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9.3: The firm's supply decision

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    108428
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    The concept of marginal revenue is key to analyzing the supply decision of an individual firm. We have used marginal analysis at several points to date. In consumer theory, we saw how consumers balance the utility per dollar at the margin in allocating their budget. Marginal revenue is the additional revenue accruing to the firm from the sale of one more unit of output.

    Marginal revenue is the additional revenue accruing to the firm resulting from the sale of one more unit of output.

    In perfect competition, a firm's marginal revenue (MR) is the price of the good. Since the price is constant for the individual supplier, each additional unit sold at the price P brings in the same additional revenue. Therefore, P=MR. For example, whether a dry cleaning business launders 10 shirts or 100 shirts per day, the price charged to customers is the same. This equality holds in no other market structure, as we shall see in the following chapters.

    Supply in the short run

    Recall how we defined the short run in the previous chapter: Each firm's plant size is fixed in the short run, so too is the number of firms in an industry. In the long run, each individual firm can change its scale of operation, and at the same time new firms can enter or existing firms can leave the industry.

    Perfectly competitive suppliers face the choice of how much to produce at the going market price: That is, the amount that will maximize their profit. We abstract for the moment on how the price in the marketplace is determined. We shall see later in this chapter that it emerges as the value corresponding to the intersection of the supply and demand curves for the whole market – as described in Chapter 3.

    The firm's MC curve is critical in defining the optimal amount to supply at any price. In Figure 9.1, MC is the firm's marginal cost curve in the short run. At the price img144.png the optimal amount to supply is img285.png, the amount determined by the intersection of the MC and the demand. To see why, imagine that the producer chose to supply the quantity img286.png. Such an output would leave the opportunity for further profit untapped. By producing one additional unit beyond img286.png, the supplier would get img144.png in additional revenue and incur an additional cost that is less than img144.png in producing this unit. In fact, on every unit between img286.png and img285.png he can make a profit, because the MR exceeds the associated cost, MC. By the same argument, it makes no sense to increase output beyond img285.png, to img287.png for example, because the cost of such additional units of output, MC, exceeds the revenue from them. The MC therefore defines an optimal supply response.

    Figure 9.1 The competitive firm's optimal output
    img288.png
    Here, q0 represents the optimal supply decision when the price is P0. At output q1 the cost of additional units is less than the revenue from such units and therefore it is profitable to increase output beyond q1. Conversely, at q2 the MC of production exceeds the revenue obtained, and so output should be reduced.
    Application Box 9.1 The law of one price

    If information does not flow then prices in different parts of a market may differ and potential entrants may not know to enter a profitable market.

    Consider the fishermen off the coast of Kerala, India in the late 1990s. Their market was studied by Robert Jensen, a development economist. Prior to 1997, fishermen tended to bring their fish to their home market or port. This was cheaper than venturing to other ports, particularly if there was no certainty regarding price. This practice resulted in prices that were high in some local markets and low in others – depending upon the daily catch. Frequently fish was thrown away in low-price markets even though it might have found a favourable price in another village's fish market.

    This all changed with the advent of cell phones. Rather than head automatically to their home port, fishermen began to phone several different markets in the hope of finding a good price for their efforts. They began to form agreements with buyers before even bringing their catch to port. Economist Jensen observed a major decline in price variation between the markets that he surveyed. In effect the 'law of one price' came into being for sardines as a result of the introduction of cheap technology and the relatively free flow of information.

    While the choice of the output img285.png is the best choice for the producer, Figure 9.1 does not tell us anything about profit. For that we need more information on costs. Accordingly, in Figure 9.2 the firm's AVC and ATC curves have been added to Figure 9.1. As explained in the previous chapter, the ATC curve includes both fixed and variable cost components, and the MC curve cuts the AVC and the ATC at their minima.

    Figure 9.2 Short-run supply for the competitive firm
    img289.png
    A price below P1 does not cover variable costs, so the firm should shut down. Between prices P1 and P3, the producer can cover variable, but not total, costs and therefore should produce in the short run if fixed costs are 'sunk'. In the long run the firm must close if the price does not reach P3. Profits are made if the price exceeds P3. The short-run supply curve is the quantity supplied at each price. It is therefore the MC curve above P1.

    First, note that any price below img290.png, which corresponds to the minimum of the ATC curve, yields no profit, since it does not enable the producer to cover all of his costs. This price is therefore called the break-even price. Second, any price below img291.png, which corresponds to the minimum of the AVC, does not even enable the producer to cover variable costs. What about a price such as img292.png, that lies between these? The answer is that, if the supplier has already incurred some fixed costs, he should continue to produce, provided he can cover his variable cost. But in the long run he must cover all of his costs, fixed and variable. Therefore, if the price falls below img291.png, he should shut down, even in the short run. This price is therefore called the shut-down price. If a price at least equal to img290.png cannot be sustained in the long run, he should leave the industry. But at a price such as img292.png he can cover variable costs and therefore should continue to produce in the short run. His optimal output at img292.png is defined by the intersection of the img292.png line with the MC curve. The firm's short-run supply curve is, therefore, that portion of the MC curve above the minimum of the AVC.

    To illustrate this more concretely, consider again the example of our snowboard producer, and imagine that he is producing in a perfectly competitive marketplace. How should he behave in response to different prices? Table 9.1 reproduces the data from Table 8.2.

    Table 9.1 Profit maximization in the short run
    Labour Output Total Average Average Marginal Total Profit
    Revenue $ Variable Total Cost Cost $ Cost $
    Cost $
    L Q TR AVC ATC MC TC TR-TC
    0 0 3,000
    1 15 1,050 66.67 266.67 66.67 4,000 –2,950
    2 40 2,800 50.0 125.0 40.0 5,000 –2,200
    3 70 4,900 42.86 85.71 33.33 6,000 –1,100
    4 110 7,700 36.36 63.64 25.0 7,000 700
    5 145 10,150 34.48 55.17 28.57 8,000 2,150
    6 175 12,250 34.29 51.43 33.33 9,000 3,250
    7 200 14,000 35.0 50.0 40.0 10,000 4,000
    8 220 15,400 36.36 50.0 50.0 11,000 4,400
    9 235 16,450 38.30 51.06 66.67 12,000 4,450
    10 240 16,800 41.67 54.17 200.0 13,000 3,800
    Output Price=$70; Wage=$1,000; Fixed Cost=$3,000. The shut-down point occurs at a price of img293.png, where the AVC attains a minimum. Hence no production, even in the short run, takes place unless the price exceeds this value. The break-even level of output occurs at a price of img161.png, where the ATC attains a minimum.

    The shut-down price corresponds to the minimum value of the AVC curve.

    The break-even price corresponds to the minimum of the ATC curve.

    The firm's short-run supply curve is that portion of the MC curve above the minimum of the AVC.

    Suppose that the price is $70. How many boards should he produce? The answer is defined by the behaviour of the MC curve. For any output less than or equal to 235, the MC is less than the price. For example, at L=9 and Q=235, the MC is $66.67. At this output level, he makes a profit on the marginal unit produced, because the MC is less than the revenue he gets ($70) from selling it.

    But, at outputs above this, he registers a loss on the marginal units because the MC exceeds the revenue. For example, at L=10 and Q=240, the MC is $200. Clearly, 235 snowboards is the optimum. To produce more would generate a loss on each additional unit, because the additional cost would exceed the additional revenue. Furthermore, to produce fewer snowboards would mean not availing of the potential for profit on additional boards.

    His profit is based on the difference between revenue per unit and cost per unit at this output: (PATC). Since the ATC for the 235 units produced by the nine workers is $51.06, his profit margin is img294.png per board, and total profit is therefore img295.png.

    Let us establish two other key outputs and prices for the producer. First, the shut-down point is the minimum of his AVC curve. Table 9.1 indicates that the price must be at least $34.29 for him to be willing to supply any output, since that is the value of the AVC at its minimum. Second, the minimum of his ATC is at $50. Accordingly, provided the price exceeds $50, he will cover both variable and fixed costs and make a maximum profit when he chooses an output where P=MC, above img296.png. It follows that the short-run supply curve for Black Diamond Snowboards is the segment of the MC curve in Figure 8.4 above the AVC curve.

    Given that we have developed the individual firm's supply curve, the next task is to develop the industry supply curve.

    Industry supply in the short run

    In Chapter 3 it was demonstrated that individual demands can be aggregated into an industry demand by summing them horizontally. The industry supply is obtained in exactly the same manner—by summing the firms' supply quantities across all firms in the industry.

    To illustrate, imagine we have many firms, possibly operating at different scales of output and therefore having different short-run MC curves. The MC curves of two of these firms are illustrated in Figure 9.3. The MC of A is below the MC of B; therefore, B likely has a smaller scale of plant than A. Consider first the supply decisions in the price range P1 to P2. At any price between these limits, only firm A will supply output – firm B does not cover its AVC in this price range. Therefore, the joint contribution to industry supply of firms A and B is given by the MC curve of firm A. But once a price of P2 is attained, firm B is now willing to supply. The img297.png schedule is the horizontal addition of their supply quantities. Adding the supplies of every firm in the industry in this way yields the industry supply.

    Industry supply (short run) in perfect competition is the horizontal sum of all firms' supply curves.

    Figure 9.3 Deriving industry supply
    img298.png
    The marginal cost curves for firms A and B indicate that at any price below P1 production is unprofitable and supply is therefore zero for both firms. At prices between P1 and P2 firm A is willing to supply, but not firm B. Consequently the market supply comes only from A. At prices above P2 both firms are willing to supply. Therefore the market supply is the horizontal sum of each firm's supply.

    Industry equilibrium

    Consider next the industry equilibrium. Since the industry supply is the sum of the individual supplies, and the industry demand curve is the sum of individual demands, an equilibrium price and quantity (PE,QE) are defined by the intersection of these industry-level curves, as in Figure 9.4. Here, each firm takes PE as given (it is so small that it cannot influence the going price), and supplies an amount determined by the intersection of this price with its MC curve. The sum of such quantities is therefore QE.

    Short-run equilibrium in perfect competition occurs when each firm maximizes profit by producing a quantity where P=MC, provided the price exceeds the minimum of the average variable cost.

    Figure 9.4 Market equilibrium
    img299.png
    The market supply curve S is the sum of each firm's supply or MC curve above the shut-down price. D is the sum of individual demands. The market equilibrium price and quantity are defined by PE and QE.

    This page titled 9.3: The firm's supply decision is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Douglas Curtis and Ian Irvine (Lyryx) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.