Giffen good. A penurious graduate student has a food budget of $100.00/week. To survive with sufficient energy to attend classes, he knows that he needs to consume 50 protein units per week. The only two foods he can stand to eat on a regular basis are beans and hamburger. He derives twice as much pleasure per protein unit from eating hamburger as he does from beans.

a. Assume that hamburger costs $3.00 per protein unit and beans cost $1.00 per protein unit. Formulate the student’s diet problem as a linear program. (You can assume he wants to maximize his total utility from his diet and that he gets 1 utile from each protein unit of beans he consumes and 2 utiles from each protein unit of hamburger.) What is the optimal consumption of beans and hamburger in this case?

b. Plot the student’s price-response function for beans as the price of beans goes from $0.01 to $2.00 per protein unit, assuming that everything else (including the price of hamburger) stays constant. Note that his individual price-response function is indeed upward sloping. Why? What happens when the price of beans exceeds $2.00 per unit?

c. The student receives a scholarship that enables him to spend $300 a week on food. What is his price-response function for beans now?