1 I. Introduction 541: Economics for Public Administration Lecture 8 Short-Run s & Supply We have presented how a business finds the least cost way of providing a given level of public good or service. In this class, we will analyze the second major production decision: how much should be produced to maximize profit. In addition, we will discuss when a firm will shut down. Before that, I would like to introduce some key cost concepts and discuss how these can be represented graphically. II. Definitions 1. Opportunity cost vs. sunk cost On the surface, the definition of costs would appear to be relatively straightforward. The total cost of producing a government service is the amount a local government pays for the inputs it uses in producing the service. In the garbage example from the previous lecture, the total cost of producing 50 tons of garbage collection was equal to the amount of trucks and labor hours used times the prices paid for these inputs. However, as we discussed at the beginning of this semester, economics also generally considers opportunity cost, which is the cost of forgone opportunities. "The costs of inputs or resources used or depleted by one production activity can be measured in terms of their value in alternative uses." For example, the cost to the government of the use of a vacant school as a senior citizen center, is the revenue it could gain from using it for another use, such as private offices. An opportunity cost is not always easy to observe but should always be considered when deciding how much to produce. In contrast, a sunk cost - a past expenditure that cannot be recovered- though easily observed, is not an opportunity cost. For example, if a firm buys a forklift for $10,000 and can resell it for the same price, it is not a sunk expenditure and the opportunity cost of the forklift is $10,000. If instead the firm buys a specialized forklift for $10,000 and cannot resell it, then the original expenditure is a sunk cost. If the specialized forklift that originally cost $10,000 can be resold for $4,000, then only $6,000 of the original expenditure is a sunk cost, and the opportunity cost is $4,000. In addition, a sunk cost is not relevant to a firm s decision on how much to produce. To illustrate this point, consider a firm that paid $50,000 for a piece of land for which the market value has fallen to $30,000. So, the land s true opportunity cost is $30,000, and the $20,000 difference between the original purchase price and the current market value is a sunk cost that has already been incurred and cannot be recovered. Now suppose the land is worth $35,000 to the firm if it builds a plant on this parcel. Is it worth carrying out production on this land or should the land be sold for its market value of $30,000? If the firm think the true opportunity cost is the original $50,000, it will falsely conclude that using the land for production will result in $15,000 loss ($50,000 - $35,000). Instead, the firm should use the land because it is worth $5,000 more as a production facility than if the firm sells the land for $30,000. Thus, the firm should use the land s opportunity cost to make its decisions and ignore the land s sunk cost. In short, there is no use crying over spilt milk. (Based on Perloff, Page183, 2016) In addition to the opportunity costs, governments or businesses need to consider what are called negative externalities, namely costs it may be imposing on private citizens by implementing the
2 program. If a landfill will result in pollution of a watershed, then some consideration should be given to the cost to society of this pollution. We will go into this later in the course. 2. Fixed vs. variable costs: The other distinction between cost measures is that between fixed and variable costs. As we discussed previously, there is a time element to production decisions. The shorter the timeframe, the less likely that changes in how the good is produced can be made. In the garbage example, if the timeframe is one month, then it may only be feasible to change the number of labor hours used in production. If the decision timeframe is one year, then the government may be able to change the number of trucks used as well as labor hours. Finally, if the timeframe is five years then the government may be able to change all inputs in the production process such as the number and location of transfer stations. Again, if the time frame is relatively short, it is important to distinguish between: Fixed costs: a cost that does not change as the quantity of output changes Variable costs: a cost that does change as the level of output changes, such as labor and materials. These inputs could be adjusted by firms to alter output level. cost: a firm s total cost is the sum of a firm s variable cost and fixed cost. 3. Average vs. marginal cost The heart of economics is studying decision makers trying to optimize some objective, whether it is maximizing satisfaction or minimize costs. Optimizing decisions involve the use of marginal values such as marginal costs, productivity or utility. The cost concepts can be defined as: Average cost: This is simply the total cost divided by the total level of output produced. Marginal cost: This is the cost of producing one more unit of output, e.g. cost of collecting the last ton of garbage. III. Short-run Curves In the short-run, a manager has only limited flexibility in how he or she can produce a good or service. Certain factors of production, such as capital equipment or facilities, may be "fixed" in the short-run. In the long-run, on the other hand, all factors of production should be variable. This implies that we need to separate the production and cost decisions in the short-run from those over the long-term. To illustrate the different cost concepts, let's use the example of a producer of furniture (chairs to be specific). We can start with a table of production possibilities, illustrated in Figure 8-1 with different levels of labor hours and machine hours to produce different numbers of chairs per month. Let us assume that in the short-run machine hours are fixed at 300 hours per month. (Based on David Hyman, Modern Microeconomics, Boston: Irwin, 1989.)
3 From this table, we can calculate the total, average and marginal product for labor (Figure 8-2). Let's also assume that the price of labor is $10 per hour, and machinery $20 per hour. Finally, to make this example a little more realistic assume that each chair requires materials costing $20. The total costs of producing chairs can then be represented as: TC = PK K + PL L + PM M = $20 K + $10 L + $20 M Ideally, we would separate the material costs into specific material and would get price and input measures for them as well. Since the number of machine hours is fixed, these costs can be represented as: TC = $20 (300) + $10 L + $20 M = $ $10 L + $20 M. Figure 8-1 Production Grid for Chiars per Month Labor Hours Machine Hours per Month per Month Figure 8-2, Average and Marginal Products of Labor for Chair Production Labor Hours Product of Labor Average Product of Labor Marginal Product of Labor The cost of machinery is a fixed cost (TFC) which cannot be altered in the short-run. This is illustrated in Figure 8-3. The labor costs and materials costs are also shown on this table for different numbers of labor hours and chairs produced. The total of labor and materials costs is the total variable cost (TVC). As the name implies, this varies with the level of output produced by the firm. Finally, we can add together the total fixed cost (TFC) and total variable cost (TVC) to get the total cost (TC) of producing a given number of chairs.
4 Figure 8-3. Short-Run s in Chair Production Variable Fixed Labor Hours Output Labor $10/labor hr Materials Variable Capital $20/machine hr $20/chair 0 0 6,000 6, , ,700 6,000 7, ,000 3,000 5,000 6,000 11, ,000 4,200 7,200 6,000 13, ,000 5,000 9,000 6,000 15, ,000 5,400 10,400 6,000 16, ,000 5,760 11,760 6,000 17, ,000 6,100 13,100 6,000 19, ,000 6,300 14,300 6,000 20,300 In choosing the optimal level of output for this furniture firm to produce, it is important that we look at the concepts of marginal cost (MC) and average cost (AC). As we defined previously, the average cost (AC) is equal to total cost divided by the total level of output. The average variable cost (AVC) is equal to total variable cost (TVC) divided by total output, and average fixed cost (AFC) is equal to total fixed cost (TFC) divided by total output. For the first 35 chairs produced: AC = $7,700 / 35 chairs = $220.00/chair AVC = $1,700 / 35 chairs = $48.57/chair AFC = $6,000 / 35 chairs = $171.43/chair For 150 chairs: AC = $11,000 / 150 chairs = $73.33/chair AVC = $5,000 / 150 chairs = $33.33/chair AFC = $6,000 / 150 chairs = $40.00/chair. You should be able to calculate the rest of the average costs in this example. The average cost results are presented in Table 8-4. The next step is to create the marginal cost (MC) of producing chairs. As we discussed previously, the marginal cost is defined as the cost of producing the last unit of output. Ideally, we would have costs associated with every chair produced by this firm. Unfortunately, we seldom have that detailed of information. In this example, we can approximate the marginal costs by calculating the costs associated with each additional level of output presented in Table 8-3. MC = ΔTC / ΔQ. Using Table 8-3, the marginal costs associated with the first 35 chairs is: ΔTC = $7,700 - $6,000 = $1,700 ΔQ = 35 chairs - 0 chairs = 35 chairs MC = $1,700 / 35 chairs = $48.57 per chair.
5 The marginal cost of the next 115 chairs is: ΔTC = $11,000 - $7,700 = $3,300 Δ Q = 150 chairs - 35 chairs = 115 chairs MC = $3,300 / 115 chairs = $28.70/ chair. The marginal costs associated with each level of output are illustrated in Table 8-4. You should feel comfortable with recreating all the numbers in this table. Output Variable Figure 8-4. Short-run Average and Marginal s in Chair Production Fixed (TC) Average Variable (AVC) Average Fixed (AFC) Average (AC) The next step is to plot these cost results in several cost curves which we can use to examine firm behavior. Essentially, all what we have to do is to take the results in Table 8-4 and plot them against the level of output. These results are shown in Figures 8-5 and Figure 8-6. Figure 8-5 shows the total cost (TC), total variable cost (TVC) and total fixed cost (TFC) curves. Δ ΔOutput Marginal (MC) 35 1,700 6,000 7, , ,000 6,000 11, , ,200 6,000 13, , ,000 6,000 15, , ,400 6,000 16, , ,760 6,000 17, , ,100 6,000 19, , ,300 6,000 20, ,
6 Figure 8-6 shows average cost (AC), average variable cost (AVC) and marginal cost (MC). We can see that average cost (purple line in figure 8-6) drops sharply at first and then levels off, reaching its low point at somewhere between 250 and 270 chairs. This makes intuitive sense. The average cost is initially high since it includes the fixed cost which is being spread across very low levels of production. The average cost drops because the fixed cost is now being spread among a greater number of chairs. Finally, the average cost starts rising again since the marginal cost which is the same as the additional variable cost of producing more chairs begins to rise. The rules for marginals and averages apply in the case of costs as well: -the marginal cost is below the average cost while the average cost is falling; -the marginal cost is above the average cost while the average cost is rising; -the marginal cost is equal to the average cost when the average cost is neither rising nor falling. The marginal cost curve approximately passes through the average cost curve at its lowest point, somewhere between 250 and 270 chairs of output. I say approximately because we are just approximating the marginal cost curve in this case.
7 IV. Demand for the Competitive Firm Before it is possible to find the optimal level of output it is necessary to lay out some key assumptions on which this analysis is based. While these assumptions can be unrealistic in many cases, they provide a good starting point for looking at production decisions. We will relax some of these assumptions later in the course. 1) Objective of firm: For the private firm, the commonly assumed objective is that of maximizing profit, defined as the difference between total revenue and total cost. 2) Single product: Another simplifying assumption is that the firm produces only one type of product. While most firms produce several types of products, this assumption will allow us to keep the analysis two-dimensional so we can use graphs. 3) Perfect competition: A crucial assumption for this analysis is that the market is "perfectly competitive". This is actually a series of assumptions: that there are many sellers and each producer is very small (1% of the market or less); that each seller is so small that they can produce as much output as they want without affecting rival firms. In other words, they can ignore their rivals; that each seller has access to "free" and "complete" information about prices, technology and the market, in general; and that there is freedom of "entry" or "exit" from the market by firms. In other words, there is no government regulation or business collusion preventing a firm from entering or exiting a certain market. These assumptions are crucially important for determining the type of market that a firm faces. If these assumptions hold, then each firm is so small that they can pretty much ignore the actions of other firms. Equally important, each firm has a negligible impact on market supply. In other words, the firm can take the market price as given since they can't affect it with their actions. The demand curve facing the perfectly competitive firm is for all practical purposes horizontal. They assume that there will be demand at the market price for as many units of output as they want to produce. This case is illustrated in Figure 8-7. While the market demand curve in the left-hand panel is downward sloping, the demand facing the competitive firm in the right-hand panel is horizontal at the market price. A horizontal demand curve implies that a small increase in price causes an infinite drop in quantity, so the firm s demand curve is perfectly elastic.
8 V. Producer Optimum-Profit Maximization By assumption, the private firm is assumed to produce that amount of output that will maximize profits. Profits are defined as: Profit = Revenue (TR) (C) Approach One: Using Revenue and to Locate Profit Maximization The obvious way to find the point of maximum profit is to record the total revenue and costs at each level of output. You would simply subtract them and find the point of maximum profit. Figure 8-8 lays out total revenue and costs for the chair example we have been using. Revenue: Assume the price to this competitive chair manufacturer is the same at all output levels, $150. To find the total revenue we simply multiply $150 by the quantity. : We determined earlier in this lecture what the total cost of producing chairs was at each level of output. Remember, these are the short-run costs of production, since the number of machine hours are being held fixed at 300. The fixed costs is $20 x 300 or $6000. Profit: The amount of profit made by the firm is the vertical distance between the total revenue and total cost curves. Column 5 in Figure 8-8 shows the different levels or profit associated with each level of production. We can see that initially the firm is losing money and doesn't "breakeven" until after producing over 100 chairs per month. The maximum profit is achieved at 318 chairs. In Figure 8-9, this is where there is the largest gap between total revenue and total cost, and where, obviously, profits are positive. The lower panel plots the level of profit for each level of production. The highest value of this profit curve is achieved at 318 chairs. Monthly Output (Chairs) Figure 8-8: Revenues, s and Profits in the Production of Chairs Price =Marginal Revenue P = MR Revenue TR C Profit = TR-C Marginal MC Marginal Profit = MR-MC ,000-6, ,250 7,700-2, ,500 11,000 11, ,500 13,200 18, ,500 15,000 22, ,500 16,400 24, ,200 17,760 25, ,750 19,100 26, ,250 20,300 26, ,400 20,425 26, ,550 20,560 26, ,700 20,710 26, ,850 20,880 26, ,000 21,080 26,
9 Approach Two: Using Marginal and Average Curves to Locate Profit Maximization We can also use the marginal and average curves to find this result. As we will show, they provide a very clear picture of the level of output that the firm will produce, and whether it will produce at all. With horizontal demand curves, marginal revenue just equals the market price, i.e. MR=P, which is constant ($150). The average cost we derived before are presented in Figure The marginal cost estimates, which we derived earlier, are also presented in Figure We can use this information to draw the average and marginal cost curves and the marginal revenue curves. You should notice that at the profit maximizing level of output, 318 chairs per month, the marginal cost curve just intersects the marginal revenue curve. This is the fundamental rule for profit maximization: profit maximization occurs when: MC = MR and the marginal cost curve intersects the marginal revenue curve from below. We will explain why this later point is important in a moment. This condition is also illustrated in Figure The point where total profits are at their maximum, 318 chairs, is where marginal revenue and marginal costs just equal price $150. Not surprisingly, marginal profit which equals MR - MC, is equal to zero at this point. If you think about it, this condition makes intuitive sense. Marginal revenue measures the revenue that the firm gets from the last unit produced, while marginal cost is the cost of the last unit. As long as marginal revenue is greater than marginal cost, then the firm is making a profit off producing another unit of output. It can continue to add to its total profit by producing more output, until the revenues from the last unit just cover the costs. If the firm continued to produce beyond this point, the costs of producing one more unit would exceed the revenue from this unit and total profits would go down. The condition that the marginal cost curve must intersect the total curve from below is necessary to assure that this is the point of maximum profit. If the marginal cost curve intersects the MR from above, this implies that marginal costs were greater than marginal revenue prior to this point. In other words, the firm was losing money.
10 Monthly Output (Chairs) After locating the producer optimum of profit maximization by using marginal curves and following the fundamental rule above (i.e. MC =MR), we can measure total profit in terms of average revenue and average costs. We have already defined profit as: Profit = TR TC, Figure 8-10: Average and Marginal, Price, and Profit in Chair Production Price =Marginal Revenue P = MR Avrage Variable AVC Average Fixed AFC Average AC Marginal MC Profit Per Unit P - AC multiply both sides by Q/Q, which is equal to one; Profit = (TR - TC) x (Q/Q) = [(TR/Q) - (TC/Q)] x Q = (AR - AC) x Q = AP x Q, where AP is average profit. Profit (P -AC )* Q , , , , , , , , , , , , , ,920 What is average profit? Since the firm's demand curve is horizontal, AR = MR = P. Namely, we can depict average profits as the vertical distance from the AR (=MR=P) line to the AC curve, at the point of profit maximization. In other words, total profits are equal to this distance times the level of output, illustrated by the shaded area in Figure 8-11.
11 VI. The Shut-Down Decision In Section V, we have clearly established the decision rule that firms in a competitive market will use to decide how much to produce. The one question we haven't addressed yet is whether they will produce at all. Since we assume free exit of firms, they certainly can decide to stop producing goods for this market. We will examine firms shut-down decision in this section in three scenarios. Scenario I: Assume the market price drops to $60, will the firm continue to produce or shut down? To get at this issue, let s continue to use the example of a firm producing chairs. This case is illustrated in Figure The profit maximizing output is somewhere between 250 and 270 chairs, i.e. the corresponding x-value of Point F (the calculation process is omitted here). Per the fundamental rule for profit maximization, marginal cost (MC) just equals marginal revenue (MR) at this point. This also happens to be the point where marginal costs (MC) just equal average costs (AC). As you should remember, this implies that the average cost curve is neither rising nor falling; it is at a maximum or minimum. In this case, we can see that the AC curve is at a minimum. Since MR=P=AR, this implies that at point F, MC = MR = AC = P = AR. Will the firm continue to produce? The answer should be clearly yes! Because the market price (P) is exactly the same as average cost (AC) at this point, the firm just breaks even in the short run! They have no incentive in the short run (and as we will show, in the long run) to stop production.
12 Scenario II: Assume the market price drops to $50, will the firm continue to produce or shut down? We can see in Figure 8-13 that MC equals MR (because MR=P=AR) at point E, namely, the profit maximization occurs at the corresponding output level of point E in this scenario. At this level of output, average revenue (AR, which equals P) is lower than the average cost (AC) at this level of output. The firm is failing to break even and losing money! Would the firm shut down? At first glance the answer would be yes. Why should the firm stay in business if it is losing money? However, this ignores the fact that in the short-run there are fixed costs. Fixed costs are sunk in the short run, and they must be paid whether or not the firm operates. In our example, the firm is committed to paying for 300 machine hours this month, a cost of $6,000. If it shuts down, it will still have to pay this cost. This implies that the firm will stay in business as long as it loses less money by operating than shutting down! In other words, as long as the market price (P) is higher than the average variable cost (AVC), the firm is making enough money to cover the variable cost of production, and also some money that it can pay off a part of these fixed costs. The fixed costs can be represented by the vertical distance between average cost and average variable cost curve times the total quantity-- the rectangle ABCD. We can see that the actual losses, represented by the shaded rectangle in yellow in Figure 8-13, are less than the total fixed cost. The firm will continue to produce in the short run.
13 Scenario II: Assume the market price drops to $20, will the firm continue to produce or shut down? Figure 8-14 shows that, in fact, the firm is not even covering all its variable costs with this market price or marginal revenue (i.e. the whole horizontal line of market price is below any point of the AVC curve). That is to say, if the firm operated, it would not even make enough money to cover its variable cost, not to mention to spreading fixed or sunk cost in the short run. The rational action from the standpoint of the firm is to shut down! VII. Short-Run Supply Curve Now that we have laid out the decision making by a firm in the short-run on how much to produce, can we derive the firm's short-run supply curve? How should a firm's output vary with price in the short-run? You should have noticed that the for almost all price levels, the optimal level of output is where MC=P. In other words, the marginal cost curve reflects the optimal amount for the firm to supply at different prices with one exception. The only exception is where the market price drops below the point where MC=AVC. Below this point the firm should shut down. The firm's supply curve is illustrated in Figure 8-15 by the pink segment of the MC curve (except for the segment where prices or MC is below AVC). The market supply curve at the beginning of this semester is just the horizontal summation of the individual firm supply curves. You simply get is by multiplying the output at each point along the firm supply curve by 1000.