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 monthlytotal production cost is: TC = 100 Q - 1.2 Q²+ 0 .004Q³  whereQ is its monthly output measured in kegs.

A. The average hauling (freight) cost is $0.8Q;that is: AHC = 0.8Q. Write the firm'saverage aggregated cost equation.

B. Now suppose the firm is facing the following market demand:

                                                                                 Q = 4,000 - 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 = 100 - 0.8 Q + 0 .012 Q²

Answer 1

A.

The complete Cost condition including the frieght cost will be (Add the cargo cost which is given as 0.8Q for every unit and thus TC will be 0.8Q per unit * (Q units) = 0.8Q^2

TC = 1000Q-1.2Q^2+0.004Q^3 + Q(0.8Q) = 1000Q + Q^2(- 1.2+0.8) + 0.004Q^3 = 1000Q - 0.4 Q^2 + 0.004Q^3

B.

The ideal benefit happens when the negligible expense is equivalent to minimal income.

To get the negligible cost condition, simply separate the Total Cost condition,

At that point you get 1000 + 2*(0.4Q) + 3*(0.004Q^2) = 1000 + 0.8Q + 0.012Q^2

The complete income is Price * Quantity = P*(760,000-10P) = 760,000 P - 10 P^2

Henceforth Marginal income (separating Total Revemue) is 760,000-2(10P) = 760,000-20P

Henceforth the crossing point of both the bends can be gotten and fathomed for Q.

You get 7961 as one postive root and that ought to be the ideal generation.

Substituting that P = (7691 - 760000)/ - 10 = 75203.9

C.

The benefit will be TR - TC

= 760,000 P - 10 P^2 - (1000Q - 0.4 Q^2 + 0.004Q^3)

D .

Additional data is expected to contrast and various areas and single area to discover drawback of transportation costs.

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