[15] Consider the operator of a small newsprint production plant. He has fixed c

Question

[15] Consider the operator of a small newsprint production plant. He has fixed costs of $1600 per day for property taxes, interest on debt, etc., and has additional costs that vary with the amount Q of newsprint he produces. His total costs per day are given by: 3. C 160040Q3/2 He sells his output to local newspaper publishers and the price he obtains depends on how much he tries to sell. Let the demand curve he faces be -100512Q-1/2 a) What are his average and marginal costs of production expressed as functions of Q? b) What are his total and marginal revenues expressed as functions of Q? c) How much output per day should he produce if he expands production just to the point where marginal revenue equals marginal cost? What profit if any will he make in $/day?

Explanation / Answer

a)

Average Cost = C/Q = 1600/Q + 40 + 2/3 x Q1/2

Marginal Cost = dC/dQ = 40 + Q1/2

b)

Total Revenue = P x Q = 100Q + 512Q1/2

Marginal Revenue = d(P x Q)/dQ = 100 + 256Q-1/2

c)

MR = MC

100 + 256Q-1/2 = 40 + Q1/2

Q0.5 - 256Q-0.5 = 60

Square both sides:

Q + 2562/Q - 512 = 3600

Q = 4096 and P = 108

Profit = P x Q - C = $102165.3

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