Suppose the production function for coffee (C)is C = min(B,W),where B = beans in pounds and W = water in gallons. Suppose 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 costs, we need to choose the input that is cheaper per unit. 
- Cost of beans = $10 per pound 
- Cost of water = $0.10 per gallon

For C = 200, we want to produce exactly 200 units of coffee. Using the production function, we can write: 
C = min(B,W) 
200 = min(B, W)

Since we want to minimize costs, we need to choose the input that is cheaper per unit. In this case, water is cheaper per unit, so we should choose W to be as small as possible.

To produce 200 units of coffee, we need to use at least 200 gallons of water. If we use any less, we won't be able to produce 200 units of coffee.

So the cost-minimizing combination is: 
C = 200 
B = min(B,W) = min(200, W) 
W = 200 gallons (the minimum amount needed to produce 200 units of coffee)

We can check that this combination satisfies the production function: 
C = min(B,W) = min(200,200) = 200

The cost of this combination is: 
Cost = Cost of beans + Cost of water 
Cost = $10 per pound x B + $0.10 per gallon x W 
Cost = $10 per pound x min(200, W) + $0.10 per gallon x 200 
Cost = $10 per pound x 200 + $0.10 per gallon x 200 
Cost = $2000 + $20 
Cost = $2020

Therefore, the best choice is D, with B = 200 pounds and W = 200 gallons.

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