The hourly output of chili at my barbeque business (measured in quarts) has the production function:
q = 20*KL

where K is the number of large pots used each hour and L is the number of worker hours employed. Pot rental costs $2/hour and worker wages are $8 per hour.

a. Graph the isoquant for which q = 2000 quarts of chili.
b. For this production function, RTS = K / L. (I will show you how to find this yourself in a future lecture, but for now it is given.). If I know that I want to produce 2000 quarts of chili, what combination of pots and workers should I use to minimize my costs? (Note that you will need to use the production function, plugging in 2000 for q and solving in terms of K or L, to plug into the cost-minimization expression in order to solve this).
c. How much will I spend if I do production this way?
d. What should I choose for K and L if I instead want to produce q = 4000? What does this tell me about returns to scale for this technology?
e. Suppose I find a way to improve the technology (fast-cooking beans perhaps?) so that my new production function is:
q = 40*KL
What are my cost-minimizing choices of K and L that will produce my original q = 2000?