# Calculating The Optimal Output of a Competitive Firm

It is assumed that the liquid soap market is perfectly competitive and the current price of a case of liquid soap is $42.00. The firm has estimated it's marginal cost function to be as follows: MC=0.006Q.

1. Calculation for # cases to maximize profits with example.

2. What happens if the firm unilaterally raises prices in this market?

3. What happens to profit max level of output if the market price quickly increased to $54.00/case? Explain why the output level changes.

4. Can the firm benefit by advertising in this perfectly competitive market?

5. What would happen to the price of liquid soap if the firm monopolizes the market, does it rise or fall? What effect does that have on the firm's profits for the liquid soap division?

https://brainmass.com/economics/monopolies/calculating-optimal-output-competitive-firm-507705

#### Solution Preview

1. Calculation for # cases to maximize profits with example.

Firm can maximize their profits by setting their output level such that market price is equal to its marginal cost.

Put MC=$42

0.006Q=42

Q=42/.006=7000 cases

2. What happens if the firm unilaterally raises prices in this market?

Size of a firm in a competitive market is so small that it cannot influence the market price. Even if it does, there will be a large number of sellers who will be ...

#### Solution Summary

The solution describes the steps to estimate the optimal output of a perfectly competitive firm. It also discusses the impact of unilateral increase in price, advertising and monopolization on output of the given firm.

Competitive Market Equilibrium

Syracuse Paper supplies printer paper in upstate New York. Like the output of other wholesale distributors, Syracuse Paper must meet strict guidelines and the printer paper supply industry can be regarded as perfectly competitive. Total and marginal cost relations are:

TC = $3,600 + $5Q + $0.01Q2

MC = dTC/ dQ = $5 + $0.02Q

where Q is cases of printer paper per day.

A. Calculate the firm's optimal output and profits if prices are stable at $20 per case.

B. Calculate optimal output and profits if prices rise to $25 per case.

C. If Syracuse Paper is typical of firms in the industry, calculate the firm's equilibrium output, price, and profit levels.