In this module, it is demonstrated that sometimes extensive diseconomies of scale, say, due to high transportation costs, would require that the firm produce its product in a multiple of plants. Suppose a beer brewing company has determined that its total production cost is: TC = 1000 Q - 1.2 Q2 + 0 .004Q3 where Q is its annual output measured in metric tons.
A. The average hauling (freight) cost is $0.8Q; that is AFC = 0.8Q. Write the firm's average aggregated cost equation.
B. Now suppose the firm is facing the following market demand: Q = 760,000 - 10 P Determine the optimal number of plants that the firm should have to take full advantage of the market demand.
C. Calculate the firm's profit.
For 5 extra bonus points: D. Compare the firm's profit with multiple plants with its profit with a single plant.
Hint: The firm's MC equation based on its aggregated total cost (including the freight cost) is: MC = 1000 - 0.8 Q + 0 .012 Q2