In this module, it is demonstrated that some times extensive diseconomies of sca

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. 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

Explanation / Answer

A) AFC = 0.8Q so FC = 0.8Q2

Aggeragted cost AC = TC+FC = 1000 Q - 1.2 Q2 + 0 .004Q3 + 0.8Q2

AAC = 1000-0.4Q+0.004Q2

B) In long run AAC=MC

1000-0.4Q+0.004Q2=1000-0.8Q+0.012Q2

0.4=0.008Q

so Q = 50 per plant

MC = 100-0.8*50+0.12*50*50 = 990

P=MC so P=990

Now Market demand Q=760000-10P = 750100

So no of plant = 750100/50 = 15002

C) Firm Profit = (MR-MC)*Q = (990-990)*50= 0

D) The firm profit with multiple plant and single plant both are zero as P=MC

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