To Understand Marginal Utility, We First Must Understand Utility:
Before we can delve into marginal utility, we first need to understand the basics of utility. The Glossary of Economics Terms defines utility as:
U(x) = 2x + 7, where U is utility and X is wealth
Utility is the economist's way of measuring pleasure or happiness and how it relates to the decisions that people make. Utility measures the benefits (or drawbacks) from consuming a good or service or from working. Although utility is not directly measurable, it can be inferred from the decisions that people make.Utility in economics is typically described by a utility function, such as:
U(x) = 2x + 7, where U is utility and X is wealth
Marginal Analysis in Economics:
The article Marginal Analysis describes the use of marginal analysis in economics:
From an economist's perspective, making choices involves making decisions 'at the margin' - that is, making decisions based on small changes in resources:
- How should I spend the next hour?
- How should I spend the next dollar?
Marginal Utility:
Marginal utility, then, asks how much a one-unit change in a variable will impact our utility (that is, our level of happiness. Marginal utility analysis answers questions such as:
- How much happier, in terms of 'utils', will an additional dollar make me (that is, what is the marginal utility of money?)
- How much less happy, in terms of 'utils', will working an additional hour make me (that is, what is the marginal disutility of labor?)
Calclulating Marginal Utility Without Calculus:
Suppose you have the following utility function:
U(b, h) = 3b * 7h
where:
b = number of baseball cards
h = number of hockey cards
And you're asked "Suppose you have 3 baseball cards and 2 hockey cards. What is the marginal utility of adding a 3rd hockey card?"
First step is to calculate the marginal utility of each scenario:
U(b, h) = 3b * 7h
U(3, 2) = 3*3 * 7*2 = 126
U(3, 3) = 3*3 * 7*3 = 189
The marginal utility is simply the difference between the two: U(3,3) - U(3, 2) = 189 - 126 = 63.
where:
b = number of baseball cards
h = number of hockey cards
And you're asked "Suppose you have 3 baseball cards and 2 hockey cards. What is the marginal utility of adding a 3rd hockey card?"
First step is to calculate the marginal utility of each scenario:
U(b, h) = 3b * 7h
U(3, 2) = 3*3 * 7*2 = 126
U(3, 3) = 3*3 * 7*3 = 189
The marginal utility is simply the difference between the two: U(3,3) - U(3, 2) = 189 - 126 = 63.
Calclulating Marginal Utility With Calculus:
Using calculus is the fastest and easiest way to calculate marginal utility. Suppose you have the following utility function:
U(d, h) = 3d / h
where:
d = dollars paid
h = hours worked
Suppose you have 100 dollars and you worked 5 hours; what is the marginal utility of dollars? To find the answer, take the first (partial) derivative of the utility function with respect to the variable in question (dollars paid):
dU/dd = 3 / h
Substitute in d = 100, h = 5.
MU(d) = dU/dd = 3 / h = 3 /5 = 0.6
That is how we calculate marginal utility. If you have any questions, please leave them at this blog entry.
d = dollars paid
h = hours worked
Suppose you have 100 dollars and you worked 5 hours; what is the marginal utility of dollars? To find the answer, take the first (partial) derivative of the utility function with respect to the variable in question (dollars paid):
dU/dd = 3 / h
Substitute in d = 100, h = 5.
MU(d) = dU/dd = 3 / h = 3 /5 = 0.6
That is how we calculate marginal utility. If you have any questions, please leave them at this blog entry.