Final answer:
The slope of the isocost line is negative and calculated by the ratio of the prices of two production inputs, representing the trade-off and opportunity cost between them.
Step-by-step explanation:
The slope of the isocost line represents the ratio between the prices of two inputs in production, commonly labor and capital. This slope is inherently negative, indicating a trade-off between the quantities of inputs that can be purchased given a certain cost constraint. Specifically, it is calculated by dividing the price of the input on the horizontal axis by the price of the input on the vertical axis. For example, if the price of bus tickets (on the horizontal axis) is $0.50 and the price of burgers (on the vertical axis) is $2, the slope would be 0.25. This also reflects the opportunity cost of substituting one good for another in production.
The negative slope of the isocost line signifies the inverse relationship between the two input factors' prices and underlines the firm's cost-minimization strategy in choosing input combinations for production.