Final answer:
The short run production function for Jacksonville Fish Fry Inc. with fixed capital is Q = 200L^0.5. The total short run cost function is TC = 1000 + 20L.
With 20 labors, the total cost is $1400, the output is approximately 282.84 units, and the average total cost is about $4.95 per unit; marginal cost cannot be determined with the given information.
Step-by-step explanation:
Given that capital is fixed in the short run, the production function for Jacksonville Fish Fry Inc., with capital fixed at 100 units, becomes Q = 20∙L⁰.⁵∙K⁰.⁵ with K = 100 units. Therefore, the short run production function simplifies to Q = 20∙L⁰.⁵∙(100)⁰.⁵, which is Q = 20∙L⁰.⁵∙10 or Q = 200∙L⁰.⁵.
To calculate the short run cost function as a function of output (Q), we consider both the fixed cost of capital, which is 100 units × $10 = $1000, and the variable cost of labor, which is w × L. Since the wage rate (w) is $20, the variable cost is 20L. The total cost (TC) in the short run is the sum of fixed and variable costs, TC = 1000 + 20L.
When the firm employs 20 labors, the total cost is TC = 1000 + 20×20, which calculates to $1400, and the output is given by Q = 200∙(20)⁰.⁵, which results in an output of 282.84 units (rounded to two decimal places). The average total cost (ATC) is TC/Q, which is approximately $4.95 per unit.
We cannot calculate marginal cost with the given information because marginal cost is the increase in total cost from producing one more unit of output, and we need information on total cost or total output immediately before or after producing the current output level to calculate the marginal cost.