Utility maximization The goal of the consumer is to maximize utility given the budget constraint. Let’s see what that means.

y I show the budget line here again. What the consumer attempts to do is find the point on the budget line that will give the maximum utility. I show some arrows to get you to think about moving up and down the line in this search. x

Here I present a few ideas we think hold in the world and then we see how they show up in the graph. The consumer wants to maximize the utility, or happiness, that can be achieved when consuming goods and services. At a given level of happiness the consumer will always give up a unit of a good if on the other good in the market an amount greater than required to maintain the given level of utility is returned. The consumer will also be happier than at the start. As an example, say you are willing to take 0.9 Cokes to give up a Pepsi, and you would be as happy. If in the market when you give up a Pepsi you get 1 Coke back you then you would give up the Pepsi and be happier.

A related idea is that At a given level of happiness the consumer will always take another unit of a good if on the other good in the market an amount less than required to maintain the given level of utility must be given up. As an example, say you will take another hamburger if you give up 2 hotdogs. If the market only requires you to give up1.5 hotdogs, the you would take the hamburger and you would be happier. Note: Remember that because of the shape of the indifference curves that the amount you are willing to give up of a product (or an amount you would take) depends on how much you already have and thus changes along the indifference curve.

Utility Maximization The individual would like to get to the highest indifference curve possible, but the budget constraint restricts the individual’s options to the budget line. On the next slide let’s see what is the best the individual can do. But, before we do remember 1) indifference curves summarize how consumers are willing to trade off good x for y, and 2) the budget line shows how the consumer can trade off good x for good y.

obtained if the individual went to point a on u2. c a u3 y Utility Maximization Because of the budget line u3 can not be reached u1 can be reached at points c and b, but even more utility would be obtained if the individual went to point a on u2. c a u3 u2 u1 b x The utility associated with u2 is the maximum this person can achieve given their income and the prices they face.

Note why b from the previous screen was not the best Utility Maximization y b x Note why b from the previous screen was not the best point. To give up a unit of x and maintain the same utility the person needed to get back a certain amount of y. But the market actually gives back more y than the individual requires. This trade is beneficial. The individual would thus give up the unit of x and be happier for the trade.

Note why c from two screens ago was not the best Utility Maximization y c x Note why c from two screens ago was not the best point. To take a unit of x and maintain the same utility the person is willing to give up a certain amount of y. But the market actually requires the individual to give up less. This is a beneficial trade. The individual would thus take the unit of x and be happier for the trade.

Utility Maximization d a b c In the final analysis, the individual maximizes utility when the indifference curve is tangent to the budget line. Tangent means equal slopes. The slope of the budget line was –Px/Py and the slope of the indifference curve is the MRS, so tangency means Px/Py = MRS.