Marginal Revenue

11 Key excerpts on "Marginal Revenue"

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  eBook - PDF

  Economics of Strategy

  • David Besanko, David Dranove, Mark Shanley, Scott Schaefer(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  Making educated conjectures about how rivals will respond to pricing moves is a fascinating subject. We will encounter this subject again in Chapter 5. T OTAL R EVENUE AND M ARGINAL R EVENUE F UNCTIONS A firm’s total revenue function, denoted by TR ( Q ), indicates how the firm’s sales rev-enues vary as a function of how much product it sells. Recalling our interpretation of the demand curve as showing the highest price P ( Q ) that the firm can charge and sell exactly Q units of output, we can express total revenue as TR ( Q ) 5 P ( Q ) Q Just as a firm is interested in the impact of a change in output on its costs, it is also interested in how a change in output will affect its revenues. A firm’s marginal reve-nue, MR ( Q ), is analogous to its marginal cost. It represents the rate of change in total revenue that results from the sale of D Q additional units of output: MR ( Q ) 5 TR ( Q 1 D Q ) 2 TR ( Q ) D Q It seems plausible that total revenue would go up as the firm sells more output, and thus MR would always be positive. But with a downward-sloping demand curve, this is not necessarily true. To sell more, the firm must lower its price. Thus, while it generates revenue on the extra units of output it sells at the lower price, it loses revenue on all the units it would have sold at the higher price. Economists call this the revenue destruction effect. For example, an online electronics retailer may sell 110 DVDs per day at a price of $11 per disc and 120 DVDs at $9 per disc. It gains additional Total Revenue and Marginal Revenue Functions • 25 revenue of $90 per day on the extra 10 DVDs sold at the lower price of $9, but it sacrifices $220 per day on the 110 DVDs that it could have sold for $2 more. The Marginal Revenue in this case would equal 2 $130/10 or 2 $13; the store loses sales revenue of $13 for each additional DVD it sells when it drops its price from $11 to $9.

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  MICROECONOMICS PRINCIPL ES & POLICY

  • William Baumol, Alan Blinder, John Solow, , William Baumol, Alan Blinder, John Solow(Authors)
  • 2019(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  5. Maximum profit requires the firm to choose the level of output at which Marginal Revenue is equal to (or most closely approximates) marginal cost. 6. Geometrically, the profit-maximizing output level occurs at the highest point on the total profit curve. There the slope of the total profit curve is zero (or as close to zero as possible), meaning that marginal profit is zero. 7. Producer surplus is the difference between the price received for each unit sold of a good and its marginal cost, added up over all the units that the firm sells. 8. A change in fixed cost will not change the profit-maximizing level of output. 9. It will generally pay a firm to expand its output if it is selling at a price greater than marginal cost, even if that price happens to be below average cost. 10. Optimal decisions must be made on the basis of mar-ginal cost and Marginal Revenue figures, not average cost and average revenue figures. This concept is one of the Ideas for Beyond the Final Exam. Key Terms average revenue (AR) 157 economic profit 156 marginal profit 160 Marginal Revenue (MR) 157 optimal decisions 153 producer’s surplus 165 total profit 155 total revenue (TR) 156 Test Yourself 1. Suppose that the firm’s demand curve indicates that at a price of $10 per unit, customers will demand 2 million units of its product. Suppose that management decides to pick both price and output; the firm produces 3 million units of its product and prices them at $18 each. What will happen? 2. Suppose that a firm’s management would be pleased to increase its share of the market but if it expands its pro-duction, the price of its product will fall. Will its profits necessarily fall? Why or why not? 3. Why does it make sense for a firm to seek to maximize total profit rather than to maximize marginal profit? 4. A firm’s Marginal Revenue is $133 and its marginal cost is $90. What amount of profit does the firm fail to pick up by refusing to increase output by one unit? 5.

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  Microeconomic Theory

  Basic Principles and Extensions

  • Walter Nicholson, Christopher Snyder(Authors)
  • 2016(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 368 Part 4: Production and Supply This result can be easily demonstrated. As before, total revenue ( R ) is the product of the quantity sold ( q ) times the price at which it is sold ( p ), which may also depend on q . Using the product rule to compute the derivative, Marginal Revenue is MR 1 q 2 5 dR dq 5 d 3 p 1 q 2 # q 4 dq 5 p 1 q # dp dq . (11.8) Notice that the Marginal Revenue is a function of output. In general, MR will be different for different levels of q . From Equation 11.8 it is easy to see that if price does not change Profits, defined as revenues ( R ) minus costs ( C ), reach a maximum when the slope of the revenue func-tion (Marginal Revenue) is equal to the slope of the cost function (marginal cost). This equality is only a necessary condition for a maximum, as may be seen by comparing points q * (a true maximum ) and q ** (a local minimum ), points at which Marginal Revenue equals marginal cost. Revenues, costs Profits Losses Output per period Output per period (a) (b) q ** q * q * C R 0 FIGURE 11.1 Marginal Revenue Must Equal Marginal Cost for Profit Maximization Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 Chapter 11: Profit Maximization 369 as quantity increases 1 dp / dq 5 0 2 , Marginal Revenue will be equal to price. In this case we say that the firm is a price-taker because its output decisions do not influence the price it receives. On the other hand, if price decreases as quantity increases 1 dp / dq , 0 2 , Marginal Revenue will be less than price. A profit-maximizing manager must know how increases in output will affect the price received before making an optimal output decision. If increases in q cause market price to decrease, this must be taken into account.

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  Microeconomics

  Principles and Policy

  • William Baumol, Alan Blinder(Authors)
  • 2015(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Marginal cost is the additional cost incurred by increasing production by one unit. 5. Maximum profit requires the firm to choose the level of output at which Marginal Revenue is equal to (or most closely approximates) marginal cost. 6. Geometrically, the profit-maximizing output level occurs at the highest point on the total profit curve. There the slope of the total profit curve is zero (or as close to zero as possible), meaning that marginal profit is zero. 7. A change in fixed cost will not change the profit- maximizing level of output. 8. It will generally pay a firm to expand its output if it is selling at a price greater than marginal cost, even if that price happens to be below average cost. 9. Optimal decisions must be made on the basis of mar-ginal cost and Marginal Revenue figures, not average cost and average revenue figures. This concept is one of the Ideas for Beyond the Final Exam. Key Terms average revenue (AR) 156 economic profit 155 marginal profit 159 Marginal Revenue (MR) 156 optimal decision 151 total profit 154 total revenue (TR) 155 Test Yourself 1. Su pp ose that the f irm’s demand curve indicates that at a p rice of $ 10 p er unit, customers will demand 2 million units o f its product. Suppose that mana g ement decides to p ick both p rice and out p ut; the firm p roduces 3 mil -lion units of its p roduct and p rices them at $ 18 each. What will ha pp en? 2 . Suppose that a firm’s mana g ement would be pleased to increase its share of the market but if it ex p ands its p ro -duction, the p rice of its p roduct will fall. Will its p rofits necessaril y fall? Wh y or wh y not? 3 . Wh y does it make sense for a firm to seek to maximize t o t al p rofit rather than to maximize mar g ina l p rofit? 4. A firm’s mar g inal revenue is $ 133 and its mar g inal cost is $ 90. What amount of p rofit does the firm fail to p ick up b y refusin g to increase output b y one unit? 5 .

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  Prices and Quantities

  Fundamentals of Microeconomics

  • Rakesh V. Vohra(Author)
  • 2020(Publication Date)
  • Cambridge University Press

    (Publisher)

  Is this what Amazon is proposing? Of course not. They want to lower the price of all e-books. The aggregate demand for e-books will increase. 5 This is good for Amazon because they care about the total revenue on e-books, not the revenue of your book alone. If aggregate demand increases with a price drop, it does not follow that the demand for your book will increase. 2.3 Marginal Revenue Marginal Revenue is the derivative of revenue with respect to quantity or output. 6 Informally, it is the increase in revenue from the production of an additional unit of output. Marginal Revenue sounds like the unit selling price; it isn’t. To see why, let us consider two examples. In the first, suppose that you can sell every unit of output for p per unit. Then, one’s revenue from q units of output would be R(q) = pq. The Marginal Revenue would be dR dq = p (i.e. the unit selling price). In the second, recall Example 4. You face a demand curve D(p) = 9 − p. To determine the Marginal Revenue, you first need to write revenue as a function of output. Why? Recall the definition. It is the derivative of revenue with respect to output. From Example 5, we know how to do this: R(q) = (9 − q)q. 5 One should ask where this extra demand is coming from. Is it current readers buying more than they otherwise would, or bringing in new readers who were perhaps playing video games before? 6 It is not the derivative of revenue with respect to price. 22 2 Margin vs. Volume Thus dR dq = 9 − 2q. Notice that Marginal Revenue depends on output level and is declining with output. Why? To sell more you have to lower the price. This is true more generally. Let q(p) be the inverse demand curve. Then the Marginal Revenue, MR(q), is given by MR(q) = dR(q) dq = p(q) + q dp(q) dq . As q increases, p(q) goes down. As dp(q) dq < 0, it follows that q dp(q) dq will also decrease as q increases, provided dp(q) dq also decreases.

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  Managerial Economics

  • William F. Samuelson, Stephen G. Marks, Jay L. Zagorsky(Authors)
  • 2022(Publication Date)
  • Wiley

    (Publisher)

  2. The firm’s profit from any decision is the difference between predicted revenues and costs. Increasing output and sales will increase profit, as long as the extra revenue gained exceeds the extra cost incurred. Conversely, the firm will profit by cutting output if the cost saved exceeds the revenue given up. 3. If economic conditions change, the firm’s optimal price and output will change according to the impact on its Marginal Revenues and marginal costs. Nuts and Bolts 1. The basic building blocks of the firm’s price and output problem are its demand curve and cost function. The demand curve describes (1) the quantity of sales for a given price or, conversely, (2) the price needed to generate a given level of sales. Multiplying prices and quantities along the demand curve produces the revenue function. The cost function estimates the cost of producing a given level of output. Combining the revenue and cost functions generates a profit prediction for any output Q. 2. The next step in finding the firm’s optimal decision is to determine the firm’s marginal profit, Marginal Revenue, and marginal cost: a. Marginal profit is the extra profit earned from producing and selling an additional unit of output. b. Marginal Revenue is the extra revenue earned from selling an additional unit of output. Questions and Problems 39 c. Marginal cost is the extra cost of producing an additional unit of output. d. By definition, marginal profit is the difference between Marginal Revenue and marginal cost: M = MR − MC. The M, MR, and MC expressions can be found by taking the derivatives of the respective profit, revenue, and cost functions. 3. The firm’s optimal output is characterized by the following conditions: (1) M = 0 or, equivalently, (2) MR = MC. Once output has been determined, the firm’s optimal price is found from the price equation, and profit can be calculated accordingly.

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  Microeconomics for Managers, 2nd Edition

  • David M. Kreps(Author)
  • 2019(Publication Date)
  • Princeton University Press

    (Publisher)

  But be careful : Marginal cost and Marginal Revenue of any good are the marginal impact of increasing production of that good on the the firm’s total revenue and total cost, not simply the impact on the total revenue or total cost of that specific good. • When you face constraints, first solve the problem without the constraints to see if the constraint binds (if the unconstrained solution violates the constraints). If the constraint is satisfied by the unconstrained solution, you’re done. If the constraint is violated by the unconstrained solution, you can typically assume that the solution will be found where the constraint just binds. • The Average Revenue function, denoted AR ( x ) , is just the inverse demand function. • Average cost (respectively, revenue) falls when marginal cost (resp., revenue) is less than average cost (resp., revenue), and rises when marginal cost (resp., revenue) is above average cost (resp., revenue). Therefore, for total cost functions that have a U-shape (have a fixed cost and rising marginal cost), marginal cost equals average Problems 151 cost at efficient scale , the level of production at which average cost is minimized. • Profit maximization, or MR = MC, bears no particular relation to efficient scale. And MR = MC at a larger quantity than where profit margin (AR -AC) is largest. • In some cases, it is entirely inappropriate to think of economic “choices” as being infinitely divisible. Some choices—“Do we do this project or not?”—are inherently discrete. In those cases, thinking “on the margin” is problematic. But the logic of thinking on the margin still holds, if you think in terms of the incremental effects of your (discrete) decision. • The concept of average cost is problematic for multiproduct firms insofar as there are fixed costs to allocate. But, since you should be thinking about marginal costs (and revenues) and not about average costs (and revenues), this is not a huge problem.

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  Economics

  Principles & Policy

  • William Baumol, Alan Blinder, John Solow, , William Baumol, Alan Blinder, John Solow(Authors)
  • 2019(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  5. Maximum profit requires the firm to choose the level of output at which Marginal Revenue is equal to (or most closely approximates) marginal cost. 6. Geometrically, the profit-maximizing output level occurs at the highest point on the total profit curve. There the slope of the total profit curve is zero (or as close to zero as possible), meaning that marginal profit is zero. 7. Producer surplus is the difference between the price received for each unit sold of a good and its marginal cost, added up over all the units that the firm sells. 8. A change in fixed cost will not change the profit- maximizing level of output. 9. It will generally pay a firm to expand its output if it is selling at a price greater than marginal cost, even if that price happens to be below average cost. 10. Optimal decisions must be made on the basis of mar- ginal cost and Marginal Revenue figures, not average cost and average revenue figures. This concept is one of the Ideas for Beyond the Final Exam. Key Terms average revenue (AR) 157 economic profit 156 marginal profit 160 Marginal Revenue (MR) 157 optimal decisions 152 producer’s surplus 165 total profit 155 total revenue (TR) 156 Test Yourself 1. Suppose that the firm’s demand curve indicates that at a price of $10 per unit, customers will demand 2 million units of its product. Suppose that management decides to pick both price and output; the firm produces 3 million units of its product and prices them at $18 each. What will happen? 2. Suppose that a firm’s management would be pleased to increase its share of the market but if it expands its pro- duction, the price of its product will fall. Will its profits necessarily fall? Why or why not? 3. Why does it make sense for a firm to seek to maximize total profit rather than to maximize marginal profit? 4. A firm’s Marginal Revenue is $133 and its marginal cost is $90. What amount of profit does the firm fail to pick up by refusing to increase output by one unit? 5.

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  eBook - ePub

  Economics For Dummies

  Book + Chapter Quizzes Online

  • Sean Masaki Flynn(Author)
  • 2023(Publication Date)
  • For Dummies

    (Publisher)

  change in total revenue, the entries in the Marginal Revenue column are displayed between the two total revenue figures to which they correspond. For instance, total revenue increases from $0 to $9 as you move from producing no output to one unit of output. That’s why I place the Marginal Revenue of $9 between the total revenue entries of $0 and $9.

  As you see in Figure 8-1 , the Marginal Revenue (MR ) curve starts at the same point as the demand curve, but it falls with twice the slope. It hits the horizontal axis at an output level of instead of the output level at which demand hits the horizontal axis (where q stands for quantity produced).

  Relating Marginal Revenue to total revenue

  You can get a handle on why the monopolist’s Marginal Revenue curve falls so quickly if you first examine total revenue, or TR. The total revenue that the monopolist can get is simply the output it produces times the price at which it can sell its output. That is, . However, the price at which a monopolist can sell depends on how much the firm produces.

  The relationship between the output produced and the price at which the product can be sold depends on the demand curve. For instance, consider Point A on the demand curve in Figure 8-1 . At that point, one unit is being produced, and it can be sold for $9. Consequently, the total revenue at that point is $9. Next, look at Point B, at which two units of output are being sold. At that output level, each unit can be sold for $8. Consequently, total revenue is . And at Point C, where three units can be sold for $7 each, total revenue is $21.

  The important thing to notice is how total revenue changes as you move from A to B to C and output increases from one to two to three units. Total revenue goes from $9 to $16 to $21. Obviously, total revenue increases. But look more deeply. Moving from A to B, TR increases by $7 (from $9 to $16). But moving from B to C,

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  Test Bank for Introductory Economics

  And Introductory Macroeconomics and Introductory Microeconomics

  • John G. Marcis, Michael Veseth(Authors)
  • 2014(Publication Date)
  • Academic Press

    (Publisher)

  less than Marginal Revenue. b. equal to average total cost. C. equal to average revenue. d. greater than average total cost. e. less than average total cost. 46. A profit-maximizing firm in perfect competition in the short run will: (561-563), (169-171) a. continue to increase the price of the prod-uct as long as some of the product will be sold. b. continue to expand output until the aver-age total cost curve is at a minimum. c. continue to expand output until the mar-ginal cost curve is at a minimum. d. continue to expand output until average total cost curve is equal to market price. E. not necessarily do any of the other responses. 47. A profit-maximizing firm in perfect competition in the short run will never knowingly expand production to a point where marginal cost exceeds Marginal Revenue because: (561-563), (169-170) a. that rate of production would involve economic losses. B. less profit (or greater losses) would result from that level of production than from a smaller level of production. c. the resulting excess profits would attract governmental attention and possible gov-ernmental intervention in the market. d. the resulting excess profits would result in larger additions to the firm's taxes which would more than offset any gain. e. the firm would be operating where demand was inelastic. 48. If the Marginal Revenue on the twentieth unit of output for a firm in a perfectly competitive market is $1.00, we know that the price of that unit of output is: (560), (168) A. $1.00. b. more than $1.00. c. $.50. d. $.05. e. unavailable with the information provided. Assume that you have gathered data for the Acme Broom Company (ABC). ABC operates as a profit-maximizing firm in a market characterized by perfect competition. Use the following data in responding to the next two questions.

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  21st Century Economics: A Reference Handbook

  • Rhona C. Free(Author)
  • 2010(Publication Date)
  • SAGE Publications, Inc

    (Publisher)

  The firm's marginal profit is the rate at which profit changes with output, or the change in profit per unit of change in output. Dividing (6) through by Aq, marginal profit is An(q) _ ATR(q) ATC{q) Aq Aq Aq (7) MR(q) -MC(q), where MR(q) is the Marginal Revenue and MC(q) is the marginal cost of the last change in output. Choice of Output Although the firm does not have all of the information assumed in the production, cost, and profit functions, it will continue to make trial-and-error adjustments of output until profit stops rising at a stationary value with TC(q) TR(q) Figure 11.1 Minimum and Maximum Profit MR(q) -MC(q) = 0, or (8a) Aq MR(q) = MC{q). (8b) This is the necessary condition for maximizing profit. However, it is also the necessary condition for minimizing profit. For example, in Figure 11.1, MR(q) = MC(q), and mar-ginal profit is zero at q x and q 2 . At q < q v Air(q)/Aq < 0, and at q > q x , Air(q)/Aq > 0, which means that moving away from q x increases profit, and profit is at a local mini-mum. The opposite is true at q 2 . At q < q 2 , ATr{q) /Aq > 0, and at q > q 2 , Air(q) /Aq < 0, which means that moving away from q 2 will cause profit to fall, and profit is at a local maximum. A firm is maximizing profit if it satisfies the necessary condition, Air{q) = = I I 0 . , I l or l Aq (9) MR(q)=MC(q), and the sufficient condition, MR(q) > MC{q) and > 0 (10a) Aq for smaller outputs, and Air{q) MR(q) < MC(q) and < 0 (10b) Aq for larger outputs. The sufficient condition for maximum profit is satisfied if the slope of MR(q) is less than the slope of MC(q) —that is, if AMR(q) AMC{q) (Π) Aq Aq Profit Maximization · 113 $/<7 MC{q) MR(q) Figure 11.2 Marginal Cost, Marginal Revenue, and Minimum and Maximum Profit and MC(q) cuts MR(q) from below. In Figure 11.2, for example, MR(q) is constant, and MR(q) = MC(q) at c7, and q r At q v AMR(q)/Aq = 0 > AMC(q)/ Aq < 0, and profit is at a local minimum.

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