The problem describes a production function for coffee $C = min(B, W)$, where $B$ is coffee beans in pounds and $W$ is water in gallons. The price of water is $0.10 per gallon and the price of coffee beans is $10 per pound. We need to determine what the expansion path depends on.

1. Problem Description

The problem describes a production function for coffee $C = min(B, W)$, where $B$ is coffee beans in pounds and $W$ is water in gallons. The price of water is $0.10 per gallon and the price of coffee beans is$10 per pound. We need to determine what the expansion path depends on.

2. Solution Steps

The production function $C = min(B, W)$ implies that coffee is produced using coffee beans and water in fixed proportions (1:1). This is a Leontief production function. To produce one unit of coffee, you need exactly one unit of coffee beans and one unit of water.

The expansion path is the path along which the firm expands its production as its budget increases. It shows the cost-minimizing combinations of inputs (coffee beans and water) for each level of output.

Since the inputs are used in fixed proportions, the cost-minimizing input ratio will always be $B = W$. Let $P_B$ be the price of coffee beans ($10) and$P_W$be the price of water ($0.10).

The total cost of producing $C$ units of coffee is $TC = P_B * B + P_W * W$.

Since $B = W = C$, $TC = P_B * C + P_W * C = C * (P_B + P_W)$.

The total cost depends on both $P_B$ and $P_W$.

Therefore, the expansion path depends on both the cost of beans and the cost of water because the optimal ratio $B=W$ depends on the ratio of the two prices.

3. Final Answer

d. depends of the costs of both beans and water.