Consumer Choice: Maximizing Utility Ch. 18, R.A. Arnold, Economics 9th Ed

Utility Theory In this chapter we study the household (consumer). The aim of households is to maximize utility i.e. They want to obtain the highest amount of utility from their limited income (or resource) Utility: Means satisfaction, happiness or benefit that results from the consumption of a good Utils: Are numbers that measure happiness or satisfaction. If the first cup of tea gives you 10 utils and the second cup gives you 9 utils. It means you get more satisfaction (utility) from the first cup of tea as compared to the second cup. Why? Can a theory explain this?

Law of Diminishing Marginal Utility The marginal utility (MU) gained by consuming equal successive units of a good will decline as the amount consumed (Q) increases during a given period of time. In symbols: if Q ↑ then MU ↓ This law explains why the first cup of tea makes us more happy than the second one. In the definition above, marginal utility (MU) is the additional satisfaction we obtain from consuming one more unit of a good (e.g. one more cup of tea). The MU1st cup = 10 and MU2nd cup = 8. What could be MU3rd cup ? Ans: MU3rd cup < MU2nd cup

Consumer Equilibrium: Maximizing Utility Here, we see how a household (consumer) maximizes utility Constraint of household: limited (fixed) income (budget) We are assuming that the household is consuming all of their income on 10 apples and 10 oranges per week. The price (P) of each apple = $1 and the price (P) of each orange = $1. What is the households total income per week? Also given, MU oranges = 30 utils and MU apples = 20 utils According to Economic theory consumers make purchasing decisions by comparing the marginal utility per dollar from different goods

Here we can see, (MU orange ÷ P orange ) > (MU apple ÷ P apple) This means the household can get more marginal utility per dollar from oranges as compared to apples. So the household should buy more oranges to increase their utility. But since they are consuming all of their limited income, they have to reduce the consumption of apples, to buy more oranges. If the household buys more oranges then we know the MU from oranges will fall. Here when the household buys 1 more orange, MU from orange falls to 25 utils. And as they buy 1 less apple, MU from apples increases to 25 utils. Now, (MU orange ÷ P orange ) = (MU apple ÷ P apple). The household is maximizing its utility and they have no further incentive to change their consumption. The household is in equilibrium. At equilibrium they are consuming 11 oranges and 9 apples.

Maximizing Utility and the Law of Demand At the end of last slide, the household had reached equilibrium and it was maximizing utility i.e. (MU from oranges ÷ P of oranges) = (MU from apples ÷ P of apples) Now, if the price of apple falls then, (MU from oranges ÷ P of oranges) < (MU from apples ÷ P of apples) So the household increases their consumption of apples (since they get more marginal utility per dollar from apples) and reduces their consumption of oranges. This is consistent with the theory of demand which tells us if P of a good (apple) falls then the quantity demanded of (apple) rises.