The firm's goal is to maximize profits, !. In order to do this it must decide what quantity of a good to produce given costs, technology and demand. A competitive firm is assumed to be able to sell as much as it wants at the market price without affecting price. So it takes price as exogenous (beyond it's control) and does not worry about demand. In addition, for our purpose we’ll assume the firm operates efficiently, that is, whatever the level of production that the firm chooses, that level of production will always be produced at the minimum possible cost. Profit is defined by the difference between total revenue (TR) and total cost (TC). Both TC and TR are functions of quantity. TR is defined as: (price per unit of the good)*(quantity of the good sold). It is a linear function, TR=Pq, where P equals the price of the good, q the quantity sold. The slope of the TR line is P and the price is the amount the firm receives if it produces and sells one more unit of the good. Marginal revenue (MR) is the additional revenue the firm gets from selling one more unit, given a particular level of sales. Therefore, marginal revenue is equal to P. The slope of the TR line is P, equal to MR. Because the firm takes price as given, our TR line has a constant slope. Total cost, TC, on the other hand, is a more complicated function of quantity. It may vary at different rates with different quantities, as we shall soon see. Marginal cost (MC) is the increase in cost from producing one more unit of the good given the amount you are already producing. The marginal cost to produce your first ton of steel, in a certain time period, is probably higher than the MC of the hundred and first ton in that same period. To produce the first ton you must build a plant, buy equipment, train labor and pay for all of the fixed costs associated with opening a steel plant. The hundred and first ton involves only the cost of the ore, the energy, the man hours and other inescapable product costs. These costs were also included in the cost of the first, and every, ton. It is important to note that your million and first ton of steel may cost considerably more to produce—at this point, your plant may be too crowded with raw materials or too many employees to be working efficiently. When the operation becomes that large, supervising gets a lot tougher and costly, and you may have to pay higher prices to draw labor and capital away from other
Let's consider an example of one firm producing steel. Assume the price of a ton of steel is $12. The graph shows TC and TR. Notice, TC increases at a decreasing rate at first but eventually increases at an increasing rate. FIGURE 1:
[Notice that even though TR is a 45° line, the slope is not 1 but 12—the units on the two axes are not the same] The owner of the firm wants to maximize profits, !, by maximizing the vertical distance between TR and TC. Remember, TR - TC = !. Just by looking you can tell that the quantity would be somewhat over 300 tons. The way to tell exactly is to find the point on the TC curve which is tangent to a line with the same slope as that of the TR line. Here the slope of the TR line is equal to 12, the price of a ton of steel and the MR that ton will generate. At the point of tangency the slope of the TC curve equals the slope of TR curve. Since the slope of the TC curve at any point is the MC, we know that at the quantity of output corresponding to the point of tangency MC equals P (which we know also equals MR). By drawing a line parallel to TR and tangent to TC we can see that the profit maximizing quantity for the firm is about 325 tons. At this quantity, labeled q* on the graph, profits equal !*. Since !* is the furthest possible distance between TR and TC a firm producing at the quantity q* will be maximizing its profit. Said another way, to find q* we find the point on the TC curve with the same
slope as the TR curve, the quantity where MC =...