5. Electron Control, Inc., a manufacturer of voltage regulators for industrial p

Question

5. Electron Control, Inc., a manufacturer of voltage regulators for industrial power generators, currently consolidates production at a single plant in Chattanooga, Tennessee, but a multiplant alternative to centralized production is being considered. Estimated demand, marginal revenue, and single-plant production cost curves for the firm are

P = 515 0.005Q
MR = 515 0.01Q
TC = 160,000 + 35Q + 0.01Q2

MC = 35 + 0.02Q

A) Find the single-plant profit-maximizing level of output.

B) Find the minimum efficient scale of the single-plant operation.

C) Assuming that multiple smaller plants production is possible under the same cost conditions described above, find the profit-maximizing multiplant level of output.

D) Given your answers to parts B and C, how many number of plants should you suggest?

Explanation / Answer

A) single-plant profit-maximizing level of output can be determined when MR = MC

    515 0.01Q = 35 + 0.02Q

     0.03Q = 480

           Q = 16000 units

B) Minimum Efficient Scale is the name given to the size of a firm when it is achieving the lowest possible        Long-Run Average Costs.

TC = 160,000 + 35Q + 0.01Q2  

    Average Cost (AC) = 160,000 + 35Q + 0.01Q2 / Q = 160000/Q + 35 +0.01Q

Average cost will be minimum when the first derivative of AC function is equal to 0.

d(AC)/dQ = -160000Q-2 + 0.01 = 0

Solving the above equation for Q, we get

    Q = 4000 units   (MES)

C) he profit-maximizing multiplant level of output = 16000 units

D) If each firm will produce equal amount and operates at MES, then 4 no. of firms are suggested

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