Econ 221 Chapter 5 handout Part 1: “The Utility-Maximizing Rule” This is not due for a grade
Definitions:
Utility is the satisfaction derived from the consumption or use of a good or service. Utility is a subjective measure, because one person’s satisfaction may be different from that of another individual. Because satisfaction is difficult to describe in quantifiable terms, we discuss measures of utility in arbitrary units. The term “utils” is often used to describe a unit of utility. This is a bit goofy, so we’ll just use “units of utility” to describe satisfaction. Soon we’ll dispense with the need for arbitrary units by putting utility in dollar terms.
Total Utility (TU) is the total satisfaction or enjoyment realized by a consumer for a given quantity of a good or service. E.g.: if you consume 2 slices of pizza, the total utility is the sum of the satisfaction from both slices.
Marginal Utility (MU) is the additional (extra, incremental) satisfaction realized from the consumption of another unit of the good. E.g.: if you consume a third slice of pizza the marginal utility is the extra utility derived from only the third slice. Hence the marginal utility is the change in total utility for each one-unit change in quantity.
Total Benefit (TB) is the dollar value of the satisfaction realized from the consumption of a given quantity of a good or service. Hence total benefit simply expresses total utility in monetary terms.
Marginal benefit (MB) is the additional dollar benefit from the consumption of an additional unit of a good or service. Hence marginal benefit simply puts marginal utility in monetary terms. Marginal benefit is the change in total benefit for each one unit change in quantity. Marginal benefit also represents the maximum willingness to pay for each unit of a good or service.
Net Benefit (NB) is the difference between marginal benefits and marginal costs. If MB is greater than MC, then net benefits are positive. IF MC is greater than MB, then net benefits are negative.
Application: Understanding the Utility Maximizing Rule (also known as the “Equimarginal Principle”) Consider your monthly purchases of two goods: CD’s and Movies. For this example, assume that the price of a CD is $10, the price of a movie is $5, and your monthly income of $65 is spent entirely on these two goods.
# movies TUM MUM MUM/$spent #CDs TUCD MUCD MUCD/$ spent 0 0 - - 0 0 - -
1 20 1 50
2 38 2 85
3 53 3 110
4 65 4 130
5 75 5 145
6 83 6 155
7 90 7 161
→ Does the law of diminishing marginal utility apply to the consumption of CD’s and movies?
Given that the price of a CD is $10, and the price of a movie is $5, and your monthly income of $65 is spent entirely on these two goods, use the space below to draw a budget line for the consumption of these two goods. For each of the listed numbers of movies, determine the number of CD’s it is possible to consume. For combinations 1 through 4 determine the total utility.
CD’s Combination Movies CD’s Total U 1 1 2 3 3 5 4 7
Movies
Spending income 1 purchase at a time:
Purchase options mu/$ choice $ spent on choice total income gone 1
2
3
4
5
6
7
8
Final consumption bundle for the month =
Econ 221 Chapter 5 handout Part 1: “The Utility-Maximizing Rule” … continued
The utility-maximizing rule (also known as the “equimarginal principle”) states that total utility from the consumption of two or more goods is maximized when the marginal utility per dollar spent is the same for all goods, and all income is spent. → Write a general formula for the utility maximizing rule (equimarginal principle) for goods “A” and “B”
Consumer Equilibrium is attained when the utility-maximizing bundle of goods is purchased and all other things are held constant. In other words, by following the equimarginal principle, consumers reach an equilibrium.
→ Why is consumer equilibrium an equilibrium?
→ Write an equation applying the equimarginal principle for the above case of CDs and movies, and use that equation with the above data to find the utility maximizing quantity of these two goods.
→ Now, assume that upon reaching the 8th purchase decision, instead of having $15 left to spend, you only have $10. What will you spend the remaining income on?