Theory of the Firm: Production, Costs and Pro t

Transcription

1 San Francisco State University Michael Bar ECON 101 Theory of the Firm: Production, Costs and Pro t 1 Introduction There are millions of businesses and rms in the world and the U.S., and they are all di erent. Nevertheless, there are some principles of economics, that apply to all rms. One feature common to all rms, is that they all want to maximize pro t, even non-pro t organizations or charity organizations. This chapter focuses on the most fundamental choices that all businesses must make: how much output to produce and how many inputs to employ in order to achieve maximum pro t. Consider a simple rm that produces a single product. The pro t of such rm, as a function of the rm s output, is given by: where - rm s output (quantity), () = R () T C () = R () T F C T V C () () - rm s pro t (as a function of output), R () - rm s Revenue (as a function of output), T C () - rm s Total Cost (as a function of output), T F C - Total Fixed Cost (cost that are committed in advance, for certain period of time, and do not depend of the amount of output produced), T V C () - Total Variable Cost (cost that depend on the amount of output produced). Before we proceed, we need to explain what do we mean by cost. Economists distinguish between explicit and implicit costs. Explicit cost - cost paid in money Implicit cost - opportunity cost of using the factors of production for other purposes When calculating pro t, economists include both types of costs. Economic Pro t = Revenue - Explicit cost - Implicit cost In all the examples below, the cost will include both explicit and implicit cost, and the resulting pro t is economic pro t. For example, say you invest $100,000 to start a business, and in that year you earn $170,000 in revenue. Your accounting pro t would be $70,000. However, say that same year you could have earned an income of $80,000 had you been employed. Therefore, you have an economic loss of $10,000 (170, ,000-80,000 = -10,000). 1

2 What is the optimal output of the rm? In other words, we would like to nd the output level that maximizes the rm s pro t. At the optimal output, a small change in output should not change the pro t, as illustrated in the next gure. Thus, the slope of the pro t at the optimum is: () R () = T C () = 0 The expression () expression R() reads "the change in pro t as we increase by 1 unit". The reads "the change in revenue as we increase by 1 unit", and this is T C() change is called marginal revenue, and denoted MR (). Finally, the expression is "the change in total cost as we increase by 1 unit", and this change is called marginal cost. Therefore, at the optimum output, we must have MR ( ) = MC ( ) That it, the marginal revenue is equal to the marginal cost. It is easy to see why MR ( ) = MC ( ) must hold whenever the rm maximizes it s pro t. Suppose that MR ( ) > MC ( ). This means that producing one more unit will bring more revenue than the cost of producing that unit, and the rm can increase its pro t by producing more. If instead, MR ( ) < MC ( ), then the last unit produced at a higher cost than the revenue it generated. The rm can then increase pro t by producing less. Even if the rm produces the optimal output, the rm may still lose money. Thus, we 2

3 also want the pro t to be positive, in order for the rm to stay in business. ( ) = R ( ) T C ( ) 0 ( ) = R ( ) T C ( ) 0 AR ( ) AT C ( ) However, in the short run, the rm is committed to pay the xed cost, even if it does not operate. Thus, in the short-run, the rm will operate (stay in business) as long as R () T V C () AR ( ) AV C ( ) We can see from the above discussion, that understanding the cost structure of the rm, is essential for its most basic decisions: how much to produce, and whether to produce at all. The next section illustrates how the rm s costs are derived from the rm s production process. 2 Production and Cost We start with describing a simple short-run production of a rm that produces a single output. Suppose that some inputs are xed in the short run, for example, physical capital (machines, building) and technology, and output can be changed only by varying the labor - number of workers. The next table describes a typical short-run relationship between labor (L, rst column) and total product of output (T P (L), second column). The third and fourth columns calculate the associated average product per worker (AP (L) = T P (L) ) and marginal product (MP (L) = T P (L) L ). TP/L TP(L)/ L L = TP( L ) AP( L ) MP( L ) L 3

4 The next gure plots the graphs of the total product, and the associated average and marginal products of labor. Notice that when the number of workers is small, there is increasing marginal return to labor (MP (L) is increasing), but after 4 workers, there is a deceasing marginal return to labor (MP (L) is decreasing). When few workers are employed, they may help each other perform task as a team, so additional worker may contributes to the productivity more than the one before him. However, with xed capital, as the number of workers increases, at some point the contribution of additional worker to output will start decreasing (due to congestion). Also notice that as long as the marginal is above the average, the average is increasing, and whenever the marginal is below the average, the average is decreasing. This is true for any marginal and average quantities in the world. For example, if your next grade is above your GPA, the GPA will increase, and if your next grade is below your GPA, the GPA will decrease. 4

5 3 Short-Run Costs Suppose that the in the short run, some inputs are xed. For example, the physical capital, i.e. the machines and the rm s plant (building). The costs associated with xed factors do not vary with the level of production, and are called xed cost, and denoted by T F C - Total Fixed Cost. The cost of the rm s variable inputs are called variable cost, and denoted T V C () - Total Variable Cost. We write T V C as a function of quantity to emphasize that variable cost vary with the level of output. In our example above, with the only variable input being labor, the T V C is the cost of labor. In real business, the variable cost can also include electricity or other energy, food ingredients for a restaurant, etc. Thus, the total cost of the rm is the sum of xed and variable cost: T C () = T F C + T V C () In the above example, lets suppose that the xed cost is T F C = 50, and labor is paid $10 per hour. Thus, the last 3 columns in the next table, show the cost gures for the above example. L = TP( L ) AP( L ) MP( L ) TFC TVC() TC()

6 These costs are plotted in the next gure. 3.1 Average and marginal cost From the total costs above, we can derive the average cost per unit produced: AF C () = T F C AV C () = T V C () AT C () = T C () = T F C + T V C () = AF C () + AV C () Notice that the Average Fixed Cost is decreasing with the volume of production. As we showed in the introduction, the importance of the average costs is that they determine whether the rm should operate or not. The marginal cost determine the optimal (pro t maximizing) output. The marginal cost is given by: MC () = T C () = T V C () The last step follows from the fact that xed cost does not change as output changes. The next table uses data from the above example, and adds 3 more columns with AT C, AV C, 6

7 and MC. TP/L TP(L)/ L TFC+TVC() TC()/ TVC()/ TC()/ L = TP( L ) AP( L ) MP( L ) TFC TVC() TC() ATC() AVC() MC() Notice once again, that when the marginal is above the average, the average goes up, and when the marginal is below average, the average must go down. This is true for marginal and average product, marginal and average cost, or any marginal and average quantities you can think of. Also notice from the last table, that marginal product of labor and marginal cost are moving in opposite directions. When M P (L) is increasing, we have M C () decreasing, and vice versa. To see why this has to be the case, compare the output produced by workers number 9 and 8. The 8th worker produces 2 units, and is paid $10, so each unit produced by the 8th worker cost $5 (see the above table). The 9th worker is also paid $10, but produces only 1 unit. So the cost of each unit produced by the 9th worker is $10. You can use Excel to plot the graphs of AT C, AV C, and MC in the above table. The average and marginal costs curves, typically look like in the next gure. In the next section we will illustrate how these curves can be used to determine the optimal output of a competitive rm, and determine whether the rm operates or not (i.e. to stay in business or not). 7

8 4 Pro t of Perfectly Competitive Firm A competitive rm takes the market price as given (a price taker). Thus, the revenue of such a rm is: R () = P where P is the market price. The marginal and the average revenue of a competitive rm is simply the market price: MR = AR = P The pro t of a competitive rm is therefore: () = P T C () The optimal output, if the rm operates, is given by: The rm operates in the short run if: The rm operates in the long run is: P = MC ( ) P min (AV C) P min (AT C) Thus, the section of the MC curve, which is above the min (AV C), is the rm s short run supply curve of the rm. At any given price, MC gives the optimal output that the rm wants to sell. The next gure illustrates these conditions graphically. Costs, price Break even point MC min(atc) ATC AVC min(avc) Shutdown point 8

9 In the short run, the rm is committed to pay its T F C, and therefore will operate if the price is above min (AV C). This way, the rm covers all of the variable cost, and some of xed cost. If the rm shuts down, it still has to pay the xed cost. The shutdown point indicates the min (AV C), so that if the price is below that point, the rm will shut down, and will not operate even in the short run. In the long run, the rm must make positive pro t. Thus, the rm will operate if the price is above min (AT C). The point of min (AT C) is called break-even point, because if the price is at the level of min (AT C), the rm has zero economic pro t (breaks even). Example 1 Suppose the Total Fixed Cost and Total Variable Cost of a competitive rm are given in the next table. TFC TVC() (a) Find the rm s Total Cost, Average Total Cost, Average Variable Cost, and Mar- 9

10 ginal Cost, and plot the graph of AT C, AV C, and MC. TFC+TVC() TC()/ TVC()/ TC()/ TFC TVC() TC() ATC() AVC() MC() (b) What is the minimal market price at which the rm will operate in the short run? That is, nd the shutdown point. min (AV C) = 74 Thus, the rm will shut down if the market price falls below $74 per unit. (c) What is the minimal market price at which the rm will operate in the long run? That is, nd the break-even point. min (AT C) = $91:43 Thus, the rm will operate in the long run, if the market price is at least $91.43 per unit. 10

11 (d) Find the rm s optimal output in the short run, and the rm s pro t, for the following market prices: $70, $74, $80, $91.43, $130. P R TC π() (e) Illustrate the economic pro t graphically, when the market price is $