, a bundle has n elements, some of which may be zero.

 

1. Assume that people have preferences over bundles.

Any two bundles A and B can be ranked as A better than/worse than/or indifferent to B. The preferences are assumed to have the following reasonable properties: I. More is better. If bundle A has strictly more of one good and does not have less of any good than bundle B, then all consumers prefer A to B. II. Transitivity. A better than B better than C means A better than C. III. A preferred to B means B is not preferred to A.

 

2. We summarize our beliefs about individuals preferences in indifference curves.

Two bundles are said to be indifferent (for a particular consumer) if the consumer is equally happy with either bundle. (Note that, if one added the teeniest bit of any good to one of the bundles, then the consumer would prefer it.) Let A ~ B be read as the consumer is indifferent between A and B. The indifference curve through A is the set of all bundles that makes the consumer just as happy as bundle A. In math speak {B: A ~ B}. There is an indifference curve through every bundle, because we assumed that people have preferences over all bundles.

 

3. Indifference curves (for a particular consumer) have the following properties.

They slope down. They do not cross. Higher indifference curves are better. For reasons that I don't care to discuss, I always draw them so that they look like a crescent moon.

 

 

 

4. Consumers can choose anything on or under their budget constraints.

Those are the only things that they can afford. Consumers will choose the bundle that they can afford that is on the highest possible indifference curve. This will occur where an indifference curve is tangent to the budget constraint. No point on the upper indifference curve lies on the budget the constraint. The consumer might like it but can't afford any such bundle. All points on the lower indifference curve are inferior to the middle indifference curve, so the Preferred and Affordable bundle must lie on the middle curve. There is only one affordable bundle on the middle curve, so that bundle (at the tangency) is the best bundle that the consumer can afford. Note that the "tangency bundle" is a bundle, an amount of both goods.

 

 

 

5. The food stamp example

shows two different budget constraints, one with and one without the food stamp program. You can draw indifference curves that make the consumer better off (higher indifference curve) with the program or without. Since consumers try to maximize happiness (get on highest possible indifference curve), you can draw the picture so that the consumers will (or will not) decide to participate in the program.

 

 

6. An increase in income shifts budget constraints up in a parallel fashion.

(x2 = y/p2 -p1/p2 x1; slope-intercept. change in y does not change slope but increases intercept.)

 

7. Inferior and Normal

If you experiment with indifference curves and budget constraints, you will discover that you can draw a picture where an increase in income leads to a decrease in the amount of one of the goods. Such a good is called an inferior good. You could also draw the picture so that amount of both goods increases. One buys more of a normal good as income increases. (Why can't all goods be inferior?)