Final answer:
To create a Cost Function for a firm that only uses labor, one would need to use the production function to find the needed labor for a certain output, and then multiply it by the labor cost per unit. At a specific level of output, the total cost is calculated by applying the identified labor requirement specific to that output level multiplied by the labor cost per unit.
Step-by-step explanation:
To write out a Cost Function for a firm whose only input is labor, you would first need to determine the production function of the firm. This production function specifies the quantity of output produced for a given amount of labor input. Once the production function is known, we can reverse this relationship to figure out the quantity of labor needed to produce a specific level of output. The cost function can then be constructed by multiplying the quantity of labor required by the cost per labor unit.
For example, if a firm's production function is given by Q = f(L), where Q is the quantity of output and L is the quantity of labor, and if the cost per labor unit is w, then the cost function is TC = w * L(Q). For a specific level of output, say Q0, the firm would need L(Q0) units of labor. Therefore, the total cost to produce Q0 units of output would be TC = w * L(Q0).