** Economic Application: Marginal rate of substitution**

This application introduces the concept of **utility functions**, **indifference curves** (the contour plots of utility functions), and **marginal rates of substitution**. In particular, it is shown that using *implicit differentiation*, the marginal rate of substitution exhibited by a utility function can be expressed as a ratio of marginal utilities - something that you will see often in your studies.

#### **Economic Application Exercise **

The following quiz allows you to test your understanding of the mathematics and economics behind the concept of marginal rate of substitution. Further, the quiz includes a common example of a utility maximization problem which can be solved by using implicit differentiation.

Economic Applications Quiz 3.2