Problem Set 2/ Economics 520
Spring 2000

Professor D. Weisman

1.  Suppose that Bob's marginal rate of substitution of pizza for beer is equal to 2.

     a) How many pizzas would Bob give up for 1 additional beer?

     b) How many beers would Bob give up for 1 additional pizza?

     c) Suppose Carol's marginal rate of substitution of pizza for beer is equal to 4. Does
         Carol value pizza more or less than Bob? Explain?
 

2.  Write down the equation of a utility function and construct an indifference map that corresponds to each of the following cases.

     a) Carol is always willing to give up 2 pizzas in exchange for 1 additional beer no matter
         how many pizzas and beers she has in her consumption bundle.

     b) Bob always consumes beer and pizza in fixed proportions. Specifically, If Bob has 1
         pizza, he consumes precisely 2 beers and additional beers represent no additional
         utility for Bob. Similarly, if Bob has 2 beers, he consumes precisely 1 pizza and
         additional pizzas represent no additional utility for Bob. In addition, when Bob has 4
         pizzas and 10 beers, his utility is 32.

     c)  Kathy loves pizza and is neutral toward beer (i.e., she neither likes nor dislikes beer).
         She derives 4 units of satisfaction from each pizza she consumes.
 

3. Consider the following utility functions: (1) U = 2P + 4B; (2) U = 2 min{P, 1/3B}, and (3) U = 4BP, where MUB = 4P and MUP = 4B. Let Pp = $4, PB = $2 and suppose that I = $100.

     a) Determine how many pizzas and many beers are consumed in consumer equilibrium for
         each of the utility functions?

     b) Illustrate your results in part a) graphically.
 

4. For each of the utility functions in question 3, compute the marginal rate of substitution of beer for pizza and pizza for beer when P = 10 and B = 20? Updated: 9/12/23