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Chapter 3

ECO204Y5 Chapter 3: Test 3 Notes

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Department
Economics
Course
ECO204Y5
Professor
Kathleen Wong
Semester
Fall

Description
7.4 Long-Run versus Short-Run Cost Curves Economies and Diseconomies of Scale • Economies of scale are often measured in terms of a cost-output elasticity, 𝐸𝐶 • 𝐸𝐶is the percentage change in the cost of production resulting from a 1- percent increase in output: %∆𝐶 𝐸𝐶= ( ) %âˆ†ğ‘ž ∆𝐶 ğ‘ž 𝐸𝐶= ( âˆ†ğ‘ž )(𝐶) = 𝑀𝐶/𝐴𝐶 • 𝐸𝐶= 1 when 𝑀𝐶 = 𝐴𝐶, costs increase proportionately with output, and there are neither economies nor diseconomies of scale (CRTS would apply if input proportions were fixed) • When there are economies of scale (when costs increase less than proportionately with output), 𝑀𝐶 < 𝐴𝐶 (both are declining) and 𝐸 𝐶 1 • when there are diseconomies of scale, 𝑀𝐶 > 𝐴𝐶 and 𝐸 > 1 𝐶 The Relationship between Short-Run and Long-Run Cost • Assume that a firm is uncertain about the future demand for its product and is considering three alternative plant sizes • The short-run AC curves for the three plants are given by 𝑆𝐴𝐶 1 𝑆𝐴𝐶 2 and 𝑆𝐴𝐶 3 • The decision is important because, once built, the firm may not be able to change the plant size for some time; there are three possible plant sizes • if the firm expects to produce ğ‘ž units of output, then it should build the 0 smallest plant • its AC of production would be $8. (If it then decided to produce an output of ğ‘ž1, its short run average cost would still be $8.) • However, if it expects to produce ğ‘ž ,2the middle-size plant is best • Similarly, with an output of ğ‘ž3, the largest of the three plants would be the most efficient choice • What is the firm’s LRAC curve? In the LR, the firm can change the size of its plant • it will always choose the plant that minimizes the AC of production • The LRAC curve is given by the crosshatched portions of the short-run AC curves because these show the minimum cost of production for any output level • The LRAC curve is the envelope of the SR average cost curves–it envelops or surrounds the SR curves • Now suppose that there are many choices of plant size, each having a different short-run AC curve • The LRAC curve is the envelope of the SR curves, it is the curve LAC • Whatever the firm wants to produce, it can choose the plant size (and the mix of K and L) that allows it to produce that output at the minimum AC • The LRAC curve exhibits economies of scale initially but exhibits diseconomies at higher output levels • To clarify the relationship between SR and LR cost curves, consider a firm that wants to produce output ğ‘ž 1 • If it builds a small plant, the short-run AC curve 𝑆𝐴𝐶 is relevant 1 • The AC of production (at B on 𝑆𝐴𝐶 ) i1 $8 • A small plant is a better choice than a medium-sized plant with an AC of production of $10 (A on curve 𝑆𝐴𝐶 ) 2 • Point B would therefore become one point on the LR cost function when only three plant sizes are possible • if plants of other sizes could be built, and if at least one size allowed the firm to produce ğ‘ž a1 less than $8 per unit, then B would no longer be on the LR cost curve • the envelope that would arise if plants of any size could be built is U-shaped • the LAC curve never lies above any of the short-run AC curves • because there are economies and diseconomies of scale in the LR, the points of minimum AC of the smallest and largest plants do not lie on the LRAC curve • a small plant operating at minimum AC is not efficient because a larger plant can take advantage of IRTS to produce at a lower AC • the long-run MC curve LMC is not the envelope of the short-run MC curves • SR marginal costs apply to a particular plant; LR marginal costs apply to all possible plant sizes • Each point on the long-run MC curve is the short-run MC associated with the most cost-efficient plant • Consistent with this relationship, 𝑆𝑀1 intersects LMC at the output level ğ‘ž0at which 𝑆𝐴𝐶 is tangent to LAC 1 7.5 Production with Two Outputs–Economies of Scope • Sometimes a firm’s products are closely linked to one another: o a chicken farm produces poultry and eggs o an automobile company produces automobiles and truck o a university produces teaching and research • At other times, firms produce physically unrelated products • In both cases a firm is likely to enjoy production or cost advantages when it produces two or more products • These advantages could result from the joint use of inputs or production facilities, joint marketing programs, or possibly the cost savings of a common administration • In some cases, the production of one product yields an automatic and unavoidable by-product that is valuable to the firm • Example: sheet metal manufacturers produce scrap metal and shavings that they can sell Product Transformation Curves • Example: o an automobile company that produces two products, cars and tractors o both products use K (factories and machinery) and L as inputs o Cars and tractors are not typically produced at the same plant, but they do share management resources, and both rely on similar machinery and skilled labor o The managers of the company must choose how much of each product to produce • Product transformation curve: curve showing the various combinations of two different outputs (products) that can be produced with a given set of inputs o shows two product transformation curves, each showing the various combinations of cars and tractors that can be produced with a given input of labor and machinery o Curve 𝑂 1escribes all combinations of the two outputs that can be produced with a relatively low level of inputs, and curve 𝑂 describes the 2 output combinations associated with twice the inputs • Why does the product transformation curve have a negative slope? Because in order to get more of one output, the firm must give up some of the other output • Example: o a firm that emphasizes car production will devote less of its resources to producing tractors o curve 𝑂 li2s twice as far from the origin as curve 𝑂 ,1signifying that this firm’s production process exhibits constant returns to scale in the production of both commodities o If curve 𝑂 w1re a straight line, joint production would entail no gains (or losses) o One smaller company specializing in cars and another in tractors would generate the same output as a single company producing both o However, the product transformation curve is bowed outward (or concave) because joint production usually has advantages that enable a single company to produce more cars and tractors with the same resources than would two companies producing each product separately o These production advantages involve the joint sharing of inputs o A single management is often able to schedule and organize production and to handle accounting and financial activities more effectively than separate managements Economies and Diseconomies of Scope • Economies of scope: situation in which joint output of a single firm is greater than output that could be achieved by two different firms when each produces a single product • Diseconomies of scope: situation in which joint output of a single firm is less than could be achieved by separate firms when each produces a single product • no direct relationship between economies of scale and economies of scope • A two-output firm can enjoy economies of scope even if its production process involves diseconomies of scale • Example: o manufacturing flutes and piccolos jointly is cheaper than producing both separately • yet the production process involves highly skilled labor and is most effective if undertaken on a small scale • a joint-product firm can have economies of scale for each individual product yet not enjoy economies of scope The Degree of Economies of Scope • If a combination of inputs used by one firm generates more output than two independent firms would produce, then it costs less for a single firm to produce both products than it would cost the independent firms • To measure the degree to which there are economies of scope, we should ask what percentage of the cost of production is saved when two (or more) products are produced jointly rather than individually • Degree of economies of scope (SC): percentage of cost savings resulting when two or more products are produced jointly rather than individually 𝐶 ğ‘ž 1 + 𝐶 ğ‘ž 2 − 𝐶(ğ‘ž 1ğ‘ž 2 𝑆𝐶 = 𝐶(ğ‘ž 1ğ‘ž 2 • 𝐶 ğ‘ž1 represents the cost of producing only output ğ‘ž 1 𝐶 ğ‘ž)2 represents the cost of producing only output ğ‘ž 2 and 𝐶(ğ‘ž 1ğ‘ž 2 the joint cost of producing both outputs SUMMARY 1. Managers, investors, and economists must take into account the o-cost associated with the use of a firm’s resources: the cost associated with the opportunities forgone when the firm uses its resources in its next best alternative. 2. Economic cost is the cost to a firm of utilizing economic resources in production. While economic cost and o-cost are identical concepts, o-cost is particularly useful in situations when alternatives that are forgone do not reflect monetary outlays. 
 3. A sunk cost is an expenditure that has been made and cannot be recovered. After it has been incurred, it should be ignored when making future economic decisions. Because an expenditure that is sunk has no alternative use, its o-cost is zero. 4. In the SR, one or more of a firm’s inputs are fixed. Total cost can be divided into FC and VC. A firm’s MC is the additional variable cost associated with each additional unit of output. The AVC is the total VC divided by the number of units of output. 5. In the SR, when not all inputs are variable, the presence of diminishing returns determines the shape of the cost curves. In particular, there is an inverse relationship between the marginal product of a single variable input and the MC of production. The AVC and ATC curves are U-shaped. The short-run MC curve increases beyond a certain point, and cuts both AC curves from below at their minimum points. 6. In the LR, all inputs to the production process are variable. As a result, the choice of inputs depends both on the relative costs of the factors of production and on the extent to which the firm can substitute among inputs in its production process. The cost-minimizing input choice is made by finding the point of tangency between the isoquant representing the level of desired output and an isocost line. 
 7. The LRAC curve is the envelope of the firm’s short-run AC curves, and it reflects the presence or absence of returns to scale. When there are IRTS initially and then DRTS, the LRAC curve is U-shaped, and the envelope does not include all points of minimum short-run AC. 
 8. A firm enjoys economies of scale when it can double its output at less than twice the cost. Correspondingly, there are diseconomies of scale when a doubling of output requires more than twice the cost. Scale economies and diseconomies apply even when input proportions are variable; RTS apply only when input proportions are fixed. 9. Economies of scope arise when the firm can produce any combination of the two outputs more cheaply than could two independent firms that each produced a single output. The degree of economies of scope is measured by the percentage reduction in cost when one firm produces two products relative to the cost of producing them individually. Appendix to Chapter 7: Production and Cost Theory–A Mathematical Treatment Cost Minimization • The theory of the firm relies on the assumption that firms choose inputs to the production process that minimize the cost of producing output • If there are two inputs, capital K and labor L, the production function F(K, L) describes the maximum output that can be produced for every possible combination of inputs • assume that each factor in the production process has positive but decreasing marginal products • Therefore, writing the marginal product of capital and labor as 𝑀𝑃 (K, L) and 𝐾 𝑀𝑃 𝐿K, L) 2 ( ) 𝜕𝐹(𝐾,𝐿) 𝜕 𝐹(𝐾,𝐿) 𝑀𝑃 𝐾,𝐿 = 𝜕𝐾 > 0, 𝜕𝐾 2 < 0 𝜕𝐹(𝐾,𝐿) 𝜕 𝐹(𝐾,𝐿) 𝑀𝑃 𝐿,𝐿 =) > 0, 2 < 0 𝜕𝐿 𝜕𝐿 • a competitive firm takes the prices of both labor w and capital r as given • the cost-minimization problem can be written as 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝐶 = 𝑤𝐿 + 𝑟𝐾 (A7.1) • subject to the constraint that a fixed outpu0 ğ‘ž be produced: 𝐹 𝐾,𝐿 = ğ‘ž (A7.2) 0 • 𝐶 represents the cost of producing the fixed level of output ğ‘ž 0 • To determine the firm’s demand for K and L inputs, we choose the values of K and L that minimize (A7.1) subject to (A7.2) Step 1. Setup the Lagrangian, which is the sum of two components: the cost of production (to be minimized) and the Lagrange multiplier 𝜆 times the output constraint faced by the firm: 𝜙 = 𝑤𝐿 + 𝑟𝐾 − 𝜆[𝐹 𝐾,𝐿 − ğ‘ž ]0 Step 2. Differentiate the Lagrangian with respect to K, L, and 𝜆. Then equate the resulting derivatives to zero to obtain the necessary conditions for a minimum. 𝜕𝜙 ( ) 𝜕𝐾 = 𝑟 − 𝜆𝑀𝑃 𝐾,𝐿 = 0 𝜕𝜙 = 𝑟 − 𝜆𝑀𝑃 𝐿,𝐿 = 0 𝜕𝐿 𝜕𝜙 = ğ‘ž0− 𝐹 𝐾,𝐿 = 0 𝜕𝜆 Step 3. In general, these equations can be solved to obtain the optimizing values of L, K, and l. It is particularly instructive to combine the first two conditions to obtain: 𝑀𝑃 𝐾,𝐿 ) 𝑀𝑃 𝐾,𝐿 ) 𝐾 = 𝐿 𝑟 𝑤 if the firm is minimizing costs, it will choose its factor inputs to equate the ratio of the marginal product of each factor divided by its price 𝑟 𝑟 − 𝜆𝑀𝑃 𝐾,𝐿 = 0 → 𝜆 = 𝑀𝑃 𝐾,𝐿 ) 𝑤 𝑤 − 𝜆𝑀𝑃 𝐾𝐿𝐿 = 0 → 𝜆 = 𝑀𝑃 𝐾,𝐿 ) 𝐿 • Suppose output increases by one unit • Because the marginal product of K measures the extra output associated with an additional input of K, 1/𝑀𝑃𝐾𝐾,𝐿 measures the extra K needed to produce one unit of output • Therefore, 𝑟/𝑀𝑃 𝐾𝐾,𝐿) measures the additional input cost of producing an additional unit of output by increasing K • 𝑤/𝑀𝑃 (𝐾,𝐿) measures the additional cost of producing a unit of output using 𝐿 additional L as an input • In both cases, the Lagrange multiplier is equal to the MC of production because it tells us how much the cost increases if the amount produced is increased by one unit Marginal Rate of Technical Substitution • isoquant is a curve that represents the set of all input combinations that give the firm the same level of output–say, ğ‘ž 0 • the condition that 𝐹 𝐾,𝐿 = ğ‘ž represents a production isoquant 0 • as input combinations are changed along an isoquant, the change in output, given by the total derivative of 𝐹(𝐾,𝐿), equals zero (i.e., ğ‘‘ğ‘ž = 0) 𝑀𝑃 𝐾𝐾,𝐿)𝑑𝐾 + 𝑀𝑃 (𝐾,𝐿)𝑑𝐿 = ğ‘‘ğ‘ž = 0 −𝑑𝐾/𝑑𝐿 = 𝑀𝑅𝑇𝑆 𝐿𝐾= 𝑀𝑃 (𝐿,𝐿)/𝑀𝑃 (𝐾,𝐾) • 𝑀𝑅𝑇𝑆 𝐿𝐾is the firm’s marginal rate of technical substitution between L and K 𝑀𝑃 (𝐾,𝐿)/𝑀𝑃 (𝐾,𝐿) = 𝑤/𝑟 𝐿 𝐾 • Because the left side of represents the negative of the slope of the isoquant, it follows that at the point of tangency of the isoquant and the isocost line, the firm’s MRTS (which trades off inputs while keeping output constant) is equal to the ratio of the input prices (which represents the slope of the firm’s isocost line) 𝑀𝑃 𝐿𝑤 = 𝑀𝑃 /𝑟 𝐾 • the marginal products of all production inputs must be equal when these marginal products are adjusted by the unit cost of each input Duality in Production and Cost Theory • The optimum choice of K and L can be analyzed not only as the problem of choosing the lowest isocost line tangent to the production isoquant, but also as the problem of choosing the highest production isoquant tangent to a given isocost line • Example: o wish to spend 𝐶 0n production o The dual problem asks what combination of K and L will let us produce the most output at a cost of 𝐶 0 ğ‘€ğ‘Žğ‘¥ğ‘–ğ‘šğ‘–ğ‘§ğ‘’ 𝐹(𝐾,𝐿) 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑤𝐿 + 𝑟𝐿 = C 0 • can solve this problem using the Lagrangian method: Step 1. Set up the Lagrangian 𝜙 = 𝐹 𝐾,𝐿 − 𝜇(𝑤𝐿 + 𝑟𝐾 − 𝐶 ) 0 𝜇 is the Lagrangian multiplier Step 2. Differentiate the Lagrangian with respect to K, L, and 𝜇 and then equate the resulting derivatives to zero to obtain the necessary conditions for a minimum 𝜕𝜙 = 𝑀𝑃 𝐾,𝐿 − 𝜇𝑟 = 0 𝜕𝜙𝐾 = 𝑀𝑃 𝐿,𝐿 − 𝜇𝑤 = 0 𝜕𝐿 𝜕𝜙 𝜕𝜆 = 𝑤𝐿 − 𝑟𝐾 + 𝐶0= 0 Step 3. Combine the first two equations: 𝑀𝑃 𝐾𝐾,𝐿) 𝜇 = 𝑟 𝑀𝑃 (𝐾,𝐿) 𝜇 = 𝐿 𝑤 → 𝑀𝑃 𝐾𝐾,𝐿) = 𝑀𝑃 𝐿𝐾,𝐿) 𝑟 𝑤 CHAPTER 8: Profit Maximization and Competitive Supply • A cost curve describes the minimum cost at which a firm can produce various amounts of output • a fundamental problem faced by every firm: How much should be produced? • perfectly competitive markets, in which all firms produce an identical product and each is so small in relation to the industry that its production decisions have no effect on market price • new firms can easily enter the industry if they perceive a potential for profit, and existing firms can exit if they start losing money • In the SR, firms in an industry choose which level of output to produce in order to maximize profit • In the LR, they not only make output choices, but also decide whether to be in a market at all • the prospect of high profits encourages firms to enter an industry, losses encourage them to leave 8.1 Perfectly Competitive Markets • use supply-demand analysis to explain how changing market conditions affect the market price • the equilibrium price and quantity of each product was determined by the intersection of the market demand and market supply curves • underlying this analysis is the model of a perfectly competitive market • The model of perfect competition rests on three basic assumptions: (1) price taking, (2) product homogeneity, and (3) free entry and exit PRICE TAKING • Because many firms compete in the market, each firm faces a significant number of direct competitors for its products • Because each individual firm sells a sufficiently small proportion of total market output, its decisions have no impact on market price • Thus, each firm takes the market price as given • In short, firms in PC markets are price takers • Price taker: firm that has no influence over market price and thus takes the price as given • Example: o You are the owner of a small electric lightbulb distribution business o you buy your lightbulbs from the manufacturer and resell them at wholesale to small businesses and retail outlets o you are only one of many competing distributors o As a result, you find that there is little room to negotiate with your customers o If you do not offer a competitive price–one that is determined in the marketplace–your customers will take their business elsewhere o In addition, you know that the number of lightbulbs that you sell will have little or no effect on the wholesale price of bulbs o You are a price taker • The assumption of price taking applies to consumers as well as firms • In a PC market, each consumer buys such a small proportion of total industry output that he/she has no impact on the market price, and therefore takes the price as given • Another way of stating the price-taking assumption is that there are many independent firms and independent consumers in the market, all of whom believe–correctly–that their decisions will not affect prices PRODUCT HOMOGENEITY • Price-taking behavior typically occurs in markets where firms produce identical, or nearly identical, products • When the products of all of the firms in a market are perfectly substitutable with one another–that is, when they are homogeneous–no firm can raise the price of its product above the price of other firms without losing most or all of its business • Example: o Most agricultural products are homogeneous: Because product quality is relatively similar among farms in a given region, for example, buyers of corn do not ask which individual farm grew the product o Oil, gasoline, and raw materials such as copper, iron, lumber, cotton, and sheet steel are also fairly homogeneous • Economists refer to such homogeneous products as commodities • In contrast, when products are heterogeneous, each firm has the opportunity to raise its price above that of its competitors without losing all of its sales • Example: o Premium ice creams such as Häagen-Dazs can be sold at higher prices because Häagen-Dazs has different ingredients and is perceived by many consumers to be a higher-quality product • The assumption of product homogeneity is important because it ensures that there is a single market price, consistent with supply–demand analysis FREE ENTRY AND EXIT • Free entry (or exit): condition under which there are no special costs that make it difficult for a firm to enter (or exit) an industry • As a result, buyers can easily switch from one supplier to another, and suppliers can easily enter or exit a market • The special costs that could restrict entry are costs which an entrant to a market would have to bear, but which a firm that is already producing would not • Example: o the pharmaceutical industry is not PC because Merck, Pfizer, and other firms hold patents that give them unique rights to produce drugs o any new entrant would either have to invest in R&D to obtain its own competing drugs or pay substantial license fees to one or more firms already in the market o R&D expenditures or license fees could limit a firm’s ability to enter the market o the aircraft industry is not PC because entry requires an immense investment in plant and equipment that has little or no resale value • The assumption of free entry and exit is important for competition to be effective, it means that consumers can easily switch to a rival firm if a current supplier raises its price • For businesses, it means that a firm can freely enter an industry if it sees a profit opportunity and exit if it is losing money • Thus a firm can hire L and purchase K and raw materials as needed, and it can release or move these factors of production if it wants to shut down or relocate • If these three assumptions of PC hold, market demand and supply curves can be used to analyze the behavior of market prices • In most markets, these assumptions are unlikely to hold exactly • This does not mean, however, that the model of PC is not useful • Some markets do indeed come close to satisfying our assumptions • But even when one or more of these three assumptions fails to hold, so that a market is not PC, much can be learned by making comparisons with the perfectly competitive ideal When Is a Market Highly Competitive? • Nevertheless, many markets are highly competitive in the sense that firms face highly elastic demand curves and relatively easy entry and exit • A simple rule of thumb to describe whether a market is close to being PC would be appealing • Example: o an industry with many firms (say, at least 10 to 20) o Because firms can implicitly or explicitly collude in setting prices, the presence of many firms is not sufficient for an industry to approximate PC o Conversely, the presence of only a few firms in a market does not rule out competitive behavior o there only three firms are in the market but that market demand for the product is very elastic o the demand curve facing each firm is likely to be nearly horizontal and the firms will behave as if they were operating in a PC market o Even if market demand is not very elastic, these three firms might compete very aggressively • although firms may behave competitively in many situations, there is no simple indicator to tell us when a market is highly competitive • Often it is necessary to analyze both the firms themselves and their strategic interactions 8.2 Profit Maximization Do Firms Maximize Profit? • The assumption of profit maximization is frequently used in microeconomics because it predicts business behavior reasonably accurately and avoids unnecessary analytical complications • For smaller firms managed by their owners, profit is likely to dominate almost all decisions • In larger firms, managers who make day-to-day decisions usually have little contact with the owners (i.e., the stockholders) • As a result, owners cannot monitor the managers’ behavior on a regular basis • Managers then have some leeway in how they run the firm and can deviate from profit-maximizing behavior • Managers may be more concerned with such goals as revenue maximization, revenue growth, or the payment of dividends to satisfy shareholders • They might also be overly concerned with the firm’s SR profit (perhaps to earn a promotion or a large bonus) at the expense of its longer-run profit, even though LR profit maximization better serves the interests of the stockholders • Because technical and marketing information is costly to obtain, managers may sometimes operate using rules of thumb that require less-than-ideal information • On some occasions they may engage in acquisition and/or growth strategies that are substantially riskier than the owners of the firm might wish • The recent rise in the number of corporate bankruptcies, especially those in the financial sector, along with the rapid increase in CEO salaries, has raised questions about the motivations of managers of large corporations • it is important to realize that a manager’s freedom to pursue goals other than LR profit maximization is limited • if they do pursue such goals, shareholders or boards of directors can replace them, or the firm can be taken over by new management • firms that do not come close to maximizing profit are not likely to survive • Firms that do survive in competitive industries make LR profit maximization one of their highest priorities • Thus our working assumption of profit maximization is reasonable • Firms that have been in business for a long time are likely to care a lot about profit, whatever else their managers may appear to be doing • Example: o a firm that subsidizes public television may seem public-spirited and altruistic yet this beneficence is likely to be in the LR financial interest of the firm because it generates goodwill 8.3 Marginal Revenue, Marginal Cost, and Profit Maximization • Profit: difference between total revenue and total cost • Suppose that the firm’s output is q, and that it obtains revenue R • This revenue is equal to the price of the product P times the number of units sold: 𝑅 = ğ‘ƒğ‘ž • The cost of production C also depends on the level of output • The firm’s profit, p, is the difference between revenue and cost: 𝑝(ğ‘ž) = 𝑅(ğ‘ž) − 𝐶(ğ‘ž) • To maximize profit, the firm selects the output for which the difference between revenue and cost is the greatest • Revenue R(q) is a curved line, which reflects the fact that the firm can sell a greater level of output only by lowering its price; The slope of this revenue curve is marginal revenue • MR: the change in revenue resulting from a one-unit increase in output • the total cost curves C(q) slope, which measures the additional cost of producing one additional unit of output, is the firm’s marginal cost • Note that total cost C(q) is positive when output is zero because there is a fixed cost in the SR • profit is negative at low levels of output because revenue is insufficient to cover fixed and variable costs • As output increases, revenue rises more rapidly than cost, so that profit eventually becomes positive • Profit continues to increase until output reaches the level q*, at this point, MR and MC are equal, and the vertical distance between revenue and cost, AB, is greatest • q* is the profit-maximizing output level • at output levels above q*, cost rises more rapidly than revenue–i.e., MR is less than MC • Thus, profit declines from its maximum when output increases above q* • The rule that profit is maximized when marginal revenue (MR) is equal to marginal cost (MC) holds for all firms, whether competitive or not • Profit, 𝜋 = 𝑅 − 𝐶, is maximized at the point at which an additional increment to output leaves profit unchanged (i.e., 𝑝/ ğ‘ž = 0): ∆𝜋 ∆𝑅 ∆𝐶 = − = 𝑀𝑅 − 𝑀𝐶 = 0
 âˆ†ğ‘ž âˆ†ğ‘ž âˆ†ğ‘ž ∆𝑅 is marginal revenue MR and ∆𝐶is marginal cost MC âˆ†ğ‘ž âˆ†ğ‘ž • conclude that profit is maximized when MR - MC = 0, so that 𝑀𝑅 ğ‘ž = 𝑀𝐶 ğ‘ž ( ) Demand and Marginal Revenue for a Competitive Firm • Because each firm in a competitive industry sells only a small fraction of the entire industry output, how much output the firm decides to sell will have no effect on the market price of the product • The market price is determined by the industry demand and supply curves • Therefore, the competitive firm is a price taker; price taking is one of the fundamental assumptions of PC • The price-taking firm knows that its production decision will have no effect on the price of the product • Example: o when a farmer is deciding how many acres of wheat to plant in a given year, he can take the market price of wheat–say, $4 per bushel–as given; That price will not be affected by his acreage decision • Often we will want to distinguish between market demand curves and the demand curves faced by individual firms • denote market output and demand by capital letters (Q and D) and the firm’s output and demand by lowercase letters (q and d) • Because it is a price taker, the demand curve d facing an individual competitive firm is given by a horizontal line • The horizontal axis measures the amount of wheat that the farmer can sell, and the vertical axis measures the price • The market demand curve shows how much wheat all consumers will buy at each possible price • It is downward sloping because consumers buy more wheat at a lower price • The demand curve facing the firm is horizontal because the firm’s sales will have no effect on price • Suppose the firm increased its sales from 100 to 200 bushels of wheat this would have almost no effect on the market because industry output is 2,000 million bushels • Price is determined by the interaction of all firms and consumers in the market, not by the output decision of a single firm • when an individual firm faces a horizontal demand curve, it can sell an additional unit of output without lowering price • when it sells an additional unit, the firm’s total revenue increases by an amount equal to the price: one bushel of wheat sold for $4 yields additional revenue of $4; Thus, MR is constant at $4 • At the same time, average revenue received by the firm is also $4 because every bushel of wheat produced will be produced will be sold at $4 • The demand curve d facing an individual firm in a competitive market is both its AR curve and its MR curve • Along this demand curve, 𝑀𝑅 = 𝐴𝑅 = 𝑃 Profit Maximization by a Competitive Firm • the demand curve facing a competitive firm is horizontal, so that 𝑀𝑅 = 𝑃, the general rule for profit maximization that applies to any firm can be simplified • A PC firm should choose its output so that marginal cost equals price: 𝑀𝐶 ğ‘ž = ) 𝑀𝑅 = 𝑃 • Note that because competitive firms take price as fixed, this is a rule for setting output, not price 8.4 Choosing Output in the Short Run Short-Run Profit Maximization by a Competitive Firm • In the SR, a firm operates with a fixed amount of K and must choose the levels of its variable inputs (labor and materials) to maximize profit • The AR and MR curves are drawn as a horizontal line at a price equal to $40 • Profit is maximized at point A, where output is q*= 8 and the price is $40, because MR is equal to MC at this point • To see that q*= 8 is the profit-maximizing output, note that at a lower output, say ğ‘ž 1 7, 𝑀𝑅 > 𝑀𝐶; profit could thus be increased by increasing output • The shaded area between ğ‘ž = 7 and q* shows the lost profit associated with 1 producing at ğ‘ž 1 • At a higher output, say ğ‘ž 2 𝑀𝐶 > 𝑀𝑅; thus, reducing output saves a cost that exceeds the reduction in revenue • The shaded area between q* and ğ‘ž = 9 s2ows the lost profit associated with producing at ğ‘ž 2 • When output is q*= 8, profit is given by the area of rectangle ABCD • The MR and MC curves cross at an output of ğ‘ž as we0l as q* • At ğ‘ž 0 however, profit is clearly not maximized • An increase in output beyond ğ‘ž inc0eases profit because MC is well below MR • shows the competitive firm’s SR profit, the distance AB is the difference between price and AC at the output level q*, which is the average profit per unit of output • Segment BC measures the total number of units produced • Rectangle ABCD is the firm’s profit • the condition for profit maximization as follows: MR equals MC at a point at which the MC curve is rising • Output Rule: if a firm is producing any output, it should produce at the level at which MR equals MC • A firm need not always earn a profit in the SR • higher fixed cost raises ATC but does not change the AVC and MC curves • At the profit-maximizing output q*, the price P is less than AC • Line segment AB measures the average loss from production • the rectangle ABCD now measures the firm’s total loss When Should the Firm Shut Down? • Suppose a firm is losing money: Should it shut down and leave the industry? The answer depends in part on the firm’s expectations about its future business conditions • If it believes that conditions will improve and the business will be profitable in the future, it might make sense to operate at a loss in the SR • But let’s assume for the moment that the firm expects the price of its product to remain the same for the foreseeable future • What, then, should it do? Note that the firm is losing money when its 𝑃 < 𝐴𝑉𝐶 at the profit-maximizing output q* • In that case, if there is little chance that conditions will improve, it should shut down and leave the industry • This decision is appropriate even if price is greater than average variable cost, as shown in Figure 8.4 • If the firm continues to produce, the firm minimizes its losses at output q*, but it will still have losses rather than profits because price is less than ATC • Note also that in Figure 8.4, because of the presence of FC, ATC exceeds AVC, and ATC also exceeds price, so that the firm is indeed losing money • fixed costs do not change with the level of output, but they can be eliminated if the firm shuts down o (Examples of fixed costs include the salaries of plant managers and security personnel, and the electricity to keep the lights and heat running.) • Will shutting down always be the sensible strategy? Not necessarily, the firm might operate at a loss in the SR because it expects to become profitable again in the future, when the price of its product increases or the cost of production falls • Operating at a loss might be painful, but it will keep open the prospect of better times in the future by staying in business, the firm retains the flexibility to change the amount of K that it uses and thereby reduce its ATC • This alternative seems particularly appealing if the price of the product is greater than the average variable cost of production, since operating at q* will allow the firm to cover a portion of its fixed costs • Example: o pizzerias have high FC (the rent that must be paid, the pizza ovens, and so on) and low VC (the ingredients and perhaps some employee wages) o the price that the pizzeria is charging its customers is below the ATC of production o Then the pizzeria is losing money by continuing to sell pizzas and it should shut down if it expects business conditions to remain unchanged in the future o But, should the owner sell the store and go out of business? Not necessarily; that decision depends on the owner’s expectation as to how the pizza business will fare in the future o Perhaps adding jalapeno peppers, raising the price, and advertising the new spicy pizzas will do the trick 8.5 The Competitive Firm’s Short-Run Supply Curve • A supply curve for a firm tells us how much output it will produce at every possible price • competitive firms will increase output to the point at which 𝑃 = 𝑀𝐶, but will shut down if 𝑃 < 𝐴𝑉𝐶 • the firm’s supply curve is the portion of the MC curve for which 𝑀𝐶 > 𝐴𝑉𝐶 • any P greater than minimum AVC, the profit-maximizing output can be read directly from the graph • At a price P the quantity supplied will be q ; and at P , it will be q 1 1 2 2 • For P less than (or equal to) minimum AVC, the profit-maximizing output is equal to zero • the entire SR supply curve consists of the crosshatched portion of the vertical axis plus the MC curve above the point of minimum AVC • SR supply curves for competitive firms slope upward for the same reason that MC increases–the presence of diminishing marginal returns to one or more factors of production • As a result, an increase in the market price will induce those firms already in the market to increase the quantities they produce • The higher price not only makes the additional production profitable, but also increases the firm’s total profit because it applies to all units that the firm produces The Firm’s Response to an Input Price Change • When the price of its product changes, the firm changes its output level to ensure that MC of production remains equal to price • the product price changes at the same time that the prices of inputs change • a firm’s MC curve that is initially given by MC whe1 the firm faces a price of $5 for its product • The firm maximizes profit by producing an output of ğ‘ž 1 • suppose the price of one input increases • Because it now costs more to produce each unit of output, this increase causes the MC curve to shift upward from 𝑀𝐶 to 𝑀𝐶1 2 • The new profit-maximizing output is ğ‘ž , at which 𝑃 = 𝑀𝐶 2 2 • Thus, the higher input price causes the firm to reduce its output • If the firm had continued to produce ğ‘ž , i1 would have incurred a loss on the last unit of production • In fact, all production beyond ğ‘ž wo2ld reduce profit • The shaded area in the figure gives the total savings to the firm (or equivalently, the reduction in lost profit) associated with the reduction in output from q t1 q 2 8.6 The Short-Run Market Supply Curve • The SR market supply curve shows the amount of output that the industry will produce in the SR for every possible price • The industry’s output is the sum of the quantities supplied by all of its individual firms • Therefore, the market supply curve can be obtained by adding the supply curves of each of these firms • At any price below 𝑃 ,1the industry will produce no output because 𝑃 is t1e minimum AVC of the lowest-cost firm • Between 𝑃 a1d 𝑃 , o2ly firm 3 will produce • The industry supply curve, therefore, will be identical to that portion of firm 3’s marginal cost curve 𝑀𝐶 3 • At price 𝑃2, the industry supply will be the sum of the quantity supplied by all three firms • Firm 1 supplies 2 units, firm 2 supplies 5 units, and firm 3 supplies 8 units • Industry supply is thus 15 units • At price 𝑃3, firm 1 supplies 4 units, firm 2 supplies 7 units, and firm 3 supplies 10 units; the industry supplies 21 units • Note that the industry supply curve is upward sloping but has a kink at price 𝑃 , 2 the lowest price at which all three firms produce • With many firms in the market, however, the kink becomes unimportant • Thus we usually draw industry supply as a smooth, upward-sloping curve Elasticity of Market Supply • finding the industry supply curve is not always as simple as adding up a set of individual supply curves • As price rises, all firms in the industry expand their output • This additional output increases the demand for inputs to production and may lead to higher input prices • As we saw in Figure 8.7, increasing input prices shifts a firm’s MC curve upward • Example: o an increased demand for beef could also increase demand for corn and soybeans (which are used to feed cattle) and thereby cause the prices of these crops to rise o In turn, higher input prices will cause firms’ MC curves to shift upward o This increase lowers each firm’s output choice (for any given market price) and causes the industry supply curve to be less responsive to changes in output price than it would otherwise be • The price elasticity of market supply measures the sensitivity of industry output to market price • The elasticity of supply𝑠𝐸 is the percentage change in quantity supplied Q in response to a 1-percent change in price P: ∆𝑄 𝐸 = %∆𝑄 = 𝑄 𝑠 %∆𝑃 ∆𝑃 𝑃 • Because MC curves are upward sloping, the SR 𝐸 is always positive 𝑠 • When MC increases rapidly in response to increases in output, the 𝐸𝑠is low • In the SR, firms are capacity-constrained and find it costly to increase output • when MC increases slowly in response to increases in output, supply is relatively elastic; in this case, a small price increase induces firms to produce much more • At one extreme is the case of perfectly inelastic supply, which arises when the industry’s plant and equipment are so fully utilized that greater output can be achieved only if new plants are built (as they will be in the LR) • At the other extreme is the case of perfectly elastic supply, which arises when MC is constant Producer Surplus in the Short Run • producer surplus: sum over all units produced of the differences between the market price of the good and the MC of production • Just as consumer surplus measures the area below an individual’s demand curve and above the market price of the product, producer surplus measures the area above a producer’s supply curve and below the market price • The profit-maximizing output is q*, where 𝑃 = 𝑀𝐶 • The surplus that the producer obtains from selling each unit is the difference between the price and the MC of producing the unit • The producer surplus is then the sum of these “unit surpluses” over all units that the firm produces; It is given by the yellow area under the firm’s horizontal demand curve and above its marginal cost curve, from zero output to the profit-maximizing output q* • When we add the MC of producing each level of output from 0 to q*, we find that the sum is the total VC of producing q* • MC reflects increments to cost associated with increases in output; because FC does not vary with output, the sum of all MCs must equal the sum of the firm’s VCs • Thus producer surplus can alternatively be defined as the difference between the firm’s revenue and its total variable cost • producer surplus is also given by the rectangle ABCD, which equals revenue (0ABq*) minus variable cost (0DCq*) PRODUCER SURPLUS VERSUS PROFIT • In the SR, producer surplus is equal to revenue minus VC, which is variable profit • Total profit is equal to revenue minus all costs, both variable and fixed: Producer surplus = 𝑃𝑆 = 𝑇𝑅 − 𝑉𝐶 Profit = 𝜋 = 𝑇𝑅 − 𝑇𝐶 = 𝑇𝑅 − 𝑉𝐶 − 𝐹𝐶 • in the SR, when FC is positive, producer surplus is greater than profit • The extent to which firms enjoy producer surplus depends on their costs of production • Higher-cost firms have less producer surplus and lower-cost firms have more • By adding up the producer surpluses of all firms, we can determine the producer surplus for a market • The market supply curve begins at the vertical axis at a point representing the AVC of the lowest-cost firm in the market • Producer surplus is the area that lies below the market price of the product and above the supply curve between the output levels 0 and Q* 8.7 Choosing Output in the Long Run • In the SR, one or more of the firm’s inputs are fixed • Depending on the time available, this may limit the flexibility of the firm to adapt its production process to new technological developments, or to increase or decrease its scale of operation as economic conditions change • in the LR, a firm can alter all its inputs, including plant size • It can decide to shut down (i.e., to exit the industry) or to begin producing a product for the first time (i.e., to enter an industry) • concerned here with competitive markets, we allow for free entry and free exit • We are assuming that firms may enter or exit without legal restriction or any special costs associated with entry Long-Run Profit Maximization • Its SR average (total) cost curve SAC and short-run MC curve SMC are low enough for the firm to make a positive profit, given by rectangle ABCD, by producing an output of ğ‘ž , where 𝑆𝑀𝐶 = 𝑃 = 𝑀𝑅 1 • The LR average cost curve LAC reflects the presence of economies of scale up to output level ğ‘ž 2nd diseconomies of scale at higher output levels • The long-run MC curve LMC cuts the LRAC from below at ğ‘ž , the p2int of minimum LRAC • If the firm believes that the market price will remain at $40, it will want to increase the size of its plant to produce at output ğ‘ž 3 at which its long-run MC equals the $40 price • When this expansion is complete, the profit margin will increase from AB to EF, and total profit will increase from ABCD to EFGD • Output ğ‘ž i3 profit-maximizing because at any lower output (say, ğ‘ž ), t2e MR from additional production is greater than the MC • Expansion is, therefore, desirable • But at any output greater than ğ‘ž ,3MC is greater than MR • Additional production would therefore reduce profit • In summary, the long-run output of a profit-maximizing competitive firm is the point at which long-run MC equals the price • Note that the higher the market price, the higher the profit that the firm can earn • as the price of the product falls from $40 to $30, the profit also falls • At a price of $30, the firm’s profit-maximizing output is ğ‘ž2, the point of LR minimum AC • In this case, because 𝑃 = 𝐴𝑇𝐶, the firm earns zero economic profit Long-Run Competitive Equilibrium • Firms in the market must have no desire to withdraw at the same time that no firms outside the market wish to enter • But what is the exact relationship between profitability, entry, and LR competitive equilibrium? ACCOUNTING PROFIT AND ECONOMIC PROFIT • Accounting profit is measured by the difference between the firm’s revenues and its cash flows for labor, raw materials, and interest plus depreciation expenses • Economic profit takes into account opportunity costs • One such o-cost is the return to the firm’s owners if their capital were used elsewhere • Suppose, for example, that the firm uses labor and capital inputs; its capital equipment has been purchased • Accounting profit will equal revenues R minus labor cost wL, which is positive • Economic profit 𝜋, however, equals revenues R minus labor cost wL minus the capital cost, rK: 𝜋 = 𝑅 − 𝑤𝐿 − 𝑟𝐾 • the correct measure of capital cost is the user cost of capital, which is the annual return that the firm could earn by investing its money elsewhere instead of purchasing capital, plus the annual depreciation on the capital ZERO ECONOMIC PROFIT • zero economic profit: a firm is earning a normal–i.e., competitive–return on that investment • This normal return, which is part of the user cost of capital, is the firm’s o-cost of using its money to buy capital rather than investing it elsewhere • a firm earning zero economic profit is doing as well by investing its money in capital as it could by investing elsewhere–it is earning a competitive return on its money • Such a firm, therefore, is performing adequately and should stay in business. (A firm earning a negative economic profit, however, should consider going out of business if it does not expect to improve its financial picture.) ENTRY AND EXIT • Figure 8.13 shows how a $40 price induces a firm to increase output and realize a positive profit • Because profit is calculated after subtracting the o-cost of capital, a positive profit means an unusually high return on a financial investment, which can be earned by entering a profitable industry • This high return causes investors to direct resources away from other industries and into this one–there will be entry into the market • Eventually the increased production associated with new entry causes the market supply curve to shift to the right • As a result, market output increases and the market price of the product falls; Figure 8.14 illustrates this • In part (b) of the figure, the supply curve has shifted from 𝑆 1o 𝑆 2 causing the price to fall from 1 ($40) to 𝑃2($30) • In part (a), which applies to a single firm, the long-run average cost curve is tangent to the horizontal price line at output ğ‘ž 2 • Suppose that each firm’s minimum long- run average cost remains $30 but the market price falls to $20 • absent expectations of a price change, the firm will leave the industry when it cannot cover all of its costs, i.e., when price is less than average variable cost • The exit of some firms from the market will decrease production, which will cause the market supply curve to shift to the left • Market output will decrease and the price of the product will rise until an equilibrium is reached at a break-even price of $30 • To summarize: In a market with entry and exit, a firm enters when it can earn a positive LR profit and exits when it faces the prospect of a LR loss • When a firm earns zero economic profit, it has no incentive to exit the industry Likewise, other firms have no special incentive to enter • LR competitive equilibrium: All firms in the industry are maximizing profit, no firm has an incentive either to enter or exit the industry because all firms are earning zero economic profit and the price of the product is such that the quantity supplied by the industry is equal to the quantity demanded by consumers • Firms enter the market because they hope to earn a profit, and likewise they exit because of economic losses • In LR equilibrium, however, firms earn zero economic profit • Why does a firm enter a market knowing that it will eventually earn zero profit? The answer is that zero economic profit represents a competitive return for the firm’s investment of financial capital • With zero economic profit, the firm has no incentive to go elsewhere because it cannot do better financially by doing so • If the firm happens to enter a market sufficiently early to enjoy an economic profit in the SR, so much the better • if a firm exits an unprofitable market quickly, it can save its investors’ money • Thus the concept of LR equilibrium tells us the direction that a firm’s behavior is likely to take • The idea of an eventual zero-profit, LR equilibrium should not discourage a manager–it should be seen in a positive light, because it reflects the opportunity to earn a competitive return FIRMS HAVING IDENTICAL COSTS • To see why all the conditions for LR equilibrium must hold, assume that all firms have identical costs • Now consider what happens if too many firms enter the industry in response to an opportunity for profit • The industry supply curve in Figure 8.14(b) will shift further to the right, and price will fall below $30–say, to $25 • At that price, however, firms will lose money • As a result, some firms will exit the industry • Firms will continue to exit until the market supply curve shifts back to 2 • Only when there is no incentive to exit or enter can a market be in LR equilibrium FIRMS HAVING DIFFERENT COSTS • suppose that all firms in the industry do not have identical cost curves • Perhaps one firm has a patent that lets it produce at a lower AC than all the others • In that case, it is consistent with long-run equilibrium for that firm to earn a greater accounting profit and to enjoy a higher producer surplus than other firms • As long as other investors and firms cannot acquire the patent that lowers costs, they have no incentive to enter the industry • Conversely, as long as the process is particular to this product and this industry, the fortunate firm has no incentive to exit the industry • The distinction between accounting profit and economic profit is important here • If the patent is profitable, other firms in the industry will pay to use it (or attempt to buy the entire firm to acquire it) • The increased value of the patent thus represents an o-cost to the firm that holds it • It could sell the rights to the patent rather than use it • If all firms are equally efficient otherwise, the economic profit of the firm falls to zero • However, if the firm with the patent is more efficient than other firms, then it will be earning a positive profit • But if the patent holder is otherwise less efficient, it should sell off the patent and exit the industry THE OPPORTUNITY COST OF LAND • There are other instances in which firms earning positive accounting profit may be earning zero economic profit • Suppose, that a clothing store happens to be located near a large shopping center • The additional flow of customers can substantially increase the store’s accounting profit because the cost of the land is based on its historical cost • However, as far as economic profit is concerned, the cost of the land should reflect its o-cost, which in this case is the current market value of the land • When the o- cost of land is included, the profitability of the clothing store is no higher than that of its competitors • Thus the condition that economic profit be zero is essential for the market to be in LR equilibrium • By definition, positive economic profit represents an opportunity for investors and an incentive to enter an industry • Positive accounting profit, however, may signal that firms already in the industry possess valuable assets, skills, or ideas, which will not necessarily encourage entry Economic Rent • some firms earn higher accounting profit than others because they have access to factors of production that are in limited supply; these might include land and natural resources, entrepreneurial skill, or other creative talent • what makes economic profit zero in the LR is the willingness of other firms to use the factors of production that are in limited supply • The positive accounting profits are therefore translated into economic rent that is earned by
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