Suppose the production function for coffee (C)is C = min(B,W)where B = beans in pounds and W = water in gallons and the price of water is $.10 per gallon and the price of beans is $10 per pound.The expansion path is
A) B = 10W
B) B = .1W
C) B = W
D) -10 = B + W

Question

Quizplus · Accepted Answer

The production function is C = min(B,W), which means the quantity of coffee produced is limited by whichever input (beans or water) is in shorter supply. Given the prices of beans and water, we want to minimize the cost of producing a given quantity of coffee. The cost-minimizing combination of inputs occurs where the marginal cost of beans is equal to the marginal cost of water, which is 10 times the price ratio of beans to water. Since the price ratio is 10 to 1, the equation for the expansion path is B = W. Therefore, the best choice is to use equal amounts of beans and water, since that would minimize costs while still satisfying the production function.

Suppose the Production Function for Coffee (C)is C = Min(B,W)where