Question

1. (10 points) Joseph has the utility function U(F,H) - 10F2H, where F is the quantity of food he consumes per year and His the quantity of housing per week. Suppose the price of food is $10 and the price of housing is $5, while Joseph has an income of $150/week. a. What can you say about the nature two goods that Joe consumes? And why so? b. Does the indifference curve exhibit diminishing marginal rate of substitution (MRS)? Provide appropriate reasons. c. Calculate Joseph's MRS as a function of the quantities F and H. Show all the work. d. What is the expression for the budget constraint?

Answer 1

A) ULFH) = lox (Fx (H) f = $10, y = 85, Ma $150. 19 Joe spends income on both goods and both goods are consumed by Joe in different proportion of their income. Also this is the case of cobb- souglas utility function and thus beth goods are normal commodities ce This is a connex-shaped indifference curve and thus the curre exhibit Marginal Rate - of indifference diminishing Housing uz lox(ExH . Food substitution. ca MRS = 20/OF = loxax&xH aulah yox (E* - 2xH F Thus, MRS of the consumer is (d) The general form of budget X. ln ty. ly = M. loxf+ SAH = 150. ginen as: 2x H constraint is ginen as- 27 TH = 30