What is the total fixed cost function for a firm with a production function Q = 4K0.5 L0.5, fixed capital of 1 unit, and capital price of $400?

To determine the total fixed cost (TFC) for the firm, we first need to clarify what total fixed cost represents. TFC consists of costs that do not change with the level of output; these are typically associated with fixed inputs in the production process, such as capital.

In this scenario, the firm is using a production function where capital (K) is fixed at 1 unit. The cost associated with capital is defined by its price, which is given as $400. Since the capital is fixed and the firm has only one unit of it, the total cost pertaining to this fixed capital is simply the price of the capital multiplied by the amount used.

Thus, TFC can be calculated as follows:

[ TFC = \text{Price of Capital} \times \text{Quantity of Capital} = 400 \times 1 = 400. ]

This indicates that the total fixed costs for this firm are indeed $400, aligning perfectly with what is expected given the parameters of the problem.

This understanding of total fixed costs is crucial in microeconomics as it lays the foundation for distinguishing between fixed and variable costs, enabling firms and economists to analyze cost structures effectively.