The Goals of the Firm
Economists use the paradigm of profit maximization to explain the behavior of the firm. There are some good reasons which support this objective. Managers' compensation often is tied to profit maximization. And stockholders may be insistent over the long run that returns excel, or they sell the stocks, the value plummets, and management loses the prestige of running a growing, valued company. Investors are more willing to provide funding to profitable companies, and so profit maximizing firms may be the survivors of market pressures.
The meaning of economic profit
Cost is defined in the context of foregone opportunities. When properly measured, the cost
of producing a good includes not only the obvious expenses for labor, raw materials and
supplies, but an accounting of the opportunity cost of investment and an entrepreneur's
time. Most specifically, the cost of capital should include a fair rate of return on
investment - defined as a sufficient return to keep investors from moving their money
to alternative uses, and generally thought of as an average risk-adjusted return.
Economists often term this a normal return to investment.
The fair rate of return defines the economic idea of profit. Economic profit is a return to investment beyond the normal rate, after taking into consideration all direct and opportunity costs. Positive profit means the investment is returning more than the fair rate of return, while negative profit means that the return on the investment is less than the fair rate. Investors look for places to put their money which return economic profits, and avoid or move money from investments with economic losses.
A definition of profit such as this one implies a big difference between insolvency, when the outflow of dollars to pay bills exceeds the inflow of revenue, and economic losses, when economic profit is negative. Negative economic profit, a less than normal return, does not necessarily imply insolvency, although the insolvency does mean economic profit is negative. It is quite possible for a firm to be solvent but have negative economic profit.
Let us look at an example. Suppose an entrepreneur invests $10,000 and borrows $40,000 to open a small firm which will produce widgets. The $40,000 has a ten year note at 10 percent interest which requires an annual payment of $6510. Instead of having her own firm, she could work for a competitor and earn $20,000 per year. Her variable cost for materials and supplies is $10,000 a year. Suppose the fair rate of return is 8 percent.
This firm would be insolvent if revenue is less than $16,510 per year, the costs that must be paid to others. If revenue falls short of this amount, the only way to keep the business going is for the investor to put more of her own money into the business. (We are assuming that insolvency precludes borrowing more money.) But revenue in excess of $16,510 does not assure an economic profit. Only if the revenue taken in by the firm exceeds the entrepreneur's opportunity cost of wages, $20,000, plus a fair return to her $10,000 investment, $800 at 8 percent, is there an economic profit. Thus, the firm must have a total revenue above $37,310 for there to be an economic profit, often termed excess returns.
If the firm has revenue lower than $37,310 economic profit is deemed to be negative, that is, there is less than a normal rate of return to the investment. While the firm may be solvent (if revenue exceeds $16,510) the return to investment is below the normal rate. Even if the opportunity cost of the entrepreneur's labor is covered, so revenue exceeds $36,510, if the return to the $10,000 investment is less than $800, economic losses occur.
This definition of profit also provides an understanding of the signal it sends to investors. Any person or organization, say a bank or insurance company, wants to make the best risk-adjusted return on its savings. (Risk-adjusted means that more risky investments - those that are less likely to bring a return - must have a higher potential return to be as desirable as a safer but lower yielding investment.) The fair-rate-of-return keeps investors satisfied. They will not move their money from an investment earning this much. But positive economic profit is a signal to investors that a better than normal return can be had with that investment. Economic losses have a similar effect. It gives investors an incentive to move their money elsewhere, to a use where they can make a fair return.
The Seller's Side of Demand
Let's look at demand from the seller's side. The demand curve fundamentally constrains the
firms behavior when it comes to setting price. A firm can decide to set a particular
price, but then the demand curve facing the firm will determine the quantity that the firm
can sell. Alternatively, the firm can decide it wishes to sell a certain amount, but then
the demand curve decrees the price at which that amount will sell. As a result, the firm
has only a tenuous control over its total revenue. Since total revenue equals price times
quantity, but quantity sold (demanded) is a function of price, the firm has only indirect
influence on its outcome.
The slope of the demand curve facing the firm has important consequences on the firm's ability to influence its revenue if all units must be sold at the same price. When a firm faces a downward sloping demand curve, lowering the price of a good to increase quantity lowers the price on all units, not just the last unit. In figure 9.1 to increase sales from 1 unit to 2 units would require both units to be sold at P2 if the same price is charged for all units. To increase quantity the seller must sell the first unit for less than she would if it was the only unit she had to sell. The result is that the additional revenue from selling more units, called the marginal revenue by economists, is less than the price. If price is lowered from P1 to P2 to increase quantity to Q2, as shown in figure 9.2, total revenue changes from P1Q1 to P2Q2. The net change is given by the rectangle cbQ2Q1 minus the rectangle P1acP2. We can show that MR=P(1+DPQ/DQP)=P(1-1/ep) where we take the price elasticity of demand (ep) as a positive value. If ep is less than infinity then the marginal revenue is less than price.
Pricing for Profit Maximization
A profit maximizing firm faces a two part decision when deciding how much to produce and
what price it can charge to sell that output. First the firm must decide if it will
produce any output at all. There are times that a firm will be better off stopping
production even if it must continue to pay for its fixed costs. We call this the shut down
rule. A firm that decides to produce must then choose an output level and concordant price
(as determined by the demand curve it faces). This is the profit maximization rule.
Although most firms decide jointly if and how much to produce, we shall discuss each in
turn.
The shut down rule
The shut down rule tells a firm when it would be best off producing zero output in the
short run. The rule is to set output equal to zero, that is "shut down" in the
short run, if price is less than average variable cost. This rule minimizes losses in the
case that revenues do not cover economic cost, including the opportunity cost of the
investment.
We can illuminate why the shut down rule works by decomposing the expression for profit
into its various components. Profit is defined simply as total revenue minus total cost,
or P=TR-TC, where P is profit, TR is total revenue, and TC is
total cost. TR=PxQ and TC=FC+VC so
P = PxQ - FC - (QxAVC) which can be rearranged to P = Qx(P - AVC) - FC which we use to determine the shut down rule.
First note that by virtue of there being fixed cost, shutting production down is a short run decision. If Q is set to zero, P = (-FC). The firm suffers a loss equal to its fixed cost. But if output is positive, the first term on the right hand side is positive (if price exceeds average variable cost) or negative (if price is less than average variable cost). Clearly, a positive term improves the profit picture, while a negative value makes losses even bigger.
Now the rule: If price exceeds average variable cost the firm should produce (set a positive Q) because losses are bigger if the firm shuts down. Alternatively, if price is less than average variable cost the firm should shut down. Revenue will not cover variable cost, much less fixed cost, and the firm can minimize its loss by paying only its fixed cost.
Graphically we can understand the shut down rule by using the average total and average variable cost curves. In figure 9.5, panel (A) shows the case where price exceeds average variable cost. Total revenue is the area of the rectangle 0P1dQ. Profit, total revenue minus total cost, is the difference between the rectangles 0P1dQ and 0caQ. Because costs are larger, the firm suffers a loss equal to the area of the rectangle cadP1, which is smaller than fixed cost (rectangle vcab). So the firm loses less money by producing. But suppose price was lower, down at P2 in panel (B). Now total revenue is the rectangle 0P2fQ, and the loss is cafP2, which is larger than fixed cost. The firm would lose less money by setting output to zero, thus the shut down rule applies.
The profit maximization rule
When a firm decides that it will produce a good, it also must assess the amount it wants
to produce. Under the paradigm of profit maximization, the rule is very simply to set
output so marginal revenue equals marginal cost. We know that profit is given by the
equation = TR - TC. When a firm increases output by one unit, both total revenue and total
cost will change. We know the definitions of these changes are marginal revenue (MR) and
marginal cost (MC), respectively. That is, normalizing by the change in Q, MR=DTR/DQ and MC=DTC/DQ. Thus, we can define marginal profit (MP)
as the change in profit that comes from a small change in output, and note that MP = D TR/DQ - DTC/DQ or MP=
MR - MC so marginal profit is just the difference between marginal revenue and marginal
cost. If marginal profit is positive, producing one more unit will add to total profit,
making profit larger. Equally obvious, if marginal profit is negative, producing one more
unit lowers total profit. But when does marginal profit equal zero? Clearly, when marginal
revenue equals marginal cost, which gives us the profit maximization rule: Produce up
to the point where the marginal revenue of the last unit sold equals the marginal cost of
producing it, that is, where MR=MC. In sum, profit maximization is very easy. As
any time, to maximize a value, we set its derivative equal to zero, so we take P=TR-TC and take the derivative with respect to output and set it to
zero, that is, dP/dQ=dTR/dQ-dTC/dQ=MR-MC=0
so MR=MC at the profit maximizing output.
So what does this tell us about price?
Earlier we found the MR=P(1-1/ep) where we took the price elasticity of demand
as a positive value. Since price is a function of output according to the inverse demand
curve, we can use this configuration to find the price a firm can charge. Once we know the
output, and thus marginal cost and marginal revenue, the firm should set price so
P=MR/(1-1/ep), or analogously, that P=MC/(1-1/ep). Since marginal
revenue is positive by virtue of being equal to marginal cost
we know that the price
elasticity of demand must exceed unity. Thus, 1/ep is less than one
(approaching zero when ep approaches infinity), so price is greater than or
equal to marginal revenue. We should note that the relationship between marginal revenue,
price and elasticity is set by the firm's demand curve, so once an output level is chosen
so marginal revenue equals marginal cost, price is determined simultaneously.