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 ich 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 I utile from each protein unit of beans he consumes and 2 utiles from each pro- tein unit of hamburger.) What is the optimal consumption of beans and ham- burger in this case? b. Plot the student's price-response curve for beans as the price of beans goes from $0.01 to $2.00, 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?
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 ich 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 I utile from each protein unit of beans he consumes and 2 utiles from each pro- tein unit of hamburger.) What is the optimal consumption of beans and ham- burger in this case? b. Plot the student's price-response curve for beans as the price of beans goes from $0.01 to $2.00, 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?
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