Economists use utility functions to assess the degree of utility or satisfaction consumers receive from consuming goods and services.

The functions are derived using regression techniques and measure satisfaction in hypothetical units called “utils.” A consumer's utility function is estimated to be U = 5X2Y0.2, where X and Y are two consumer goods.

a. Based on returns to scale, by how much will utility rise if the consumption of X and Y is doubled?

b. If the consumer is consuming eight units of X and four of Y, what is his total utility? Calculate utility if 16 units of X and eight units of Y are consumed. Does this agree with your answer in part A?

c. What are the elasticities for both X and Y? Calculate and interpret.