Suppose that the hourly output of chili at a barbecue (q measured in pounds) is characterized by: = 20SQRT(KL) , Where K is the number of large pots used each hour and L is the number of worker hours employed.
a) Graph the q=2000 pounds isoquant.
b) Calculate the rate of technical substitution at the point K=100, L=100 and interpret the result. Repeat the calculation for K=25 and L=400.
c) What is the minimum cost of achieving production level of 2000 pounds, if capital rents are $10 per hour and wages are $10 per hour? What is the optimal combination of inputs that the firm should use?
d) Technical progress shifted the production function to = 40SQRT(KL). Graph the new isoquant q=2000 on the same graph as above.
e) What is the minimum cost of achieving production level of 2000 associated with the new production function (assume capital rent and wages stay the same)? What is the optimal combination of inputs that the firm should use? Compare your results with those obtained at point c) above and explain the effect of technical change.