# Calculating profit maximizing output level

Please refer attached file for graph.

The graph on the left shows the short-run marginal cost curve for a typical firm selling in a perfectly competitive industry. The graph on the right shows current industry demand and supply.

a. What is the marginal revenue that this perfectly competitive firm will earn on its 60th unit of output?

b. What level of output should this firm produce in order to maximize profit or minimize losses?

c. Given your answer to question (b) above, assume that ATC at that level of output is $10. What are the firm's profits?

d. Now assume that the firm produces 100 units of output and at that level of output ATC = $11. How many firms in total will there be in this market?

e. Finally, assume the firm produces 100 units of output and at that level of output its ATC are $13 but its AVC are $11. What should the firm do and why?

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#### Solution Preview

Please refer attached file for graph.

a. What is the marginal revenue that this perfectly competitive firm will earn on its 60th unit of output?

Refer to the graph on the right side, demand and supply curves intersect each other at a price level of $12 per unit. This is equilibrium price. In case of perfectly competitive firm marginal revenue is equal to market price.

So, Marginal Revenue at 60th units=$12

b. What ...

#### Solution Summary

Solution describes the steps to calculate optimal output level, profit and number of firms in the given case.

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.