Profit Maximization

Economic theory is based on the reasonable notion that people attempt to do as well as they can for themselves, given the constraints facing them. For example, consumers purchase things that they believe will make them feel more satisfied, but their purchases are limited (at least in the long run) by the amount of income they earn. A consumer can borrow to finance current purchases but must (if honest) repay the loans at a later date.

Business owners also attempt to manage their businesses so as to improve their well being. Since the real world is a complicated place, a business owner may improve his well being in a number of ways. For example, if the business doesn't lack customers, the owner could respond by reducing operating hours and enjoying more leisure. Or, the business owner may seek satisfaction by earning as much profit as possible. This is the alternative we will focus on in class - for a very good reason. If a business faces tough competition, the only way the business can survive is to pay attention to revenues and costs. In many industries, profit maximization is not simply a potential goal; it's the only feasible goal, given the desire of other businesspeople to drive their competitors out of business.

In economic terms, profit is the difference between a firm's total revenue and its total opportunity cost. Total revenue is the amount of income earned by selling products. In our simplified examples, total revenue equals P x Q, the (single) price of the product multiplied times the number of units sold. Total opportunity cost includes both the costs of all inputs into the production process plus the value of the highest-valued alternatives to which owned resources could be put. For example, a firm that has $100,000 in cash could invest in new, more efficient, machines to reduce its unit production costs. But the firm could just as well use the $100,000 to purchase bonds paying a 7% rate of interest. If the firm uses the money to buy new machinery, it must recognize that it is giving up $7000 per year in forgone interest earnings. The $7000 represents the opportunity cost of using the funds to buy the machinery.

We will assume that the overriding goal of the managers of firms is to maximize profit: P = TR - TC. The managers do this by increasing total revenue (TR) or reducing total opportunity cost (TC) so that the difference rises to a maximum.

An Example

Suppose you are running a business that produces and sells office furniture. It's a small operation, and in a typical day you produce three custom desks. You are able sell these desks for $500 apiece. You employ five workers, each of whom earns $15 per hour ($120 per day), and you work alongside them and pay yourself at the same rate. Material inputs cost $150 per desk. Of course, you have additional "overhead" expenses, including rent, a secretary/bookkeeper, electricity, etc. This overhead, which we will assume does not vary with the number of desks produced (i.e., it's a fixed cost) comes to $130 per day. Thus, your company earns a profit of P = ($500 x 3) - ($720 + 450 + 130) = $1500 - $1300 = $200 per day. (Wages for six workers come to $720. Materials for three desks cost $450. Overhead is $130.) Working five days a week for 50 weeks a year, that comes to an annual profit of $50,000. Pretty nice - but could you do better?

Suppose you decide to increase production to four desks per day. This requires you to hire two more workers (at another $240) and purchase another $150 worth of materials. Overhead expense doesn't change. Your total cost rises to $1690. You find that you are able to sell the fourth desk for $500. Was this a good decision? [Engage brain here.]

You're right. [I'm giving you the benefit of the doubt here.] Total revenue rises to $2000 per day, while total costs rise to $1690. Profit increases to $310 per day. Good show, old man/woman/[insert desired politically correct term here]!

This nice result may lead you to increase production to five desks a day. If you are able to sell all five desks for $500 each, and if your variable costs of producing the desks - what you pay in labor and materials - doesn't increase, producing a fifth desk makes sense. TR rises to $2500, TC rises to $2080, and profit increases to $420. So you sell five desks.

Suppose, however, that you find that the labor market is so tight that you cannot hire another two workers at $15 per hour. In fact, to hire your ninth and tenth workers, you must pay $20 per hour. That increases the labor cost of the fifth desk by $80 ($40 per worker times two workers). TC rises to $2160, which still allows profit to increase to $340. But we have a problem brewing. Can you really get away with paying your veteran workers $15 an hour, while at the same time hiring new workers at $20 per hour? Not likely. So when you hire the ninth and tenth workers, you are forced to raise the wages of your first eight workers (Pay yourself more; hey, you deserve it.). Let's recalculate profit for Q = 5. TR = $500 x 5 = $2500. TC = ($160 x 10) + ($150 x 5) + $130 = $2480. That leaves a profit of $20. Doesn't look like such a good idea now, does it Einstein? Thus, if you realize that your costs will rise sharply if you produce a fifth desk each day, you will decline to produce the desk.

Application

Our little example illustrates the situation every business owner or manager faces. Businesspeople know what their current position is (revenue and costs) and they can estimate TR and TC for a higher (or lower) level of production. By actually changing output levels, they learn by experience what their demand and cost curves look like. In the process, they discover what happens to profit as they change output levels. Through this discovery process, businesspeople seek to find the output level that maximizes profit.

As omniscient onlookers, we can describe this process a bit more analytically. A firm should increase its output so long as the marginal revenue earned from additional units of production is greater than the marginal cost of those units. Marginal revenue is the additional revenue earned by selling one more unit of a product. (In our example, MR = $500.) Marginal cost is the additional cost incurred in producing one more unit of output. So long as MR > MC, profit grows. However, when MR < MC, profit shrinks. So firms expand output only to the point at which MR = MC. This point maximizes profit.

The profit-maximization rule applies both to firms that are able to sell their product at a constant price (as in our example) and to firms that find they must reduce the price of their product to increase sales. In the real world, firms have to engage in trial-and-error discovery processes, searching for the profit-maximization point. But the process can be succinctly described by the marginal revenue-marginal cost rule.

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