Question

John has preferences for food F and clothing C described by a utility function U(F,C) = min (F, 2C). Suppose that food costs $1 a unit and that clothing costs $2 a unit. John has $12 to spend on food and clothing. (10 pts.) a) On a graph, draw indifference curves corresponding to u = 6, u = 10, u = 14. Make sure to label coordinates clearly. Using the graph, find the optimal choice of food and clothing. Let the amount of food be on the horizontal axis and the amount of clothing be on the vertical axis. (5 pts.) b) c) What is the marginal rate of substitution of food for clothing at his optimal basket? Show this graphically and algebraically. (2 pts.) Suppose John decides to buy 4 units of food and 4 units of clothing with his $12 budget. Would his marginal utility per dollar spent on food be greater than or less than his marginal utility per dollar spent on clothing? What does this tell you about how he should substitute food for clothing if he wanted to increase his utility without spending any more money? (3 pts.)

Answer 1

-ICI=Uzlo -Ilo=u=6 3 Budget line 6 1 2 Budget F+22=12 At optimality +=20 rc=3 418-6 uc=12 b) MR S = MUG Muc Ž = ' Дс Graphically 6 12 M- AF الوع budget =12 4 und off 4 4 unit of C Mucro Mur=1 This producomon f 4 less e Yes, substitute for c. nader to maximisi utility 4 final conspn should be (= 34 F-6