a. What is the marginal benefit to Wimpy of the first burger consumed? 5

b. What is the marginal benefit to Wimpy of the 4th burger consumed? 1

c. Suppose the price is $2 per burger. How many burgers will Wimpy consume? 3

d. What is the total benefit accruing to Wimpy from the burgers consumed in part c? 10

e.  What is the cost to Wimpy of buying the burgers consumed in part c? 2x3 = 6

f. What is his net benefit?  10-6 = 4

g. If the price falls to $1 per burger, how many will Wimpy consume? 4

h. Now what is his net benefit?  11 - 4 = 7

2.  Blanche duBois likes to ride the streetcar. She also likes to listen to sultry records. Her utility from these activities is given by

U = 5*S*R

Blanche has an income of $25. Rides on the streetcar are $1.25 each, and records are $6 each. This means that her budget constraint is given by

25 = 1.25*S + 6*R

Solve the budget for S to get S = (25-6*R)/1.25 or S = 20-4.8R.  Plug this into Blanche's utility function to get U = 5*((25-6*R)/1.25)*R, or U = 100R - 24 R².  You will recognize this as a quadratic in R, or a parabola.  You can use your graphing calculator or EXCEL to graph this and see that the maximum occurs where R = 2.083. Plug that back into the budget to get S = 10.002.

Alternatively, you know from Stat 11/12 that the maximum occurs where the slope is zero.  The slope of U is given by its derivative with respect to R. That is, derivative = slope = 100 - 48R.  Set the derivative equal to zero and solve for R.

How should Blanche allocate her $25 between records and streetcar rides?

Hint: Solve the budget constraint for S. Now plug your equation for S into her utility function.  You now have utility as a function of just R.   What value of R makes U as great as possible?  Plug that value of R back into the budget constraint to get S.

Alternatively, you can use "guess and check". Try some test numbers and check to see if you have spent all of Blanche's money.