E&S Textbook 154-183 PDF

6 Sellers and Incentives How would an ethanol subsidy affect ethanol producers?...

6 Sellers and Incentives How would an ethanol subsidy affect ethanol producers? In every market, there are buyers and sellers. Taco Bell sells tacos, Apple sells iPods, Old Navy sells casual clothing, and Amazon.com sells Kindles. Service mar- kets also feature buyers and sellers: you purchase tune-ups from mechanics, guitar lessons from music instructors, and haircuts from barbers. In the previous chapter, you learned a set of decision rules that led to optimal outcomes for the buyer. In this chapter, you’ll learn a set of decision rules that optimize outcomes for the seller. We begin with the seller’s problem, which is nearly identical to the buyer’s problem discussed in Chapter 5. In much the same way that consumers choose the optimal bundle of goods and services to maximize their net benefits, sellers choose what to produce and how much to produce to maximize their net ben- efits: profits. Our discussion in this chapter continues to focus on perfectly competitive markets. We show that like optimizing consumers, optimizing sellers rely on marginal thinking. We will learn that simply knowing market prices and how much it costs a firm to produce a good or a service leads to a set of decision rules that govern the seller’s problem. These insights will help you understand and predict how proposed public policies influence behavior and outcomes of firms. They also provide general guidance into how you should run your own business inter- ests should your entrepreneurial spirit inspire you to start up an Internet company, open a Subway sandwich shop, or open an ethanol plant. CHAPTER OUTLINE 6.1 6.2 6.3 6.4 6.5 6.6 EBE Sellers in a The Seller’s From the Seller’s Producer From the From the Firm How would Perfectly Problem Problem to the Surplus Short Run to the Market: an ethanol Competitive Supply Curve to the Long-Run subsidy Market Long Run Competitive affect Equilibrium ethanol producers? 152 M06_ACEM9202_01_GE_CH06.indd 152 14/03/15 2:29 PM  KEY IDEAS The seller’s problem has three parts: production, costs, and revenues. An optimizing seller makes decisions at the margin. The supply curve reflects a willingness to sell a good or service at various price levels. Producer surplus is the difference between the market price and the marginal cost curve. Sellers enter and exit markets based on profit opportunities. 6.1 Sellers in a Perfectly Competitive Market We will begin our study of how firms make decisions by assuming that they do so in per- fectly competitive markets. Three conditions characterize perfectly competitive markets: No buyer or seller is big enough to influence the market price. Sellers in the market produce identical goods. There is free entry and exit in the market. The first two assumptions are important because they ensure that agents in this type of market are price-takers—a term we’ve already met in Chapters 4 and 5. Just as a consumer is a price-taker by buying as much as she wants at the market price if she has enough money, sellers in perfectly competitive markets are price-takers in that they can sell as much as they want at the market price. The rationale behind this assumption is that an individual seller tends to sell only a tiny fraction of the total amount of a good produced. Because the seller’s output is small relative to that of the market, the individual choice of how much to produce isn’t going to be important for market outcomes. But the combined effect of many sellers’ decisions will affect the market price. We can see this through the lens of the decisions of a local farmer. If the farmer decides to rotate crops and grow corn this year rather than soybeans, this choice does not cause price fluctuations throughout the world. However, if every farmer in the world decided to grow corn this year instead of soybeans, the price of corn would decrease dramatically and the price of soybeans would increase. The third assumption—that firms can enter and exit industries as they please—has important consequences for the market as a whole. One example of a market where sellers can enter and exit as they please is selling on eBay. At any time you can decide to enter the DVD market by auctioning off your DVD collection on eBay. Sellers can pretty much en- ter and exit freely in many other familiar markets, including lawn care, automobile repair, retail shops, and farming. 6.2 The Seller’s Problem The overarching goal of the seller is to maximize net benefits, or profits. The seller’s prob- lem therefore revolves around the question: “How do sellers decide what and how much to produce?” We can frame this question as a problem—the seller’s problem—just as when Section 6.2 | The Seller’s Problem 153 M06_ACEM9202_01_GE_CH06.indd 153 14/03/15 2:29 PM  we looked at the buyer’s problem in Chapter 5 and discussed how consumers make buying decisions. 6.1 Think of your local pizzeria. The owner first buys ingredients, then creates a master- piece with dough, sauce, and toppings, after which he takes it to the market. In this anal- ogy, the seller’s problem has three main components. First, the seller must know how the 6.2 inputs combine to make the outputs. For example, how many tomatoes are necessary for just the right sauce? Second, the seller must know how much it costs to produce a pizza. For instance, how much does the brick oven cost, and what about the electricity cost and 6.3 workers’ wages? And, does it matter that new ingredients need to be purchased each time he produces a pizza, while the oven sits ready for use? Finally, the seller must know how much he can sell the pizza for once it is produced. So we can say that the three elements of the seller’s problem are: 6.4 Making the goods The cost of doing business 6.5 The rewards of doing business We’ll now look at each of these elements in more detail. 6.6 Making the Goods: How Inputs Are Turned into Outputs A firm is any business entity that A firm is a business entity that produces and sells goods or services; it can consist of thou- produces and sells goods or sands of people, a few people, or a single person. Every firm faces the decision of how to services. combine inputs to create outputs. Production is the process by which the transformation Production is the process by which of inputs (such as labor and machines) to outputs (such as goods and services) occurs. The the transformation of inputs to relationship between the quantity of inputs used and the quantity of outputs produced is outputs occurs. called the production function. To begin to understand the production function, let’s consider a real-life company in Sun Prairie, Wisconsin: The Wisconsin Cheeseman. The firm is a mail-order gift company that packs and mails food and floral products and ships them all over the world. Let’s focus exclusively on one of the services that it provides: packing cheese into cheese boxes. The Cheeseman relies on two main inputs, labor to pack the cheese into boxes—a task that one Physical capital is any good, of the co-authors of this book spent two teenage summers doing—and including machines and buildings (equipment and structures). Physical capital is any good, including machines and buildings used for production. used for production. Whereas hiring and firing workers can be done in a short period of time, altering The short run is a period of time physical capital takes a much longer period of time. Economists denote the as when only some of a firm’s inputs a period of time when only some of a firm’s inputs can be varied—for The Cheeseman, can be varied. labor. Alternatively, the is defined as a period of time wherein a firm can The long run is a period of time change any input. This means that physical capital is a — when all of a firm’s inputs can be an input that cannot change in the short run—and that labor is a varied. —an input that can change in the short run. A fixed factor of production is an Exhibit 6.1 provides information on The Wisconsin Cheeseman’s short-run produc- input that cannot be changed in the tion function. It shows how the output varies with the number of workers employed short run. (we’ve changed actual numbers because those are proprietary information). Columns 1 and 2 show how The Cheeseman’s daily production of cheese boxes varies with the num- A variable factor of production is an input that can be changed in the ber of employees it hires. The first worker can complete 100 cheese boxes per day. Two short run. workers can pack 207 cheese boxes per day. As such, the of adding the second worker is 107 cheese boxes in a day because this is the amount by which total Marginal product is the change in output changes with the addition of the second worker (207 − 100). So we can define total output associated with using one more unit of input. marginal product as the additional amount of output obtained from adding one more unit of input (in this case, workers). For The Cheeseman, the only way to change production in the short run is to change the number of workers. Exhibit 6.2 provides a graphical summary of the relationship between the number of workers and the number of cheese boxes packed: the short-run production function. Exhibits 6.1 and 6.2 reveal three important characteristics of production for The Cheeseman. The marginal product increases with the first few workers. This feature suggests that, for example, two laborers working together can produce more than the sum of their produc- tion in isolation. This might happen because the first two workers specialize in a particular 154 Chapter 6 | Sellers and Incentives M06_ACEM9202_01_GE_CH06.indd 154 14/03/15 2:29 PM  Exhibit 6.1 Production 6.1 Details of Production Data for The Wisconsin Cheeseman (1) Output Per Day (2) # Employed (3) Marginal Product 0 0 The Wisconsin Cheeseman 100 1 100 6.2 is tasked with choosing how 207 2 107 much output to generate 321 3 114 per day, and the table 444 4 123 558 5 114 6.3 summarizes the number 664 6 106 of workers the firm will 762 7 98 need for any given level of 854 8 92 output. The first column 939 9 85 6.4 is the number of cheese 1019 10 80 boxes produced per day, 1092 11 73 the second column is 1161 12 69 the number of workers 1225 13 64 6.5 1284 14 59 employed, and the third 1339 15 55 column is marginal product: 1390 16 51 the additional output 1438 17 48 produced by each additional... 6.6 input (in this case, workers)....... 1934 38 10 1834 39 −100 Exhibit 6.2 The Short-Run Number of 2,100 Production Function for cheese boxes The Cheeseman produced 1,800 Plotted here is the number of 1,500 workers on the x-axis and the number of cheese boxes produced 1,200 on the y-axis. As the number of workers goes up, the number 900 of cheese boxes that can be produced tends to increase, but 600 notice that the first 10–15 workers 300 lead to much steeper increases in production than the 25th–35th additional worker. Also notice that 0 5 10 15 20 25 30 35 40 45 the last worker actually reduces Number of workers productivity. Specialization is the result of portion of the cheese-packing task that they are good at completing. In specialization, work- workers developing a certain ers develop specific skill sets so as to increase total productivity. To see specialization in skill set in order to increase total action, during your next visit to Subway, watch how the first worker prepares the bread and productivity. places the meats just right. Then watch the second worker prepare the veggies, sprinkle oils, and cut the sandwich. After which, the third worker prepares the final product and tallies the bill. A true assembly line of beauty, something that specialization has created naturally. The marginal product eventually decreases with successive additions of workers. This characteristic means that as more and more workers are added they begin to add less and less to total production. For example, the marginal product of the fourth worker is 123 boxes, whereas it is only 114 boxes for the fifth worker. Economists call this decreas- The Law of Diminishing Returns states that successive increases ing production pattern the. This law states that at a cer- in inputs eventually lead to less tain point of successive increases in inputs, marginal product begins to decrease. This law additional output. might apply for a number of reasons. For example, with a set amount of physical capital, Section 6.2 | The Seller’s Problem 155 M06_ACEM9202_01_GE_CH06.indd 155 14/03/15 2:29 PM  successive increases in labor eventually lead to lower output per worker because there is idle time—workers cannot use the machines as often as they would like. 6.1 Adding too many workers can actually decrease overall production. This point refers to the fact that adding too many workers can be counterproductive. Indeed, this is exactly the situation with the last worker that The Cheeseman hires: Exhibit 6.1 shows that adding 6.2 the thirty-ninth worker has a negative marginal product of 100 boxes! You can see this situ- ation vividly in Exhibit 6.2, where the production curve begins to slope downward at that point. Management should send this worker home, dispatch him to a different task, or even 6.3 have him wash the owner’s dog, because he is lowering production of cheese boxes. This might happen because congestion causes workers to get in the way of one another. 6.4 The Cost of Doing Business: Introducing Cost Curves We now look at the second component of the seller’s problem: what the firm must pay for The cost of production is what a its inputs, or the. Similar to the two factors of production discussed 6.5 firm must pay for its inputs. above, there is a natural division in the total cost of production: = Variable cost + Fixed cost. 6.6 Total cost is the sum of variable and This equation has three parts. is the sum of variable and fixed cost. fixed costs. are those costs associated with variable factors of production. In The Cheeseman’s case, these A variable cost is the cost of are costs associated with workers and therefore change with the level of production in the short variable factors of production, which run. In contrast to variable costs, a is a cost associated with a fixed factor of produc- change along with a firm’s output. tion, such as structures or equipment, and therefore does not change with production in the short run. Indeed, in the short run, The Wisconsin Cheeseman has to pay for these factors even A fixed cost is the cost of fixed factors of production, which a firm if it produces nothing because the firm cannot sell its plant and equipment in the short run. must pay even if it produces zero These costs are summarized in Exhibit 6.3. Column 4 shows variable costs (VC)— output. because workers at The Cheeseman are paid a daily wage of $72 ($9 per hour, 8 hours per day), the daily variable costs increase by $72 for each worker hired. We assume that The Cheeseman can hire as many workers as it wants at this wage. The cost of structures and machinery represents the cost of physical capital, and this is computed by management to be Exhibit 6.3 Costs Cost of Production of Production with Additional (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Marginal Cost Concepts Cost for The Wisconsin Variable Average Average Average (MC) = Cheeseman Output Marginal Cost Total Total Variable Fixed change The Wisconsin Per Product = (VC) = Fixed Cost Cost Cost Cost in (6)/ Day change $72 × Cost (TC) = (ATC) = (AVC) = (AFC) = change Cheeseman produces (Q) # Employed in (1) (2) (FC) (4) + (5) (6)/(1) (4)/(1) (5)/(1) in (1) cheese boxes; this 0 0 $ 0 $200 $ 200 exhibit summarizes 100 1 100 $ 72 $200 $ 272 $2.72 $0.72 $2.00 $0.72 the cost of various 207 2 107 $ 144 $200 $ 344 $1.66 $0.70 $0.97 $0.67 levels of production. 321 3 114 $ 216 $200 $ 416 $1.29 $0.67 $0.62 $0.63 The total cost is the 444 4 123 $ 288 $200 $ 488 $1.10 $0.65 $0.45 $0.59 sum of fixed and vari- 558 5 114 $ 360 $200 $ 560 $1.00 $0.65 $0.36 $0.63 able cost. The aver- 664 6 106 $ 432 $200 $ 632 $0.95 $0.65 $0.30 $0.68 age total cost is the 762 7 99 $ 504 $200 $ 704 $0.92 $0.66 $0.26 $0.73 854 8 92 $ 576 $200 $ 776 $0.91 $0.67 $0.23 $0.78 sum of average fixed 939 9 85 $ 648 $200 $ 848 $0.90 $0.69 $0.21 $0.85 and average variable 1019 10 80 $ 720 $200 $ 920 $0.90 $0.71 $0.20 $0.90 cost. The marginal 1092 11 73 $ 792 $200 $ 992 $0.91 $0.73 $0.18 $0.99 cost is the change in 1161 12 69 $ 864 $200 $1,064 $0.92 $0.74 $0.17 $1.04 total cost associated 1225 13 64 $ 936 $200 $1,136 $0.93 $0.76 $0.16 $1.13 with producing one 1284 14 59 $1,008 $200 $1,208 $0.94 $0.79 $0.16 $1.22 more unit of output. 1339 15 55 $1,080 $200 $1,280 $0.96 $0.81 $0.15 $1.31 For convenience 1390 16 51 $1,152 $200 $1,352 $0.97 $0.83 $0.14 $1.41 1438 17 48 $1,224 $200 $1,424 $0.99 $0.85 $0.14 $1.50 the numbers are rounded. 156 Chapter 6 | Sellers and Incentives M06_ACEM9202_01_GE_CH06.indd 156 14/03/15 2:29 PM  $200 per day. These are the fixed costs (FC) given in column 5 of Exhibit 6.3. These costs are the same no matter how many workers are hired. Thus, fixed costs do not vary in the 6.1 short-run, but variable costs do. Column 6 shows total cost (TC), which is the sum of vari- able and fixed costs for a particular quantity of output. We are provided with three more interesting cost concepts if we divide both sides of our total cost equation by output (quantity The Cheeseman produces): 6.2 Total cost Variable cost Fixed cost = +. Q Q Q 6.3 Average total cost (ATC) is the total The term on the left-hand side of this equation is called ATC , which cost divided by the total output. is total cost divided by total output. Column 7 in Exhibit 6.3 shows the average total cost for The Cheeseman. For example, the ATC for The Wisconsin Cheeseman with an output 6.4 of 321 units is computed by taking the total cost of $416 and dividing it by the total output of 321, which yields $1.29, as shown in Exhibit 6.3. This means that when it produces 321 units, the average cost per cheese box packed is $1.29. 6.5 Average variable cost (AVC) is the The first term on the right-hand side of this equation is called the total variable cost divided by the (AVC , which is the total variable cost divided by total output. For The Cheeseman, when it total output. produces 321 units, its AVC is $0.67, which means that it pays its variable factor of produc- 6.6 tion (labor) an average of $0.67 per cheese box packed. Average fixed cost (AFC) is the Finally, AFC is the total fixed cost divided by the total output. For total fixed cost divided by the total The Cheeseman, when it produces 321 units, its AFC is $0.62, which means that it pays its output. fixed factor of production (physical capital) an average of $0.62 per cheese box packed. What this all means is that of the $1.29 average total cost when The Cheeseman produces 321 units, $0.67 goes to variable costs (labor) and $0.62 goes to fixed costs (physical capital). Marginal cost is the change in total Our last cost concept is , which is presented in column 10 of Exhibit 6.3. cost associated with producing one Marginal cost (MC) is the change in total cost associated with producing one more unit of more unit of output. output. Marginal cost can be written as: Change in total cost Marginal cost =. Change in output When The Wisconsin Cheeseman produces 321 units, a MC of $0.63 means that it costs The Cheeseman $0.63 to produce the 321st cheese box. Exhibit 6.3 also reveals another interesting relationship: marginal cost and marginal product are inversely related to one another. As one increases the other automatically decreases. To see why, consider The Cheeseman’s production and cost relationships. When The Cheeseman adds its first few workers (up to 4), the total output goes up and the marginal product also increases, decreas- ing marginal cost. After too many workers are hired, they find themselves wasting time, waiting to use equipment. This leads to lower marginal product and higher marginal cost. Using the data from Exhibit 6.3, Exhibit 6.4 shows a graphical representation of the im- portant relationships between costs and quantity produced: the marginal cost curve, average total cost curve, and average variable cost curve for The Cheeseman. Output quantity is plot- ted on the x-axis and costs (in dollars) on the y-axis. One interesting feature about these cost curves is that when the marginal cost curve is below the average cost curves (both average total cost and average variable cost), they must be falling or sloping downward, and when the marginal cost curve is above the average cost curves, they must be rising or upward-sloping. Why? This is by itself the very nature of the definition of marginal cost. To capture this intuition, think of your overall grade point average (GPA) as average total cost and your semester GPA as marginal cost. Say that in your freshman year you earn all B’s, a 3.0 GPA. Now let’s say that in your sophomore year you earn straight A’s, a 4.0 GPA. What will hap- pen to your overall GPA? It will rise; in fact, if you take the exact same number of credits in each of your freshman and sophomore years, your cumulative GPA will now be 3.5. Now what happens to your overall GPA if in your junior year you earn all C’s, a GPA of 2.0? It decreases. This is because your new grades are below the average that you established in your first two years. This also provides the intuition for why MC intersects AVC and ATC at their minimums: when MC is below ATC and AVC they must be falling, and when MC is above ATC and AVC they must be rising, as in Exhibit 6.4. An understanding of these curves leads to powerful implications, as we discuss next. Section 6.2 | The Seller’s Problem 157 M06_ACEM9202_01_GE_CH06.indd 157 14/03/15 2:30 PM  6.1 Exhibit 6.4 Marginal Cost, Average Price $2.5 Total Cost, and Average Variable Cost Marginal Cost Curves for The Wisconsin Cheeseman 2.0 6.2 This figure plots several cost measures Average with the output (or quantity) on the Total Cost 1.5 x-axis and the cost (or price) on the Average y-axis. Each cost measure is plotted Variable Cost 6.3 across various output levels. Notice 1.0 that the MC curve intersects the ATC and AVC curves at their respective minimums. 0.5 6.4 500 1,000 1,500 2,000 2,500 6.5 Quantity 6.6 CHOICE & CONSEQUENCE Average Cost Versus Marginal Cost Imagine that you are asked to help in a number of calls to obtain the average fund-raising effort for your college.1 You total cost of a call. Of course, they learn that your college has an old call cen- didn’t take into account the fact that the ter that it doesn’t use. You ask why and school had already bought the comput- the reply is “Well, the cost of making a ers and that the marginal cost of every call is $1, while the cost of mailing a let- call was very, very low—equal only to ter is only $0.50.” You are shocked: how the amount you would have to pay a could each call be that expensive? caller for a minute of time! If you know After a little prodding, your college that the donation rate over the phone is admits how the people who prepare much higher than the donation rate from their mailings calculated this figure of mailings, and the marginal cost of send- a dollar per call. They had simply summed the cost of ing a letter exceeds that of making a phone call, then the computer-networked phone-banking system your after reading this chapter, you will know to immediately school had purchased years before and the cost of advise your college to pick up the phones and start paying students to make calls and divided by the total dialing! The Rewards of Doing Business: Introducing Revenue Curves We are now ready to look at the third component of the seller’s problem: the price at which a firm can sell its goods. A firm makes money from selling goods, and The Wisconsin Revenue is the amount of money Cheeseman is no different. The revenue of a firm is the amount of money it brings in from the firm brings in from the sale of its the sale of its outputs. Revenue is determined by the price of goods sold times the number outputs. of units sold: Total revenue = Price × Quantity sold. Recall that in perfectly competitive markets, sellers can sell all they want at the market price. Thus, they are price-takers. But what determines the price of cheese boxes? Chapter 4 can lend insights to this question: the price comes from the intersection of the market demand curve and the market 158 Chapter 6 | Sellers and Incentives M06_ACEM9202_01_GE_CH06.indd 158 14/03/15 2:30 PM  supply curve. This is just like any other market equilibrium you learned about in Chapter 4: the intersection of market supply and 6.1 The overarching goal of the seller is market demand gives the equilibrium price. to maximize net benefits, or profits. Exhibit 6.5 reveals this intuition. Panel (a) of Exhibit 6.5 shows the market supply and market demand curves. Recall that we can construct the market demand curve as described in Chapters 4 6.2 and 5. We can construct the market supply curve in exactly the same manner as the market demand curve—through horizontally summing the individual supply curves. To see how this works, let’s assume that in equilibrium, the cheese box packing industry has 10,000 6.3 identical firms, which each produce 1,225 cheese boxes per day. Thus, a total of 12,250,000 cheese boxes are packed daily in this market. As shown in panel (b) of Exhibit 6.5, this equilibrium quantity occurs at an equilibrium price of $1.13 per cheese box packed. 6.4 At this point, it is important to recognize the difference between the demand curve fac- ing The Cheeseman and the demand curve in a perfectly competitive market. As panel (b) of Exhibit 6.5 reveals, a perfectly competitive firm, such as The Wisconsin Cheeseman, faces a horizontal demand curve, or a demand curve that is perfectly elastic. What this 6.5 means is that The Cheeseman can pack as many cheese boxes as it desires and be paid the market equilibrium price ($1.13) for every cheese box packed. If The Cheeseman attempts to charge a little bit more than $1.13 per box, it will have no customers because buyers 6.6 can go to a different packer and pay $1.13 per box. In addition, there is no reason for The Cheeseman to lower its price below $1.13 to attract buyers because it can sell all it wants at $1.13 per box. Besides showing the demand curve facing The Cheeseman, panel (b) of Exhibit 6.5 Marginal revenue is the change shows the marginal revenue curve. is the change in total revenue asso- in total revenue associated with ciated with producing one more unit of output. In a perfectly competitive market, marginal producing one more unit of output. revenue is equal to the market price. Therefore, the marginal revenue curve is equivalent to the demand curve facing sellers. Because the price that The Cheeseman faces is $1.13, the marginal revenue is $1.13 for every cheese box packed. We are now in a position to learn about the good stuff—making money! Price $3.5 Price $3.5 Demand Supply 3.0 3.0 2.5 2.5 2.0 2.0 Marginal Cost 1.5 1.5 P = MR = $1.13 D = MR 1.0 1.0 0.5 0.5 5 10 15 20 25 500 1,000 1,500 2,000 2,500 Quantity (in millions) Quantity (a) The Market (b) The Cheeseman Exhibit 6.5 Supply and Demand: The Market Versus The Wisconsin Cheeseman Panel (a) summarizes the market supply and market demand curves for cheese boxes. The price determined by the market equilibrium is the price The Cheeseman faces, which is shown in panel (b). We think of that price as representing the demand curve The Cheeseman faces, which is the flat blue line. This demand curve is equal to marginal revenue because it represents the change in revenues from selling one more cheese box. Section 6.2 | The Seller’s Problem 159 M06_ACEM9202_01_GE_CH06.indd 159 14/03/15 2:30 PM  Putting It All Together: Using the Three Components 6.1 to Do the Best You Can Now that we have the three components of the seller’s problem in place, we can begin to The profits of a firm are equal to its construct how these three elements are used to maximize the firm’s profits. The profits of 6.2 revenues minus its costs. a firm are the difference between total revenues and total costs: Profits = Total revenues − Total costs. 6.3 For The Wisconsin Cheeseman to determine its profits, there is only one more question to answer: how much to produce? To figure out what quantity maximizes profits, we need to think about a production level and conduct a thought experiment as to how producing a bit 6.4 more or a bit less affects both revenues and costs. That is, the key behind maximizing prof- its is to think about the firm’s marginal revenues and marginal costs. This is an application of optimizing from Chapter 3. 6.5 To see how this works, consider Exhibit 6.6, which recreates panel (b) of Exhibit 6.5. Let’s first think about point A in the exhibit. At this point, The Cheeseman hires 9 workers and it produces 939 cheese boxes. At this production level it costs $0.85 to pack the last 6.6 cheese box, as given by the marginal cost in Exhibit 6.3. We know that The Cheeseman is paid $1.13 for each packed box. Can The Cheeseman earn higher profits? Yes. If it produces one more cheese box, it increases revenues by $1.13, which is greater than the $0.85 it costs to produce. Profit could be increased by $0.28 just by selling one more cheese box! This provides a gen- eral rule: if a firm can produce another unit of output at a marginal cost that is less than the market price (that is, MC < price), it should do so, because it can make a profit on producing that unit. Consider the other side of the coin: if The Cheeseman was producing at point B—hiring 17 workers and producing 1,438 units. Its marginal cost of producing the last unit is now greater than the market price ($1.50 versus $1.13); thus it loses money by producing that last unit. It therefore shouldn’t produce it and should hire fewer workers. In fact, with this marginal decision making in mind, it’s straightforward to see how a firm maximizes its profits. It should expand production until the point where: Marginal revenue = Marginal cost. This is the same as producing where price equals marginal cost because marginal rev- enue equals price in a perfectly competitive market. Exhibit 6.6 Movement of Price $3.5 Production toward Equilibrium 3.0 The red curve is The Cheeseman’s marginal cost curve, and the blue 2.5 line is The Cheeseman’s marginal revenue curve. At point A, The 2.0 Marginal Cost Cheeseman should produce more to increase profits. At point B, The Cheeseman should produce less. 1.5 B To maximize profits, Cheeseman MR = Price produces where marginal cost 1.0 equals marginal revenue. A 0.5 500 1,000 1,500 2,000 2,500 Quantity Q = 1,225 160 Chapter 6 | Sellers and Incentives M06_ACEM9202_01_GE_CH06.indd 160 14/03/15 2:30 PM  How can we compute the level of profits at this point? One aid is to overlay the aver- age total cost curve to Exhibit 6.6, which we do in Exhibit 6.7. Because total revenues = 6.1 price × Q and total costs = ATC × Q, we can write total profits as: Price × Q − ATC × Q = (Price − ATC) × Q. 6.2 In other words, we can compute total profits by taking the difference between price and average total cost at the point of production and multiplying that difference by the total quantity produced. In the case of producing at MR = MC, this provides the shaded area in 6.3 Exhibit 6.7. We can compute this area as follows: (P − ATC) × Q = ($1.13 − $0.93) × 1,225 = $245. 6.4 This follows because The Cheeseman is paid $1.13 per box at a production level of 1,225 boxes. At this level of production, the average total cost is $0.93 (see Exhibit 6.3). So, taking the price of $1.13 and subtracting the average total cost of $0.93, we get $0.20, 6.5 which is per-unit profit. We then multiply this per-unit profit by quantity sold, or 1,225, to find the daily profit figure of $245. This profit level is equal to the base times the height of the shaded rectangle in Exhibit 6.7. Because marginal revenue equals marginal 6.6 cost (MR = MC) at this level of production, we know that this choice optimizes profits and represents the equilibrium for The Cheeseman: once producing at this point, The Cheeseman will not change its production activities unless something else in the market changes. Profits of only $245 a day might seem trivial, but note that when economists discuss profits we are expressing something much different from what you’re used to reading about in the newspapers. For example, when a major corporation reports “record profits,” it is re- Accounting profits are equal to porting what economists call. Accounting profits are equal to revenues total revenue minus explicit costs. minus explicit costs. Explicit costs are the sorts of line-item expenditures that accountants carefully tally and report, like wages for workers or equipment expenditures. But firms also face implicit costs. For example, the owner of The Wisconsin Cheeseman may have a high opportunity cost of time that he is sacrificing in order to run The Cheeseman (to see where an implicit cost like this would play out in Exhibit 6.3, the cost of the owner’s time would be in the Fixed Cost column). Much like the cost of labor and machines, this implicit cost Economic profits are equal to total is subtracted away from revenues to produce our conception of profits,. revenue minus both explicit and Economic profits are equal to total revenue minus both explicit and implicit costs. As a re- implicit costs. sult, it is still feasible to run a business that is earning small (or even zero) economic profits, as we demonstrate later in this chapter. Exhibit 6.7 Visualizing The Price $3.5 Wisconsin Cheeseman’s Profits with MC, MR, and ATC 3.0 Adding The Cheeseman’s ATC to 2.5 Exhibit 6.6 allows us to visualize profits graphically. The shaded box Marginal Cost represents The Cheeseman’s profits. 2.0 To see why, remember that profits are Average the difference between total revenue 1.5 Total Cost and total costs. Because MR repre- 1.13 Marginal sents price and ATC represents the 1.0 Revenue cost per unit produced, their differ- 0.93 ence at the quantity where marginal 0.5 cost equals marginal revenue mul- tiplied by quantity produced yields total profits: ($1.13 − $0.93) × 1225 500 1,000 1,500 2,000 2,500 = $245. Quantity Section 6.2 | The Seller’s Problem 161 M06_ACEM9202_01_GE_CH06.indd 161 14/03/15 2:30 PM  6.1 CHOICE & CONSEQUENCE Maximizing Total Profit, Not Per-Unit Profit 6.2 One common way of thinking is that if you maximize per- The data in Exhibit 6.3 show this intuition for The unit profit, you will maximize total profit. It only makes Wisconsin Cheeseman. Because marginal revenue is a sense, right? If the firm is earning $10 per unit, it must be horizontal line, the per-unit profit is maximized when the 6.3 doing better than if it were earning $8 per unit. The flaw ATC is at its lowest point. This happens to be point A in this reasoning is that it only takes half of the optimal in Exhibit 6.6. But it’s not difficult to compute that The solution into consideration. That is, from the total profit Cheeseman’s profit at this point is lower than when pro- equation it only takes (price − ATC) into consideration. duction is expanded until MR = MC. In fact, at point A 6.4 Recall that total profit comprises not only how much daily profit is $215.97. This is much smaller than the daily you sell each unit for in the market but also how many profit of $245 when profits are optimized. This might units you actually sell. If the $10 per unit is earned with seem like a trivial difference, but if you translate these 6.5 500 units of sales, then total profits are $5,000. But if the numbers across several plants and over several years, $8 per unit is earned with 1,000 units of sales, then the you’re talking about big money. profit is $8,000—considerably more, even though the per- unit profits are lower. 6.6 6.3 From the Seller’s Problem to the Supply Curve The MR = MC rule is powerful because, by linking the market price to the marginal cost curve, we can determine in the short run how a competitive firm changes its output when the market price changes. That is, it permits us to describe the firm’s supply curve, which relates output to prices. To see why, The firm’s supply curve relates output think about how the market price determines the firm’s output to prices. choice. For instance, how would The Cheeseman change its behavior if the price for packing cheese increased to $1.41 per box, as shown in Exhibit 6.8? We would expect The Cheeseman to increase its quantity supplied, but by how much? Using the intuition discussed earlier, we expect The Cheeseman to ex- pand production until MC = MR3, which occurs at 1,390 units. Exhibit 6.8 Impact of Price $3.0 Price Changes on The Wisconsin Cheeseman 2.5 If the market price 2.0 Marginal Cost changes, the marginal revenue curve that The Cheeseman faces will also 1.5 1.41 MR3 change. Here, when The MR1 Cheeseman faces an up- 1.0 ward shift of the marginal 0.78 MR2 revenue curve to MR3, 0.5 production will increase. On the other hand, if The Cheeseman faces a down- 500 1,000 1,500 2,000 2,500 ward shift of the marginal Quantity Q = 854 Q = 1,390 revenue curve to MR2, production will decrease. Q = 1,225 162 Chapter 6 | Sellers and Incentives M06_ACEM9202_01_GE_CH06.indd 162 14/03/15 2:30 PM  If, however, the market price for cheese boxes decreased to $0.78 per box (also shown in Exhibit 6.8), The Cheeseman would decrease production until MC = MR2, which occurs at 6.1 854 units. Importantly, we can trace out The Cheeseman’s supply curve by completing this exercise for various price levels. 6.2 Price Elasticity of Supply When considering how responsive the firm is to price changes, much like the case with demand in Chapter 5, we can use elasticity measures. In this case, the most important 6.3 Price elasticity of supply is the measure that economists use is called the , the measure of how measure of how responsive quantity responsive quantity supplied is to price changes is computed as: supplied is to price changes. Percentage change in quantity supplied 6.4 Price elasticity of supply (εs) =. Percentage change in price The price elasticity of supply will tend to be positive because as price increases, firms 6.5 tend to increase their quantity supplied. Characterizing supply curves is quite similar to the descriptions we used to describe demand curves in Chapter 5. For example, an elastic supply means that quantity supplied is quite responsive to price changes: any given percentage change in price leads to a larger 6.6 percentage change in quantity supplied. Panel (a) in Exhibit 6.9 shows the extreme case: a perfectly elastic supply curve. In this case, even a very small change in price leads to an infinite change in quantity supplied. Alternatively, an inelastic supply means that any given percentage change in price causes a smaller percentage change in quantity supplied. An extreme case is depicted in panel (c) of Exhibit 6.9. Here the supply curve is perfectly inelastic: at every price level the same quantity is supplied. An example of such a case is an oil refinery that is operating at full capacity: even if gasoline prices increase, it cannot increase production in the short run. Similarly, if corn prices suddenly jump in July, it is difficult for Iowan farmers to produce more corn in the short run. They can plant more corn next year, but not this year. In between these two extremes are typical supply curves—those that are upward- sloping. One example is presented in panel (b) of Exhibit 6.9. In these cases, the steeper the supply curve, the less sensitive quantity supplied is to price changes. Panel (b) of Exhibit 6.9 shows a special type of supply curve, one that is unit-elastic. A price increase from $5 to $6 (a 20 percent increase) leads to a 20 percent increase in quantity supplied; likewise, a price decrease from $6 to $5 (a 17 percent decrease) leads to a 17 percent decrease in quantity supplied. For unit-elastic supply curves, the elasticity is equal to 1: a 1 percent change in price leads to a 1 percent change in quantity supplied. Price Price Price εS = 0 1. 20% increase in price. Supply εS = 1 1. 20% increase in price. Supply $6 $6 Supply 2. 20% increase in 2. And a 0% increase $5 εS = ∞ 5 5 quantity supplied. in quantity supplied. Quantity 100 120 Quantity 100 Quantity (a) Perfectly Elastic Supply (b) Unit-Elastic Supply (c) Perfectly Inelastic Supply Exhibit 6.9 Various Supply Curves The three panels visually summarize, in order from left to right, a perfectly elastic sup- ply curve, a unit-elastic supply curve, and a perfectly inelastic supply curve. Section 6.3 | From the Seller’s Problem to the Supply Curve 163 M06_ACEM9202_01_GE_CH06.indd 163 14/03/15 2:30 PM  Much like demand elasticities, the size of supply elasticities is determined by several factors. Key determinants include whether the firm has excess inventories—if The Cheese- 6.1 man has several tons of cheese on hand, it can more easily increase production quantities. Likewise, how long the firm has to respond to price changes is important—the longer the time to respond, the more elastic the supply. Finally, if workers are readily available, then 6.2 supply will be more elastic because the firm can respond to price increases by quickly hir- ing workers. 6.3 Shutdown With an understanding of how quantity supplied responds to price changes, we can con- Shutdown is a short-run decision sider extreme market situations, such as when the firm should , or suspend, op- 6.4 to not produce anything during a erations. A shutdown is a short-run decision to not produce anything during a specific time specific period. period. Think about the case when the market price drops to $0.59 per cheese box. Now the MR = MC rule directs The Cheeseman to produce at point S in Exhibit 6.10 (444 units). Is 6.5 this a profit-maximizing point of production? The answer is no. This is because at this particular price the firm does not even bring in enough money to cover its average variable cost of $0.65 per unit. Why? Note that the 6.6 price is below average variable cost at this point ($0.59 < $0.65); thus if The Cheeseman continues operations, it is paying the variable input—workers—more to produce cheese boxes than the firm is bringing in per cheese box. The Cheeseman should shut down because by doing so it would lose only the fixed costs of production ($200) rather than the fixed costs ($200) plus the uncovered variable costs ($0.06 per unit, or 444 × $0.06 = $26.64). This is so because by shutting down the plant, it employs no workers, and hence has zero variable cost. You might think, “Wait a second! Why shut down and absorb the fixed costs? By pro- ducing, The Cheeseman can at least earn some revenues.” That is true. The Cheeseman would bring in money by remaining in operation, but for every unit it produces it is paying labor $0.06 more than it is receiving in marginal revenue. The optimization rule that fol- lows is that if revenues do not cover all of the variable costs, then shutdown is optimal in the short run: The firm should shut down if price is less than AVC. So, should The Cheeseman ever produce in the short run if total costs exceed total rev- enues? The answer is yes. Consider point C in Exhibit 6.10. This is a point of production where price is greater than average variable cost, but price is less than average total cost. In this case, the price is greater than the average variable cost; thus all of the variable costs are covered by revenues. This is an instance when The Cheeseman should continue operations Exhibit 6.10 The Price $2.0 Wisconsin Cheeseman’s Marginal Cost Shutdown Decision 1.8 This exhibit shows sev- 1.6 Average eral different MR curves, Total Cost allowing us to visualize 1.4 Average when The Cheeseman Variable Cost produces and when it 1.2 Original MR shuts down. The original 1.0 MR curve is well above the other two MR curves C 0.8 MR at C introduced, which intersect the MC curve 0.6 MR at S at points C and S. S 500 1,000 1,500 2,000 2,500 Quantity 164 Chapter 6 | Sellers and Incentives M06_ACEM9202_01_GE_CH06.indd 164 14/03/15 2:30 PM  Exhibit 6.11 Short-Run Supply Curve: Price $2.5 6.1 Short-Run Supply Portion of the MC Above AVC Here we reproduce Exhibit 6.4, but 2.0 we’ve done two things to the original Average 6.2 MC curve. First, we’re now referring Total Cost 1.5 to it as the short-run supply curve and Average second, the portion below the AVC Variable Cost curve is cut off because at prices below 1.0 6.3 the minimum AVC the firm shuts down. 0.5 6.4 500 1,000 1,500 2,000 2,500 Quantity 6.5 6.6 even though it is losing money because besides covering all of the variable costs, it is also covering a fraction of the fixed costs. You might think that it does not make sense for The Cheeseman to continue production at point C; after all, the firm is losing money! Why not shut down? The key is that we as- Sunk costs are costs that, once sume fixed costs are , which are a special type of cost that, once they have been committed, can never be recovered committed, can never be recovered (think of a 5-year building lease—The Cheeseman is and should not affect current and by law required to pay rent over the entire 5-year period). That is, The Cheeseman can’t future production decisions. retrieve sunk costs in the short run. One of the important things to remember about sunk costs is that once they are committed, they shouldn’t affect current or future production decisions. The reason for this is simple: these costs are sunk—that is, lost, regardless of what action is chosen next—they can’t affect the relative costs and benefits of current and future production decisions. By continuing operations at point C, The Cheeseman is at least covering some of the fixed cost. These examples lead to construction of the short-run supply curve for The Cheeseman: it is the portion of its marginal cost curve that lies above average variable cost. If the market price puts The Cheeseman at a point on its marginal cost curve that lies below the minimum of the average variable cost curve, then the firm should shut down. Otherwise, it should produce. Exhibit 6.11 shows The Cheeseman’s short-run supply curve as the mar- ginal cost curve above the average variable cost curve. 6.4 Producer Surplus Similar to the concept of consumer surplus, economists have a means of measuring surplus for sellers. This is called producer surplus. Producer surplus is the difference is computed by taking the between the market price and the difference between the market price and the marginal cost curve. marginal cost curve. Thus, graphically, producer surplus is the area above the marginal cost curve and below the equilibrium price line. In this way, it is distinct from economic profits, as we measured in Producer surplus is computed by Exhibit 6.7, because economic profits include a consideration of taking the difference between the total cost, not just marginal cost. Let’s consider producer surplus for The Cheeseman. Assume market price and the marginal cost that The Cheeseman is facing a market price of $2, as depicted in curve. Exhibit 6.12. As it turns out, The Cheeseman can produce many units at a mar- ginal cost below the market price. In Exhibit 6.12, we depict this surplus as the pink-shaded region that is below the market price and above The Cheeseman’s marginal cost curve. Notice the similarity between this and consumer surplus—whereas a Section 6.4 | Producer Surplus 165 M06_ACEM9202_01_GE_CH06.indd 165 14/03/15 2:30 PM  6.1 Exhibit 6.12 Measuring Producer Price $2.5 Marginal Surplus Cost The vertical distance between the PMARKET = $2.0 6.2 market price and the marginal cost to produce each unit represents producer surplus. 1.5 Producer Surplus 6.3 1.0 0.5 6.4 500 1,000 1,500 2,000 2,500 6.5 Quantity 6.6 consumer’s surplus arises from having a willingness to pay above the market price, a pro- ducer’s surplus arises from selling units at a price that is above marginal cost. Similar to consumer surplus, we can add up sellers’ producer surplus to obtain the total producer surplus in the market. We do this by measuring the area above the marginal cost curve that is below the equilibrium price line to compute producer surplus for the entire market. When we have linear supply curves, we can use a mathematical formula to compute the producer surplus. Consider panel (a) of Exhibit 6.13, which shows a supply curve for daily trucking services to ship cheese from Madison, Wisconsin to Milwaukee, Wisconsin. If the equilibrium market price is $100 per trip, then we compute the producer surplus as the base of the triangle multiplied by the height of the triangle multiplied by ½: Producer surplus = ½ × (Base of triangle × Height of triangle) = ½ × (4 × $80) = $160. This means that total producer surplus per day is $160 in this market. There are several ways in which producer surplus can increase or decrease. For exam- ple, if there is a shift in the market demand curve that causes a higher equilibrium market price, producer surplus increases because the area above the supply curve and below the equilibrium price line gets larger. This is shown in panel (b) of Exhibit 6.13. Now producer surplus is ½ × (5 × $100) = $250. Exhibit 6.13 Producer Price $140 Marginal Cost Price $140 Marginal Cost Surplus for Trucking (Supply) (Supply) 120 Pnew = $120 Services Producer The two panels show the P = $100 Pold = $100 Surplus supply curve for trucking, Producer 80 Surplus 80 with dotted red lines representing the MR curve 60 60 faced by the producer. 40 40 Panel (a) shows that producer surplus is the 20 20 triangle below MR and above the supply (marginal 1 2 3 4 5 6 7 1 2 3 4 5 6 7 cost) curve. Panel (b) shows Quantity Quantity what happens to producer (a) (b) surplus when the price increases. 166 Chapter 6 | Sellers and Incentives M06_ACEM9202_01_GE_CH06.indd 166 14/03/15 2:30 PM  6.5 From the Short Run 6.1 to the Long Run Thus far we have only considered The Cheeseman’s daily production decision, and in doing 6.2 so, we’ve treated the facilities and machinery (or physical capital) that The Cheeseman uses as fixed. But firms often think about more than just each day’s production. For example, many businesses issue quarterly or annual reports that discuss the firm’s long-term out- 6.3 look. In this section we move from the daily supply decision to the long run, where The Cheeseman can combine any quantity of labor and physical capital to maximize profits. What exactly is the long run, though? As we have already noted, the long run is defined 6.4 as a period of time in which all factors of production are variable. That is, in the