In this module, it is demonstrated that some times extensive diseconomies of sca
ID: 1100797 • Letter: I
Question
In this module, it is demonstrated that some times 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.
Explanation / Answer
Avg Production cost = 1000-1.2Q+.004Q^2
Avg Freight cost = .8Q
Avg aggregate cost = .8Q+1000-1.2Q+.004Q^2
= 1000+2Q+.004Q^2
Revenue = (76000-Q/10)*Q
for profit maximization
MR = MC
MR = 76000-Q/5
TC = 1000Q+2Q^2+.004Q^3
MC = 1000+4Q+.004*3*Q^2
MR = MC
76000-Q/5 = 1000+4Q+.012Q^2
75000 = 4.2Q+.012Q^2
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