# Tutorial 9: Firms With No Market Power

Now we have traveled from the production function to the costs of production. That gives us half the information we need to model a firm producing goods in a capitalist economy. But a firm produces goods and services in order to sell them in the hope that the revenue the goods bring exceeds the cost, both direct and opportunity, of producing them. In Tutorial 9 we explore how to model the revenue earned by firms from the sale of their output.

Then we combine that revenue model with the cost model developed in Tutorial 8, and use the new model to see how the firm with no market power goes about determining how much output to produce. Then, as always, we will alter the models parameters and see how the firm's price, output, and economic profit changes in response.

## Profit Maximization

Why are firm's in business? To earn an income for the firm's owner(s). This income is called profit and its role is quite often misunderstood. To some, profit is used synonymously with greed, and it is assumed that most firms earn an enormous (read "unfair") profit. Profit is simply the difference between the revenue brought in from the sale of goods, and the cost of producing those goods, including opportunity cost. It serves as the reward to the owners for taking risk. And it is surprisingly small: the national average rate of return on invested capital (i.e., profit) is about 7%. So for every \$100 the firm invests in the business, it will, on average, get a return of \$7.

It is through this reward that goods and services get produced. So it is not surprising that the first assumption economists make about the firm's interest in profit, it that the firm seeks to maximize profit.

### Marginal Revenue, Marginal Cost, and Profit Maximization

We define economic profit, P(Q), as the difference between total revenue from the sale of a given level of output, R(Q), less the total cost of producing that output, C(Q), including opportunity costs. That is, P(Q) = R(Q) - C(Q). We learned how to calculate C(Q) in Tutorial 8, now we'll learn how to calculate R(Q).

Total revenue is calculated as the price of each item sold times the quantity of units sold per time period, i.e., R(Q) = P · Q. Note that this equation is written with price as a constant. This may seem odd at first, because we know from the law of demand that as price varies the quantity demanded varies inversely. But we are not talking about market demand here. Rather, we are focused only on the demand for the output of a single firm in a competitive market. Now a competitive market is made up of large numbers of buyers and sellers. Any one seller, therefore, produces a small percentage of the total market output. So even if our representative firm produced the maximum quantity possible in the short run (when capital is fixed), its total output is not large enough to make the market notice its coming or going. So we can safely assume here that the firm takes the market price as given and does not vary price with the quantity it wants to sell. We also assume the firm produces a product that is identical to that of the other firms in the market.

If the market determines the price the firm must set for each unit of output it sells, then marginal revenue, MR(Q), the additional revenue from the sale of one more unit of output, is equal to that market price, P. Mathemagically,

MR(Q) = DR/DQ.

If the firm takes price as given, then the change in total revenue is equal to the change in output times the price the firm gets for each unit. So

MR(Q) = (P · DQ)/DQ

\ MR(Q) = P

Graphically, the price charged for a given unit of output does not vary with the level of output. In Figure 1, the market price is \$175 per unit. The firm calculates its total revenue as R(Q) = \$175·Q. So marginal revenue, MR1 in Figure 1, is plotted as a horizontal line at the price level, P*, set by the market, i.e., \$175.

### Figure 1

Because the firm takes the market price as given, we say it has 'no market power'. One implication of this is that the firm is not able to set a price different from its rival sellers. For example, if the firm charges a price higher than the market price, say, \$176 per unit, it would sell nothing -- buyers would find another of the thousands of sellers producing the identical product, and buy from them. If the firm charged a lower price, say \$174 per unit, it could still sell no more than the maximum it could produce. So why sell that output at \$174 each when the firm could easily get \$175 each? Hence the firm faces a demand curve that is perfectly elastic at the market price P*.

To sum up, a firm with no market power sells a non unique product in a competitive market and produces so little of the total market output that it is forced to charge a price equal to the market determined price. That market price, P*, is equal to MR and is the demand curve for the firm's output, P* = MR = d.

## Profit-Maximization by a Competitive Firm

The firm's goal is to choose that level of output that maximizes economic profit. How do we model that activity, that is, how do we model how the firm selects the level of output that it produces? Let's start from the top. Economic profit is defined as the difference between revenue and cost, including opportunity costs:

P(Q) = R(Q) - C(Q).

Each unit of output that a firm produces adds to its total cost (i.e., marginal cost is positive). Each unit of output it sells adds to its total revenue (i.e., marginal revenue is positive and, we now know, is equal to market price). The difference between the additional cost of one more unit of output and the additional revenue from the sale of that output is additional profit for the firm.

We know from the law of diminishing returns that the marginal cost of output will eventually be rising as output increases. That means that at some level of output MR will equal MC and the addition to profit from the last unit of output sold will be zero. Continuing with our mathemagical model:

DP = DR - DC.

If we divide both sides of the equation above by DQ:

DP/DQ = DR/DQ - DC/DQ,
or marginal profit = MR - MC,

When economic profit is at a maximum, the additional profit from the sale of one more unit of output equals zero. (Using calculus to find a local maximum, you would differentiate the total profit function and set it equal to zero.) So at a maximum economic profit:

DP/DQ = DR/DQ - DC/DQ = 0
or DR/DQ = DC/DQ

i.e., MR(Q) = MC(Q).

Because MR(Q) = P, the maximum economic profit occurs at an output level such that P = MC(Q). In other words, the firm continues to produce and sell more output, until the rising marginal cost of production reaches the price the firm is forced by the market to charge.

In this first part of Tutorial 9 we have learned that profit, in a capitalist economic system, is the reward for taking a risk and gathering resources to produce a good or service. Economic profit is the difference between total revenue from the sale of goods and the explicit PLUS opportunity costs of producing those goods. A firm seeking to maximize economic profits should set its output level such that the marginal cost of the last unit produced equals the marginal revenue from the sale of that unit.

In the next part of this Tutorial we will explore this latter point further.

 Copyright © 1996-2002 Mark S. Walbert, Illinois State University. Original graphics © FTSS. URL: http://www.ilstu.edu/~mswalber/ECO240/ Revised: 31-Jul-2002