Suppose that the hourly output of chili at a barbecue (q, measured in pounds) is characterized by

q = 20√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 = 2,000 pounds per hour is oquant.

b. The point K = 100, L = 100 is one point on the q = 2,000 is oquant. What value of K corresponds to L = 101 on that is oquant? What is the approximate value for the RTS at K = 100, L = 100?

c. The point K = 25, L = 400 also lies on the q = 2,000 is oquant. If L = 401, what must K be for this input combination to lie on the q = 2,000 is oquant? What is the approximate value of the RTS at K = 25, L = 400?

d. For this production function, the RTS is

RTS = K/L

Compare the results from applying this formula to those you calculated in part b and part c. To convince yourself further, perform a similar calculation for the point K = 200, L = 50.

e. If technical progress shifted the production function to

q = 40 √KL

all of the input combinations identified earlier can now produce q = 4,000 pounds per hour. Would the various values calculated for the RTS be changed as a result of this technical progress, assuming now that the RTS is measured along the q = 4,000 is quant?