CHAPTER 6
Competitive markets never leave profit opportunities unexploited for long.©Pixtal/age fotostock
LEARNING OBJECTIVES
After reading this chapter, you should be able to:
1. LO1Explain how opportunity cost is related to the supply curve.
2. LO2Discuss the relationship between the supply curve for an individual firm and the market supply curve for an industry.
3. LO3Determine a perfectly competitive firm’s profit-maximizing output level and profit in the short run and long run.
4. LO4Connect the determinants of supply with the factors that affect individual firms’ costs and apply the theory of supply.
5. LO5Define and calculate producer surplus.
Cars that took more than 50 hours to assemble in the 1970s are now built in less than 8 hours. Similar productivity growth has occurred in many other manufacturing industries. Yet in many service industries, productivity has grown only slowly, if at all. For example, the London Philharmonic Orchestra performs Beethoven’s Fifth Symphony with no fewer musicians today than it did in 1850. And it still takes a barber about half an hour to cut someone’s hair, just as it always has.
Given the spectacular growth in manufacturing workers’ productivity, it’s no surprise that their real wages have risen more than fivefold during the last century. But why have real wages for service workers risen just as much? If barbers and musicians are no more productive than they were at the turn of the century, why are they now paid five times as much?
An answer is suggested by the observation that the opportunity cost of pursuing any given occupation is the most one could have earned in some other occupation. Most people who become barbers or musicians could instead have chosen jobs in manufacturing. If workers in service industries were not paid roughly as much as they could have earned in other occupations, many of them would not have been willing to work in service industries in the first place.
The trajectories of wages in manufacturing and service industries illustrate the intimate link between the prices at which goods and services are offered for sale in the market and the opportunity cost of the resources required to produce them.
In Chapter 5, Demand, we saw that the demand curve is a schedule that tells how many units buyers wish to purchase at different prices. Our task here is to gain insight into the factors that shape the supply curve, the schedule that tells how many units suppliers wish to sell at different prices.
Why are barbers paid five times as much now as in 1900, even though they can’t cut hair any faster than they could then?
Although the demand side and the supply side of the market are different in several ways, many of these differences are superficial. Indeed, the behavior of both buyers and sellers is, in an important sense, fundamentally the same. After all, the two groups confront essentially similar questions—in the buyer’s case, “Should I buy another unit?” and in the seller’s, “Should I sell another unit?” What is more, buyers and sellers use the same criterion for answering these questions. Thus, a rational consumer will buy another unit if its benefit exceeds its cost and a rational seller will sell another unit if the cost of making it is less than the extra revenue he can get from selling it (the familiar Cost-Benefit Principle again).
Cost-Benefit
THINKING ABOUT SUPPLY: THE IMPORTANCE OF OPPORTUNITY COST
Do you live in a state that requires refundable soft drink container deposits? If so, you’ve probably noticed that some people always redeem their own containers while other people pass up this opportunity, leaving their used containers to be recycled by others. Recycling used containers is a service and its production obeys the same logic that applies to the production of other goods and services. The following sequence of recycling examples shows how the supply curve for a good or service is rooted in the individual’s choice of whether to produce it.
EXAMPLE 6.1Opportunity Cost and Supply
How much time should Harry spend recycling soft drink containers?
Harry is trying to decide how to divide his time between his job as a dishwasher in the dining hall, which pays $6 an hour for as many hours as he chooses to work, and gathering soft drink containers to redeem for deposit, in which case his pay depends on both the deposit per container and the number of containers he finds. Earnings aside, Harry is indifferent between the two tasks, and the number of containers he’ll find depends, as shown in the table below, on the number of hours per day he searches:
If the containers may be redeemed for 2 cents each, how many hours should Harry spend searching for containers?
For each additional hour Harry spends searching for soft drink containers, he loses the $6 he could have earned as a dishwasher. This is his hourly opportunity cost of searching for soft drink containers. His benefit from each hour spent searching for containers is the number of additional containers he finds (shown in column 3 of the table) times the deposit he collects per container. Since he can redeem each container for 2 cents, his first hour spent collecting containers will yield earnings of 600($0.02) = $12, or $6 more than he could have earned as a dishwasher.
Cost-Benefit
By the Cost-Benefit Principle, then, Harry should spend his first hour of work each day searching for soft drink containers rather than washing dishes. A second hour searching for containers will yield 400 additional containers, for additional earnings of $8, so it too satisfies the cost-benefit test. A third hour spent searching yields 300 additional containers, for 300($0.02) = $6 of additional earnings. Since this is exactly what Harry could have earned washing dishes, he’s indifferent between spending his third hour of work each day on one task or the other. For the sake of discussion, however, we’ll assume that he resolves ties in favor of searching for containers, in which case he’ll spend three hours each day searching for containers.
What is the lowest redemption price that would induce Harry to spend at least one hour per day recycling? Since he’ll find 600 containers in his first hour of search, a 1 cent deposit on each container would enable him to match his $6 per hour opportunity cost. More generally, if the redemption price is p, and the next hour spent searching yields ΔQ additional containers, then Harry’s additional earnings from searching the additional hour will be p(ΔQ). This means that the smallest redemption price that will lead Harry to search another hour must satisfy the equation
(6.1)
How high would the redemption price of containers have to be to induce Harry to search for a second hour? Since he can find ΔQ = 400 additional containers if he searches for a second hour, the smallest redemption price that will lead him to do so must satisfy p(400) = $6, which solves for p = 1.5 cents.
CONCEPT CHECK 6.1
In the example above, calculate the lowest container redemption prices that will lead Harry to search a third, fourth, and fifth hour.
By searching for soft drink containers, Harry becomes, in effect, a supplier of container-recycling services. In Concept Check 6.1, we saw that Harry’s reservation prices for his third, fourth, and fifth hours of container search are 2, 3, and 6 cents, respectively. Having calculated these reservation prices, we can now plot his supply curve of container-recycling services. This curve, which plots the redemption price per container on the vertical axis and the number of containers recycled each day on the horizontal axis, is shown in Figure 6.1. Harry’s individual supply curve of container- recycling services tells us the number of containers he is willing to recycle at various redemption prices.
FIGURE 6.1 An Individual Supply Curve for Recycling Services.When the deposit price increases, it becomes attractive to abandon alternative pursuits to spend more time searching for soft drink containers.
The supply curve shown in Figure 6.1 is upward-sloping, just like those we saw in Chapter 3, Supply and Demand. There are exceptions to this general rule, but sellers of most goods will offer higher quantities at higher prices.
INDIVIDUAL AND MARKET SUPPLY CURVES
The relationship between the individual and market supply curves for a product is analogous to the relationship between the individual and market demand curves. The quantity that corresponds to a given price on the market demand curve is the sum of the quantities demanded at that price by all individual buyers in the market. Likewise, the quantity that corresponds to any given price on the market supply curve is the sum of the quantities supplied at that price by all individual sellers in the market.
Suppose, for example, that the supply side of the recycling-services market consists only of Harry and his identical twin, Barry, whose individual supply curve is the same as Harry’s. To generate the market supply curve, we first put the individual supply curves side by side, as shown in Figure 6.2(a) and (b). We then announce a price, and for that price add the individual quantities supplied to obtain the total quantity supplied in the market. Thus, at a price of 3 cents per container, both Harry and Barry wish to recycle 1,500 cans per day, so the total market supply at that price is 3,000 cans per day. Proceeding in like manner for a sequence of prices, we generate the market supply curve for recycling services shown in Figure 6.2(c). This is the same process of horizontal summation by which we generated market demand curves from individual demand curves in Chapter 5, Demand.
FIGURE 6.2 The Market Supply Curve for Recycling Services.To generate the market supply curve (c) from the individual supply curves (a) and (b), we add the individual supply curves horizontally.
Alternatively, if there were many suppliers with individual supply curves identical to Harry’s, we could generate the market supply curve by simply multiplying each quantity value on the individual supply curve by the number of suppliers. For instance, Figure 6.3 shows the supply curve for a market in which there are 1,000 suppliers with individual supply curves like Harry’s.
FIGURE 6.3 The Market Supply Curve with 1,000 Identical Sellers.To generate the market supply curve for a market with 1,000 identical sellers, we simply multiply each quantity value on the individual supply curve by 1,000.
Why do individual supply curves tend to be upward-sloping? One explanation is suggested by the Principle of Increasing Opportunity Cost, or the Low-Hanging-Fruit Principle. Container recyclers will tend to be more productive if they always look first for the containers that are easiest to find—such as those in plain view in readily accessible locations. As the redemption price rises, it will pay to incur the additional cost of searching farther from the beaten path.
Increasing Opportunity Cost
If all individuals have identical upward-sloping supply curves, the market supply curve will be upward-sloping as well. But there is an important additional reason for the positive slope of market supply curves: Individual suppliers generally differ with respect to their opportunity costs of supplying the product. (The Principle of Increasing Opportunity Cost applies not only to each individual searcher, but also across individuals.) Thus, whereas people facing unattractive employment opportunities in other occupations may be willing to recycle soft drink containers even when the redemption price is low, those with more attractive options will recycle only if the redemption price is relatively high.
Increasing Opportunity Cost
In summary, then, the upward slope of the supply curve reflects the fact that costs tend to rise at the margin when producers expand production, partly because each individual exploits her most attractive opportunities first, but also because different potential sellers face different opportunity costs.
PROFIT-MAXIMIZING FIRMS IN PERFECTLY COMPETITIVE MARKETS
To explore the nature of the supply curve of a product more fully, we must say more about the goals of the organizations that supply the product and the kind of economic environment in which they operate. In virtually every economy, goods and services are produced by a variety of organizations that pursue a host of different motives. The Red Cross supplies blood because its organizers and donors want to help people in need; the local government fixes potholes because the mayor was elected on a promise to do so; karaoke singers perform because they like public attention; and car-wash employees are driven primarily by the hope of making enough money to pay their rent.
PROFIT MAXIMIZATION
Notwithstanding this rich variety of motives, most goods and services that are offered for sale in a market economy are sold by private firms whose main reason for existing is to earn profit for their owners. A firm’s profit is the difference between the total revenue it receives from the sale of its product and all costs it incurs in producing it.
A profit-maximizing firm is one whose primary goal is to maximize the amount of profit it earns. The supply curves that economists use in standard supply and demand theory are based on the assumption that goods are sold by profit-maximizing firms in perfectly competitive markets, which are markets in which individual firms have no influence over the market prices of the products they sell. Because of their inability to influence market price, perfectly competitive firms are often described as price takers.
The following four conditions are characteristic of markets that are perfectly competitive:
1. All firms sell the same standardized product. Although this condition is almost never literally satisfied, it holds as a rough approximation for many markets. Thus, the markets for concrete building blocks of a given size, or for apples of a given variety, may be described in this way. This condition implies that buyers are willing to switch from one seller to another if by so doing they can obtain a lower price.
2. The market has many buyers and sellers, each of which buys or sells only a small fraction of the total quantity exchanged. This condition implies that individual buyers and sellers will be price takers, regarding the market price of the product as a fixed number beyond their control. For example, a single farmer’s decision to plant fewer acres of wheat would have no appreciable impact on the market price of wheat, just as an individual consumer’s decision to become a vegetarian would have no perceptible effect on the price of beef.
3. Productive resources are mobile. This condition implies that if a potential seller identifies a profitable business opportunity in a market, he or she will be able to obtain the labor, capital, and other productive resources necessary to enter that market. By the same token, sellers who are dissatisfied with the opportunities they confront in a given market are free to leave that market and employ their resources elsewhere.
4. Buyers and sellers are well informed. This condition implies that buyers and sellers are aware of the relevant opportunities available to them. If that were not so, buyers would be unable to seek out sellers who charge the lowest prices, and sellers would have no means of deploying their resources in the markets in which they would earn the most profit.
The market for wheat closely approximates a perfectly competitive market. The market for operating systems for desktop computers, however, does not. More than 80 percent of desktop operating systems are sold by Microsoft, giving the company enough influence in that market to have significant control over the price it charges. For example, if it were to raise the price of its latest edition of Windows by, say, 20 percent, some consumers might switch to Macintosh or Linux, and others might postpone their next upgrade; but many—perhaps even most—would continue with their plans to buy Windows. That pattern, however, appears to be changing with the growing importance of mobile computing.
By contrast, if an individual wheat farmer were to charge even a few cents more than the current market price for a bushel of wheat, he wouldn’t be able to sell any of his wheat at all. And since he can sell as much wheat as he wishes at the market price, he has no motive to charge less.
THE DEMAND CURVE FACING A PERFECTLY COMPETITIVE FIRM
From the perspective of an individual firm in a perfectly competitive market, what does the demand curve for its product look like? Since it can sell as much or as little as it wishes at the prevailing market price, the demand curve for its product is perfectly elastic at the market price. Figure 6.4(a) shows the market demand and supply curves intersecting to determine a market price of P0. Figure 6.4(b) shows the product demand curve, Di, as seen by any individual firm in this market, a horizontal line at the market price level P0.
FIGURE 6.4 The Demand Curve Facing a Perfectly Competitive Firm.The market demand and supply curves intersect to determine the market price of the product (a). The individual firm’s demand curve, Di (b), is a horizontal line at the market price.
Many of the conclusions of the standard supply and demand model also hold for imperfectly competitive firms—those firms, like Microsoft, that have at least some ability to vary their own prices. But certain other conclusions do not, as we shall see when we examine the behavior of such firms more closely in Chapter 8, Monopoly, Oligopoly, and Monopolistic Competition.
Because a perfectly competitive firm has no control over the market price of its product, it needn’t worry about choosing the level at which to set that price. As we’ve seen, the equilibrium market price in a competitive market comes from the intersection of the industry supply and demand curves. The challenge confronting the perfectly competitive firm is to choose its output level so that it makes as much profit as it can at that price. As we investigate how the competitive firm responds to this challenge, we’ll see that some costs are more important than others.
PRODUCTION IN THE SHORT RUN
To gain a deeper understanding of the origins of the supply curve, it is helpful to consider a perfectly competitive firm confronting the decision of how much to produce. The firm in question is a small company that makes glass bottles. To keep things simple, suppose that the silica required for making bottles is available free of charge from a nearby desert and that the only costs incurred by the firm are the wages it pays its employees and the lease payment on its bottle-making machine. The employees and the machine are the firm’s only two factors of production—inputs used to produce goods and services. In more complex examples, factors of production also might include land, structures, entrepreneurship, and possibly others, but for the moment we consider only labor and capital.
When we refer to the short run, we mean a period of time during which at least some of the firm’s factors of production cannot be varied. For our bottle maker, we will assume that the number of employees can be varied on short notice but that the capacity of its bottle-making machine can be altered only with significant delay. For this firm, then, the short run is simply that period of time during which the firm cannot alter the capacity of its bottle-making machine. By contrast, when we speak of the long run, we refer to a time period of sufficient length that all the firm’s factors of production are variable.
Table 6.1 shows how the company’s bottle production depends on the number of hours its employees spend on the job each day. The output–employment relationship described in Table 6.1 exhibits a pattern that is common to many such relationships. Each time we add an additional unit of labor, output grows, but beyond some point the additional output that results from each additional unit of labor begins to diminish. Note in the right column, for example, that output gains begin to diminish with the third employee. Economists refer to this pattern as the law of diminishing returns, and it always refers to situations in which at least some factors of production are fixed.
Law of Diminishing Returns: When some factors of production are held fixed, increased production of the good eventually requires ever-larger increases in the variable factor.
Here, the fixed factor is the bottle-making machine, and the variable factor is labor. In the context of this example, the law of diminishing returns says simply that successive increases in the labor input eventually yield smaller and smaller increments in bottle output. (Strictly speaking, the law ought to be called the law of eventually diminishing returns because output may initially grow at an increasing rate with additional units of the variable factor.)
Typically, returns from additional units of the variable input eventually diminish because of some form of congestion. For instance, in an office with three secretaries and only a single desktop computer, we would not expect to get three times as many letters typed per hour as in an office with only one secretary because only one person can use a computer at a time.
SOME IMPORTANT COST CONCEPTS
For the bottle-making firm described in Table 6.1, suppose the lease payment for the company’s bottle-making machine is $40 per day, which must be paid whether the company makes any bottles or not. This payment is both a fixed cost (since it does not depend on the number of bottles per day the firm makes) and, for the duration of the lease, a sunk cost. The first two columns of Table 6.2 reproduce the employment and output entries from Table 6.1, and the firm’s fixed cost appears in column 3.
The company’s payment to its employees is called variable cost because, unlike fixed cost, it varies with the number of bottles the company produces. The variable cost of producing 200 bottles per day, for example, is shown in column 4 of Table 6.2 as $24 per day. Column 5 shows the firm’s total cost, which is the sum of its fixed and variable costs. Column 6, finally, shows the firm’s marginal cost, a measure of how its total cost changes when its output changes. Specifically, marginal cost is defined as the change in total cost divided by the corresponding change in output. Note, for example, that when the firm expands production from 80 to 200 bottles per day, its total cost goes up by $12, which gives rise to the marginal cost entry of ($12/day)/(120 bottles/day) = $0.10 per bottle. To emphasize that marginal cost refers to the change in total cost when quantity changes, we place the marginal cost entries between the corresponding quantity rows of the table.
CHOOSING OUTPUT TO MAXIMIZE PROFIT
In the following examples and exercises, we’ll explore how the company’s decision about how many bottles to produce depends on the price of bottles, the wage, and the cost of capital. Again, our starting assumption is that the firm’s basic goal is to maximize the amount of profit it earns from the production and sale of bottles, where profit is the difference between its total revenue and its total cost.
Profit = Total revenue − Total cost = Total revenue − Variable cost − Fixed cost(6.2)
EXAMPLE 6.2The Profit-Maximizing Output Level
If bottles sell for 35 cents each, how many bottles should the company described in Table 6.2 produce each day?
Cost-Benefit
To answer this question, we need simply apply the Cost-Benefit Principle to the question “Should the firm expand its level of output?” If its goal is to maximize its profit, the answer to this question will be to expand as long as the marginal benefit from expanding is at least as great as the marginal cost. Since the perfectly competitive firm can sell as many bottles as it wishes at the market price of $0.35 per bottle, its marginal benefit from selling an additional bottle is $0.35. If we compare this marginal benefit with the marginal cost entries shown in column 6 of Table 6.2, we see that the firm should keep expanding until it reaches 300 bottles per day (four employees per day). To expand beyond that level, it would have to hire a fifth employee, and the resulting marginal cost ($0.40 per bottle) would exceed the marginal benefit.
To confirm that the Cost-Benefit Principle thus applied identifies the profit-maximizing number of bottles to produce, we can calculate profit levels directly, as in Table 6.3. Column 3 of this table reports the firm’s revenue from the sale of bottles, which is calculated as the product of the number of bottles produced per day and the price of $0.35 per bottle. Note, for example, that in the third row of that column, total revenue is (200 bottles/day)($0.35/bottle) = $70 per day. Column 5 reports the firm’s total daily profit, which is just the difference between its total revenue (column 3) and its total cost (column 4). Note that the largest profit entry in column 5, $17 per day, occurs at an output of 300 bottles per day, just as suggested by our earlier application of the Cost-Benefit Principle.
As the Concept Check 6.2 demonstrates, an increase in the price of the product gives rise to an increase in the profit-maximizing level of output.
CONCEPT CHECK 6.2
How would the profit-maximizing level of bottle production change in Example 6.2 if bottles sell for 62 cents each?
The Concept Check 6.3 illustrates that a fall in the wage rate leads to a decline in marginal cost, which also causes an increase in the profit-maximizing level of output.
CONCEPT CHECK 6.3
How would the profit-maximizing level of bottle production change in Example 6.2 if bottles sell for 35 cents each, but wages fall to $6 per day?
Suppose that in the example the firm’s fixed cost had been not $40 per day but $45 per day. How, if at all, would that have affected the firm’s profit-maximizing level of output? The answer is “not at all.” Each entry in the profit column of Table 6.3 would have been $5 per day smaller than before, but the maximum profit entry still would have been 300 bottles per day.
Cost-Benefit
The observation that the profit-maximizing quantity does not depend on fixed costs is not an idiosyncrasy of this example. That it holds true in general is an immediate consequence of the Cost-Benefit Principle, which says that a firm should increase its output if, and only if, the marginal benefit exceeds the marginal cost. Neither the marginal benefit of expanding (which is the market price of bottles) nor the marginal cost of expanding is affected by a change in the firm’s fixed cost.
When the law of diminishing returns applies (i.e., when some factors of production are fixed), marginal cost goes up as the firm expands production beyond some point. Under these circumstances, the firm’s best option is to keep expanding output as long as marginal cost is less than price.
Note that if the bottle company’s fixed cost had been any more than $57 per day, it would have made a loss at every possible level of output. As long as it still had to pay its fixed cost, however, its best bet would have been to continue producing 300 bottles per day. It’s better, after all, to experience a smaller loss than a larger one. If a firm in that situation expected conditions to remain the same, though, it would want to get out of the bottle business as soon as its equipment lease expired.
A NOTE ON THE FIRM’S SHUTDOWN CONDITION
It might seem that a firm that can sell as much output as it wishes at a constant market price would always do best in the short run by producing and selling the output level for which price equals marginal cost. But there are exceptions to this rule. Suppose, for example, that the market price of the firm’s product falls so low that its revenue from sales is smaller than its variable cost at all possible levels of output. The firm should then cease production for the time being. By shutting down, it will suffer a loss equal to its fixed costs. But by remaining open, it would suffer an even larger loss.
More formally, if P denotes the market price of the product and Q denotes the number of units produced and sold, then P × Q is the firm’s total revenue from sales, and if we use VC to denote the firm’s variable cost, the rule is that the firm should shut down in the short run if P × Q is less than VC for every level of Q:
Short-run shutdown condition: P × Q < VC for all levels of Q.(6.3)
CONCEPT CHECK 6.4
Using the bottle company example, suppose bottles sold not for $0.35 but only $0.10. Calculate the profit corresponding to each level of output, as in Table 6.3, and verify that the firm’s best option is to cease operations in the short run.
AVERAGE VARIABLE COST AND AVERAGE TOTAL COST
Suppose that the firm is unable to cover its variable cost at any level of output—that is, suppose that P × Q < VC for all levels of Q. It must then also be true that P < VC/Q for all levels of Q, since we obtain the second inequality by simply dividing both sides of the first one by Q. VC/Q is the firm’s average variable cost ( AVC )—its variable cost divided by its output. The firm’s short-run shutdown condition may thus be restated a second way: Discontinue operations in the short run if the product price is less than the minimum value of its average variable cost (AVC). Thus,
Short-run shutdown condition (alternate version): P < minimum value of AVC.(6.4)
As we’ll see in the next section, this version of the shutdown condition often enables us to tell at a glance whether the firm should continue operations.
A related cost concept that facilitates assessment of the firm’s profitability is average total cost ( ATC ), which is total cost (TC) divided by output (Q): ATC = TC/Q. The firm’s profit, again, is the difference between its total revenue (P × Q) and its total cost. And since total cost is equal to average total cost times quantity, the firm’s profit is also equal to (P × Q) − (ATC × Q). A firm is said to be profitable if its revenue (P × Q) exceeds its total cost (ATC × Q). A firm can thus be profitable only if the price of its product price (P) exceeds its ATC for some level of output.
Keeping track of all these cost concepts may seem tedious. In the next section, however, we’ll see that the payoff from doing so is that they enable us to recast the profit- maximization decision in a simple graphical framework.
A GRAPHICAL APPROACH TO PROFIT MAXIMIZATION
For the bottle-making firm we’ve been discussing, average variable cost and average total cost values are shown in columns 4 and 6 of Table 6.4. Using the entries in this table, we plot the firm’s average total cost, average variable cost, and marginal cost curves in Figure 6.5. (Because marginal cost corresponds to the change in total cost as we move between two output levels, each marginal cost value in Table 6.4 is plotted at an output level midway between those in the adjacent rows.)
FIGURE 6.5 The Marginal, Average Variable, and Average Total Cost Curves for a Bottle Manufacturer.The MC curve cuts both the AVC and ATC curves at their minimum points. The upward-sloping portion of the marginal cost curve corresponds to the region of diminishing returns.
We call your attention to several features of the cost curves in Figure 6.5. Note, for example, that the upward-sloping portion of the marginal cost curve (MC) corresponds to the region of diminishing returns discussed earlier. Thus, as the firm moves beyond two employees per day (200 bottles per day), the increments to total output become smaller with each additional employee, which means that the cost of producing additional bottles (MC) must be increasing in this region.
Note also that the definition of marginal cost implies that the marginal cost curve must intersect both the average variable cost curve (AVC) and the average total cost curve (ATC) at their respective minimum points. To see why, consider the logic that explains what happens to the average weight of children in a third-grade class when a new student joins the class. If the new (marginal) student is lighter than the previous average weight for the class, average weight will fall, but if the new student is heavier than the previous average, average weight will rise. By the same token, when marginal cost is below average total cost or average variable cost, the corresponding average cost must be falling, and vice versa. And this ensures that the marginal cost curve must pass through the minimum points of both average cost curves.
Seeing the bottle maker’s AVC curve displayed graphically makes the question posed in Concept Check 6.4 much easier to answer. The question, recall, was whether the firm should shut down in the short run if the price per bottle was only $0.10. A glance at Figure 6.5 reveals that the firm should indeed shut down because this price lies below the minimum value of its AVC curve, making it impossible for the firm to cover its variable costs at any output level.
PRICE = MARGINAL COST: THE MAXIMUM-PROFIT CONDITION
So far, we’ve implicitly assumed that the bottle maker could employ workers only in whole-number amounts. Under these conditions, we saw that the profit-maximizing output level was one for which marginal cost was somewhat less than price (because adding yet another employee would have pushed marginal cost higher than price). In the next example, we’ll see that when output and employment can be varied continuously, the maximum-profit condition is that price be equal to marginal cost.
EXAMPLE 6.3The Graphical Approach to Profit Maximization
For the bottle maker whose cost curves are shown in Figure 6.6, find the profit-maximizing output level if bottles sell for $0.20 each. How much profit will this firm earn? What is the lowest price at which this firm would continue to operate in the short run?
FIGURE 6.6 Price = Marginal Cost: The Perfectly Competitive Firm’s Profit-Maximizing Supply Rule.If price is greater than marginal cost, the firm can increase its profit by expanding production and sales. If price is less than marginal cost, the firm can increase its profit by producing and selling less output.
Cost-Benefit
The Cost-Benefit Principle tells us that this firm should continue to expand as long as price is at least as great as marginal cost. In Figure 6.6 we see that if the firm follows this rule, it will produce 260 bottles per day, the quantity at which price and marginal cost are equal. To gain further confidence that 260 must be the profit-maximizing quantity when the price is $0.20 per bottle, first suppose that the firm had sold some amount less than that—say, only 200 bottles per day. Its benefit from expanding output by one bottle would then be the bottle’s market price, here 20 cents. The cost of expanding output by one bottle is equal (by definition) to the firm’s marginal cost, which at 200 bottles per day is only 10 cents (see Figure 6.6). So by selling the 201st bottle for 20 cents and producing it for an extra cost of only 10 cents, the firm will increase its profit by 20 − 10 = 10 cents per day. In a similar way, we can show that for any quantity less than the level at which price equals marginal cost, the seller can boost profit by expanding production.
Conversely, suppose that the firm was currently selling more than 260 bottles per day—say, 300—at a price of 20 cents each. In Figure 6.6 we see that marginal cost at an output of 300 is 30 cents per bottle. If the firm then contracted its output by one bottle per day, it would cut its costs by 30 cents while losing only 20 cents in revenue. As a result, its profit would grow by 10 cents per day. The same argument can be made regarding any quantity larger than 260, so if the firm is currently selling an output at which price is less than marginal cost, it can always do better by producing and selling fewer bottles.
We’ve thus established that if the firm sold fewer than 260 bottles per day, it could earn more profit by expanding; and if it sold more than 260, it could earn more by contracting. It follows that at a market price of 20 cents per bottle, the seller maximizes its profit by selling 260 units per day, the quantity for which price and marginal cost are exactly the same.
At that quantity the firm will collect total revenue of P × Q = ($0.20/bottle) (260 bottles/day) = $52 per day. Note in Figure 6.6 that at 260 bottles per day the firm’s average total cost is ATC = $0.12 per bottle, which means that its total cost is ATC × Q = ($0.12/bottle)(260 bottles/day) = $31.20 per day. The firm’s profit is the difference between its total revenue and its total cost, or $20.80 per day. Note, finally, that the minimum value of the firm’s AVC curve is $0.07. So if the price of bottles fell below 7 cents each, the firm would shut down in the short run.
Another attractive feature of the graphical method of finding the profit-maximizing output level is that it permits us to calculate the firm’s profit graphically. Thus, for the firm in the preceding example, daily profit is simply the difference between price and ATC times the number of units sold: ($0.20/bottle − $0.12/bottle)(260 bottles/day) = $20.80 per day, which is the area of the shaded rectangle in Figure 6.7.
FIGURE 6.7 Measuring Profit Graphically.Profit is equal to (P − ATC) × Q, which is equal to the area of the shaded rectangle.
Not all firms are as fortunate as the one shown in Figure 6.7. Suppose, for example, that the price of bottles had been not 20 cents but only 8 cents. Since that price is greater than the minimum value of AVC (see Figure 6.8), the firm should continue to operate in the short run by producing the level of output for which price equals marginal cost (180 bottles per day). But because price is less than ATC at that level of output, the firm will now experience a loss, or negative profit, on its operations. This profit is calculated as (P − ATC) × Q = ($0.08/bottle − $0.10/bottle) × (180 bottles/day) = −$3.60 per day, which is equal to the area of the shaded rectangle in Figure 6.8.
FIGURE 6.8 A Negative Profit.When price is less than ATC at the profit-maximizing quantity, the firm experiences a loss, which is equal to the area of the shaded rectangle.
In Chapter 7, Efficiency, Exchange, and the Invisible Hand in Action, we’ll see how firms move resources from one market to another in response to the incentives implicit in profits and losses. But such movements occur in the long run, and our focus here is on production decisions in the short run.
THE “LAW” OF SUPPLY
The law of demand tells us that consumers buy less of a product when its price rises. If there were an analogous law of supply, it would say that producers offer more of a product for sale when its price rises. Is there such a law? We know that supply curves are essentially marginal cost curves and that because of the law of diminishing returns, marginal cost curves are upward-sloping in the short run. And so there is indeed a law of supply that applies as stated in the short run.
In the long run, however, the law of diminishing returns does not apply. (Recall that it holds only if at least some factors of production are fixed.) Because firms can vary the amounts of all factors of production they use in the long run, they can often double their production by simply doubling the amount of each input they use. In such cases, costs would be exactly proportional to output and the firm’s marginal cost curve in the long run would be horizontal, not upward-sloping. So for now we’ll say only that the “law” of supply holds as stated in the short run but not necessarily in the long run. For both the long run and the short run, however, the perfectly competitive firm’s supply curve is its marginal cost curve.1
Every quantity of output along the market supply curve represents the summation of all the quantities individual sellers offer at the corresponding price. So the correspondence between price and marginal cost exists for the market supply curve as well as for the individual supply curves that lie behind it. That is, for every price–quantity pair along the market supply curve, price will be equal to each seller’s marginal cost of production.
This is why we sometimes say that the supply curve represents the cost side of the market, whereas the demand curve represents the benefit side of the market. At every point along a market demand curve, price represents what buyers would be willing to pay for an additional unit of the product—and this, in turn, is how we measure the amount by which they’d benefit by having an additional unit of the product. Likewise, at every point along a market supply curve, price measures what it would cost producers to expand production by one unit.
RECAP
PROFIT-MAXIMIZING FIRMS IN PERFECTLY COMPETITIVE MARKETS
The perfectly competitive firm faces a horizontal demand curve for its product, meaning that it can sell any quantity it wishes at the market price. In the short run, the firm’s goal is to choose the level of output that maximizes its profits. It will accomplish this by choosing the output level for which its marginal cost is equal to the market price of its product, provided that price exceeds average variable cost. The perfectly competitive firm’s supply curve is the portion of its marginal cost curve that lies above its average variable cost curve. At the profit-maximizing quantity, the firm’s profit is the product of that quantity and the difference between price and average total cost.
DETERMINANTS OF SUPPLY REVISITED
What factors give rise to changes in supply? (Again, remember that a “change in supply” refers to a shift in the entire supply curve, as opposed to a movement along the curve, which we call a “change in the quantity supplied.”) A seller will offer more units if the benefit of selling extra output goes up relative to the cost of producing it. And since the benefit of selling output in a perfectly competitive market is a fixed market price that is beyond the seller’s control, our search for factors that influence supply naturally focuses on the cost side of the calculation. The preceding examples suggest why the following factors, among others, will affect the likelihood that a product will satisfy the cost-benefit test for a given supplier.
TECHNOLOGY
Perhaps the most important determinant of production cost is technology. Improvements in technology make it possible to produce additional units of output at lower cost. This shifts each individual supply curve downward (or, equivalently, to the right) and hence shifts the market supply curve downward as well. Over time, the introduction of more sophisticated machinery has resulted in dramatic increases in the number of goods produced per hour of effort expended. Every such development gives rise to a rightward shift in the market supply curve.
But how do we know technological change will reduce the cost of producing goods and services? Might not new equipment be so expensive that producers who used it would have higher costs than those who relied on earlier designs? If so, then rational producers simply would not use the new equipment. The only technological changes that rational producers will adopt are those that will reduce their cost of production.
INPUT PRICES
Whereas technological change generally (although not always) leads to gradual shifts in supply, changes in the prices of important inputs can give rise to large supply shifts literally overnight. As discussed in the chapter on elasticity, for example, the price of crude oil, which is the most important input in the production of gasoline, often fluctuates sharply, and the resulting shifts in supply cause gasoline prices to exhibit corresponding fluctuations.
Similarly, when wage rates rise, the marginal cost of any business that employs labor also rises, shifting supply curves to the left (or, equivalently, upward). When interest rates fall, the opportunity cost of capital equipment also falls, causing supply to shift to the right.
THE NUMBER OF SUPPLIERS
Just as demand curves shift to the right when population grows, supply curves also shift to the right as the number of individual suppliers grows. For example, if container recyclers die or retire at a higher rate than new recyclers enter the industry, the supply curve for recycling services will shift to the left. Conversely, if a rise in the unemployment rate leads more people to recycle soft drink containers (by reducing the opportunity cost of time spent recycling), the supply curve of recycling services will shift to the right.
EXPECTATIONS
Expectations about future price movements can affect how much sellers choose to offer in the current market. Suppose, for example, that recyclers expect the future price of aluminum to be much higher than the current price because of growing use of aluminum components in cars. The rational recycler would then have an incentive to withhold aluminum from the market at today’s lower price, thereby to have more available to sell at the higher future price. Conversely, if recyclers expected next year’s price of aluminum to be lower than this year’s, their incentive would be to offer more aluminum for sale in today’s market.
CHANGES IN PRICES OF OTHER PRODUCTS
Apart from technological change, perhaps the most important determinant of supply is variation in the prices of other goods and services that sellers might produce. Prospectors, for example, search for those precious metals for which the surplus of benefits over costs is greatest. When the price of silver rises, many stop looking for gold and start looking for silver. Conversely, when the price of platinum falls, many platinum prospectors shift their attention to gold.
RECAP
THE DETERMINANTS OF SUPPLY
Among the relevant factors causing supply curves to shift are new technologies, changes in input prices, changes in the number of sellers, expectations of future price changes, and changes in the prices of other products that firms might produce.
APPLYING THE THEORY OF SUPPLY
Whether the activity is producing new soft drink containers or recycling used ones, or indeed any other production activity at all, the same logic governs all supply decisions in perfectly competitive markets (and in any other setting in which sellers can sell as much as they wish to at a constant price): keep expanding output until marginal cost is equal to the price of the product. This logic helps us understand why recycling efforts are more intensive for some products than others.
The Economic Naturalist 6.1
When recycling is left to private market forces, why are many more aluminum beverage containers recycled than glass ones?
In both cases, recyclers gather containers until their marginal costs are equal to the containers’ respective redemption prices. When recycling is left to market forces, the redemption price for a container is based on what companies can sell it (or the materials in it) for. Aluminum containers can be easily processed into scrap aluminum, which commands a high price, and this leads profit-seeking companies to offer a high redemption price for aluminum cans. By contrast, the glass from which glass containers are made has only limited resale value, primarily because the raw materials required to make new glass containers are so cheap. This difference leads profit-seeking companies to offer much lower redemption prices for glass containers than for aluminum ones.
In states that don’t have beverage container deposit laws, why are aluminum cans more likely to be recycled than glass bottles?
The high redemption prices for aluminum cans induce many people to track these cans down, whereas the low redemption prices for glass containers lead most people to ignore them. If recycling is left completely to market forces, then, we would expect to see aluminum soft drink containers quickly recycled, whereas glass containers would increasingly litter the landscape. This is in fact the pattern we do see in states without recycling laws. (More on how these laws work in a moment.) This pattern is a simple consequence of the fact that the supply curves of container-recycling services are upward-sloping.
The acquisition of valuable raw materials is only one of two important benefits from recycling. The second is that, by removing litter, recycling makes the environment more pleasant for everyone. As the next example suggests, this second benefit might easily justify the cost of recycling substantial numbers of glass containers.
EXAMPLE 6.4Why the Optimal Amount of Pollution Isn’t Zero
What is the socially optimal amount of recycling of glass containers?
Suppose that the 60,000 citizens of Burlington, Vermont, would collectively be willing to pay 6 cents for each glass container removed from their local environment. If the local market supply curve of glass container recycling services is as shown in Figure 6.9, what is the socially optimal level of glass container recycling?
FIGURE 6.9 The Supply Curve of Container Recycling Services for Burlington, Vermont.
Suppose the citizens of Burlington authorize their city government to collect tax money to finance litter removal. If the benefit of each glass container removed, as measured by what residents are collectively willing to pay, is 6 cents, the government should offer to pay 6 cents for each glass container recycled. To maximize the total economic surplus from recycling, we should recycle that number of containers for which the marginal cost of recycling is equal to the 6-cent marginal benefit. Given the market supply curve shown, the optimal quantity is 16,000 containers per day, and that is how many will be redeemed when the government offers 6 cents per container.
Although 16,000 containers per day will be removed from the environment in the preceding example, others will remain. After all, some are discarded in remote locations, and a redemption price of 6 cents per container is simply not high enough to induce people to track them all down.
So why not offer an even higher price and get rid of all glass container litter? For the example given, the reason is that the marginal cost of removing the 16,001st glass container each day is greater than the benefit of removing it. Total economic surplus is largest when we remove litter only up to the point that the marginal benefit of litter removal is equal to its marginal cost, which occurs when 16,000 containers per day are recycled. To proceed past that point is actually wasteful.
Scarcity
Many people become upset when they hear economists say that the socially optimal amount of litter is greater than zero. In the minds of these people, the optimal amount of litter is exactly zero. But this position completely ignores the Scarcity Principle. Granted, there would be benefits from reducing litter further, but there also would be costs. Spending more on litter removal therefore means spending less on other useful things. No one would insist that the optimal amount of dirt in his own home is zero. (If someone does make this claim, ask him why he doesn’t stay home all day vacuuming the dust that is accumulating in his absence.) If it doesn’t pay to remove all the dust from your house, it doesn’t pay to remove all the bottles from the environment. Precisely the same logic applies in each case.
If 16,000 containers per day is the optimal amount of litter removal, can we expect the individual spending decisions of private citizens to result in that amount of litter removal? Unfortunately we cannot. The problem is that anyone who paid for litter removal individually would bear the full cost of those services while reaping only a tiny fraction of the benefit. In Example 6.4, the 60,000 citizens of Burlington reaped a total benefit of 6 cents per container removed, which means a benefit of only (6/60,000) = 0.0001 cent per person! Someone who paid 6 cents for someone else to remove a container would thus be incurring a cost 60,000 times greater than his share of the resulting benefit.
Note that the incentive problem here is similar to the one discussed in the chapter on supply and demand for the person deciding whether to be vaccinated against an illness. The problem was that the incentive to be vaccinated was too weak because, even though the patient bears the full cost of the vaccination, many of the resulting benefits accrue to others. Thus, an important part of the extra benefit from any one person being vaccinated is that others also become less likely to contract the illness.
The case of glass container litter is an example in which private market forces do not produce the best attainable outcome for society as a whole. Even people who carelessly toss containers on the ground, rather than recycle them, are often offended by the unsightly landscape to which their own actions contribute. Indeed, this is why they often support laws mandating adequate redemption prices for glass containers.
Is the socially optimal quantity of litter zero?©PhotoAlto
Equilibrium
Activities that generate litter are a good illustration of the Equilibrium Principle described in Chapter 3, Supply and Demand. People who litter do so not because they don’t care about the environment, but because their private incentives make littering misleadingly attractive. Recycling requires some effort, after all, yet no individual’s recycling efforts have a noticeable effect on the quality of the environment. The soft drink container deposit laws enacted by numerous states were a simple way to bring individual interests more closely into balance with the interests of society as a whole. The vast majority of container litter disappeared almost literally overnight in states that enacted these laws.
CONCEPT CHECK 6.5
If the supply curve of glass container recycling services is as shown in the diagram, and each of the city’s 60,000 citizens would be willing to pay 0.00005 cent for each glass container removed from the landscape, at what level should the city government set the redemption price for glass containers, and how many will be recycled each day?
SUPPLY AND PRODUCER SURPLUS
The economic surplus received by a buyer is called consumer surplus. The analogous construct for a seller is producer surplus, the difference between the price a seller actually receives for the product and the lowest price for which she would have been willing to sell it (her reservation price, which in general will be her marginal cost).
As in the case of consumer surplus, the term producer surplus sometimes refers to the surplus received by a single seller in a transaction, while on other occasions it describes the total surplus received by all sellers in a market or collection of markets.
CALCULATING PRODUCER SURPLUS
In Chapter 5, Demand, we saw that consumer surplus in a market is the area bounded above by the demand curve and bounded below by the market price. Producer surplus in a market is calculated in an analogous way. As the following example illustrates, it is the area bounded above by the market price and bounded below by the market supply curve.
EXAMPLE 6.5Measuring Producer Surplus
How much do sellers benefit from their participation in the market for milk?
Consider the market for milk, whose demand and supply curves are shown in Figure 6.10, which has an equilibrium price of $2 per gallon and an equilibrium quantity of 4,000 gallons per day. How much producer surplus do the sellers in this market reap?
FIGURE 6.10 Supply and Demand in the Market for Milk.For the supply and demand curves shown, the equilibrium price of milk is $2 per gallon and the equilibrium quantity is 4,000 gallons per day.
In Figure 6.10, note first that for all milk sold up to 4,000 gallons per day, sellers receive a surplus equal to the difference between the market price of $2 per gallon and their reservation price as given by the supply curve. Total producer surplus received by buyers in the milk market is thus the shaded triangle between the supply curve and the market price in Figure 6.11. Note that this area is a right triangle whose vertical arm is h = $2/gallon and whose horizontal arm is b = 4,000 gallons/day. And since the area of any triangle is equal to (1/2)bh, producer surplus in this market is equal to
FIGURE 6.11 Producer Surplus in the Market for Milk.Producer surplus is the area of the shaded triangle ($4,000/day).
(1/2)(4,000 gallons/day)($2/gallon) = $4,000/day.
Producer surplus in this example may be thought of as the highest price sellers would pay, in the aggregate, for the right to continue participating in the milk market. It is $4,000 per day since that’s the amount by which their combined benefits exceed their combined costs.
As discussed in Chapter 3, Supply and Demand, the supply curve for a good can be interpreted either horizontally or vertically. The horizontal interpretation tells us, for each price, the total quantity that producers wish to sell at that price. The vertical interpretation tells us, for each quantity, the smallest amount a seller would be willing to accept for the good. For the purpose of computing producer surplus, we rely on the vertical interpretation of the supply curve. The value on the vertical axis that corresponds to each point along the supply curve corresponds to the marginal seller’s reservation price for the good, which is the marginal cost of producing it. Producer surplus is the cumulative sum of the differences between the market price and these reservation prices. It is the area bounded above by market price and bounded below by the supply curve.
SUMMARY
· The supply curve for a good or service is a schedule that, for any price, tells us the quantity that sellers wish to supply at that price. The prices at which goods and services are offered for sale in the market depend, in turn, on the opportunity cost of the resources required to produce them. (LO1)
· The demand curve facing a perfectly competitive firm is a horizontal line at the price for which industry supply and demand intersect. (LO2)
· Supply curves tend to be upward-sloping, at least in the short run, in part because of the Principle of Increasing Opportunity Cost. In general, rational producers will always take advantage of their best opportunities first, moving on to more difficult or costly opportunities only after their best ones have been exhausted. Reinforcing this tendency is the law of diminishing returns, which says that when some factors of production are held fixed, the amount of additional variable factors required to produce successive increments in output grows larger. The industry supply curve is the horizontal summation of the supply curves of individual firms in the industry. (LO2, LO3)
· For perfectly competitive markets—or, more generally, for markets in which individual sellers can sell whatever quantity they wish at a constant price—the seller’s best option is to sell that quantity of output for which price equals marginal cost, provided price exceeds the minimum value of average variable cost. The supply curve for the seller thus coincides with the portion of his marginal cost curve that exceeds average variable cost. This is why we sometimes say the supply curve represents the cost side of the market (in contrast to the demand curve, which represents the benefit side of the market). (LO3)
· Remember a “change in supply” means a shift in the entire supply curve, whereas a “change in quantity supplied” means a movement along the supply curve, Among the relevant factors causing supply curves to shift are new technologies, changes in input prices, changes in the number of sellers, expectations of future price changes, and changes in the prices of other products that firms might produce. You are now ready to apply the theory of supply. The logic that governs all supply decisions in perfectly competitive markets is as follows: keep expanding output until marginal cost is equal to the price of the product. (LO4)
· Producer surplus is a measure of the economic surplus reaped by a seller or sellers in a market. It is the cumulative sum of the differences between the market price and their reservation prices, which is the area bounded above by market price and bounded below by the supply curve. (LO5)
KEY TERMS
average total cost (ATC)
average variable cost (AVC)
factor of production
fixed cost
fixed factor of production
imperfectly competitive firm
law of diminishing returns
long run
marginal cost
perfectly competitive market
price taker
producer surplus
profit
profit-maximizing firm
profitable firm
short run
total cost
variable cost
variable factor of production
REVIEW QUESTIONS
1. 1.Explain why you would expect supply curves to slope upward on the basis of the Principle of Increasing Opportunity Cost. (LO1)
2. 2.True or false: The perfectly competitive firm should always produce the output level for which price equals marginal cost. (LO3)
3. 3.Economists often stress that congestion helps account for the law of diminishing returns. With this in mind, explain why it would be impossible to feed all the people on Earth with food grown in a single flowerpot, even if unlimited water, labor, seed, fertilizer, sunlight, and other inputs were available. (LO4)
4. 4.Which do you think is more likely to be a fixed factor of production for an ice cream producer during the next two months: its factory building or its workers who operate the machines? Explain. (LO4)
5. 5.Why do we use the vertical interpretation of the supply curve when we measure producer surplus? (LO5)
PROBLEMS
1. 1.Zoe is trying to decide how to divide her time between her job as a wedding photographer, which pays $27 per hour for as many hours as she chooses to work, and as a fossil collector, in which her pay depends on both the price of fossils and the number of fossils she finds. Earnings aside, Zoe is indifferent between the two tasks, and the number of fossils she can find depends on the number of hours a day she searches, as shown in the table below: (LO1)
a. Using the information above, compute the lowest price that Zoe would accept per fossil in order to justify her spending more time collecting fossils and less time working as a wedding photographer.
b. Plot these points in a graph with price on the vertical axis and quantity per day on the horizontal. What is this curve called?
2. 2. The supply curves for the only two firms in a competitive industry are given by, respectively, P = 2Q1 and P = 2 + Q2, where Q1 is the output of firm 1 and Q2 is the output of firm 2. What is the market supply curve for this industry? (Hint: Graph the two curves side by side; then add their respective quantities at a sample of different prices.) (LO2)
3. 3. A price-taking firm makes air conditioners. The market price of one of its new air conditioners is $120. The firm’s total cost information is given in the table below:
How many air conditioners should the firm produce per day if its goal is to maximize its profit? (LO3)
4. 4.For the pizza seller whose marginal, average variable, and average total cost curves are shown in the accompanying diagram, what is the profit-maximizing level of output and how much profit will this producer earn if the price of pizza is $2.50 per slice? (LO3)
5. 5.*For the pizza seller whose marginal, average variable, and average total cost curves are shown in the accompanying diagram, what is the profit-maximizing level of output and how much profit will this producer earn if the price of pizza is $0.50 per slice? (LO3)
6. 6.*For the pizza seller whose marginal, average variable, and average total cost curves are shown in the accompanying diagram (who is the same seller as in Problem 5), what is the profit-maximizing level of output and how much profit will this producer earn if the price of pizza is $1.18 per slice? (LO3)
7. 7.Paducah Slugger Company makes baseball bats out of lumber supplied to it by Acme Sporting Goods, which pays Paducah $10 for each finished bat. Paducah’s only factors of production are lathe operators and a small building with a lathe. The number of bats it produces per day depends on the number of employee-hours per day, as shown in the table below. (LO3, LO4)
a. If the wage is $15 per hour and Paducah’s daily fixed cost for the lathe and building is $60, what is the profit-maximizing quantity of bats?
b. What would be the profit-maximizing number of bats if the government imposed a tax of $10 per day on the company? (Hint: Think of this tax as equivalent to a $10 increase in fixed cost.)
c. What would be the profit-maximizing number of bats if the government imposed a tax of $2 per bat? (Hint: Think of this tax as equivalent to a $2-per-bat increase in marginal cost.)
d. Why do the taxes in parts b and c have such different effects?
8. 8.The demand and supply curves for the pizza market are shown in the graph below. Calculate daily producer surplus. (LO5)
ANSWERS TO CONCEPT CHECKS
1. 6.1Since Harry will find 300 containers if he searches a third hour, we find his reservation price for searching a third hour by solving p(300) = $6 for p = 2 cents. His reservation prices for additional hours of search are calculated in an analogous way. (LO1)
2. 6.2If bottles sell for 62 cents each, the firm should continue to expand up to and including the sixth employee (350 bottles per day). (LO3)
3. 6.3The relevant costs are now as shown at the bottom of this page. With each variable and marginal cost entry half what it was in the original example, the firm should now hire six employees and produce 350 bottles per day. (LO3)
4. 6.4Because the firm makes its smallest loss when it hires zero employees, it should shut down in the short run. (LO3)
5. 6.5The fact that each of the city’s 60,000 residents is willing to pay 0.00005 cent for each bottle removed means that the collective benefit of each bottle removed is (60,000)(0.00005) = 3 cents. So the city should set the redemption price at 3 cents, and from the supply curve, we see that 15,000 bottles per day will be recycled at that price. (LO4)
1Again, this rule holds subject to the provision that total revenue exceed variable production cost at the output level for which price equals marginal cost.
*Denotes more difficult problem.