# Calculating Profit Maximizing output level

Suppose that the total cost function for a single firm in a purely competitive industry is given by the following equation:

TC = $5,625 + $5Q + $0.01Q2

Because this industry is purely competitive in nature, each firm behaves as a price taker and market price is given at $20 per unit (so that P = MR = $20). Finally, assume that each of the 100 firms in the industry are characterized by identical cost functions to the one presented above, and the output in the TC function (Q) represents monthly output by an individual firm.

a)For an individual firm, what is the profit maximizing level of output (Q).

b)At the optimal level of output, what is the monthly profit earned by the typical firm.

c)Given the number of perfectly competitive firms in this market, what is total industry output per month.

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#### Solution Preview

Solution:

a) For an individual firm, what is the profit maximizing level of output (Q).

TC=5625+5Q+0.01Q^2

MC=dTC/dQ=5+0.02Q

An individual firm sets its out such that ...

#### Solution Summary

Solution describes the steps to calculate profit maximizing output level and profit in a perfectly competitive environment.

Calculating profit maximizing output level and price

Suppose a company has just introduced a new line of ceramic insulators for which it has received patent protection, effectively granting the company monopoly status in the industry. The company's revenue and cost relations are given as:

TR = $300Q - $0.001Q2

TC = $9,000,000 + $20Q + $0.0004Q2

where TR is total revenue, Q is output, and TC is total cost.

a) As a monopolist, calculate this firm's optimal output (Q) and price per unit (P).

b) Calculate the level of total profit at this output level and also the value of per unit profit at this output level.