solution

Recent research by economists David Cutler, Edward Glaeser, and Jesse Shapiro on Americans’ increasing obesity points to improved technology in the preparation of tasty and more caloric foods as a possible explanation of weight gain. Before World War II, people rarely prepared French fries at home because of the significant amount of peeling, cutting, and cooking required. Today, French fries are prepared in factories using low-cost labor, shipped frozen, and then simply reheated in homes. Paul consumes two goods: potatoes and leisure, N. The number of potatoes Paul consumes does not vary, but their tastiness, T, does. For each extra unit of tastiness, he must spend p_t hours in the kitchen. Thus, Paul’s time constraint is N + p_tT = 24. Paul’s utility function is U = TN^0.5.

a. What is Paul’s marginal rate of substitution, MU_T /MU_N?

b. What is the marginal rate of transformation, p_T / p_N?

c. What is Paul’s optimal choice, (T*, N*)

d. With a decrease in the price of taste (the ability to produce a given level of tastiness faster), does Paul consume more taste (and hence gain weight) or spend more of his time in leisure? Does a decrease in the price of taste contribute to weight gain?