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 cost minimizing combination of beans and water for C = 200 is
A) B = 200, W = 2000
B) B = 2000, W = 200
C) B = 100, W = 100
D) B = 200, W = 200

Question

Quizplus · Accepted Answer

To minimize cost, we need to choose the input that has the lowest cost per unit of output. In this case, the cost per unit of water is $.10 per gallon, while the cost per unit of beans is $10 per pound. Therefore, the cost-minimizing combination will involve using as much water as possible, since it is the cheaper input.

For C=200, we need to produce 200 units of coffee using the production function C = min(B,W). Since we want to use as much water as possible, we will set W = 200 gallons. Then we solve for B:

C = min(B,W) 
200 = min(B,200) 
B = 200

Therefore, the cost-minimizing combination is B=200, W=200 gallons. The total cost will be:

Cost = (10 per pound)(200 pounds) + ($.10 per gallon)(200 gallons) 
Cost = $2000 + $20 
Cost = $2020

Any other combination that produces 200 units of coffee would have a higher cost. For example, if we used only beans (B=200) and no water, the cost would be:

Cost = (10 per pound)(200 pounds) + ($.10 per gallon)(0 gallons) 
Cost = $2000 + $0 
Cost = $2000

This is more expensive than using 200 gallons of water and 200 pounds of beans.

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