Isoquant Curve

9 Key excerpts on "Isoquant Curve"

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  eBook - ePub

  Microeconomics For Dummies

  • Lynne Pepall, Peter Antonioni, Manzur Rashid(Authors)
  • 2016(Publication Date)
  • For Dummies

    (Publisher)

  2 .

  We allow C to change to create a set of lines, each of which has the same total cost, and has the same slope of –w 1 /w 2 . Called isocosts (see Figure 8-4 ), these are all downward-sloping parallel lines. Every point on an isocost has the same cost and higher isocost lines have higher costs.

  The final step is to put the isoquant and isocost together. We restate the problem as finding a point on an isoquant line with the lowest possible isocost associated with it. This happens at a point of tangency between the isoquant and isocost, which is a more mathematical way of saying that at the optimal point or input combination, the slopes of the isocost and the isoquant are equal (see Figure 8-5 ).

  © John Wiley & Sons, Inc.

  Figure 8-5: Cost minimization using isocosts and isoquants.

  The only input combination that can be optimal to use is the point where the two curves are tangent. Taking a look at the isoquant, you can see that an infinite number of combinations of inputs can make up that fixed desired level of output. However, point A for example is on a higher isocost than the optimal and therefore wouldn’t be chosen, because the same output can be produced for a lower cost, and the firm wants to minimize those costs.

  You can derive a cool further condition from knowing about the slopes of the isoquant and isocost and how they must match. Remember that the slope of something is generally an indication of how much it’s changing at a given point. Economists are interested in what the changes along the isoquant reveal about the marginal product (MP) of the two inputs x 1 and x 2 , and what the ratio of the marginal products says about the technology a firm is using.

  The slope of the isocost must match the slope of the isoquant. You already know the slope of the isocost: –w 1 /w 2

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  Water Utility Benchmarking

  • Sanford Berg(Author)
  • 2010(Publication Date)
  • IWA Publishing

    (Publisher)

  Economies of vertical integration are also labeled economies of sequence . . Isoquants: when characterizing production functions graphically, the isoquants represents combinations of inputs that yield the same output. . Elasticity of Input Substitution captures the extent to which inputs can be substituted for one another. Isoquants can be used to illustrate how inputs might substitute for one another. Let us take the production function used earlier, Q ¼ N (10L – 0.2L 2 ) to graph the different combinations of Labor and Network size that can be used to produce a given level of output (Figure 2). The isoquant labeled Q ¼ 30 shows that 30 units of output can be produced by using the combinations of N and L shown by points a , b , c , and d (or, assuming that inputs can be continuous, on other points shown in the Q ¼ 30 isoquant). Similarly, 120 units of output can be produced by using 6 units of L and 2.27 units of N (as shown by point h ), 3 units of L and 4.25 units of N (as shown by point f ), or other point on the isoquant corresponding to Q ¼ 120. Note that the production function that we have been using allows for the firm to substitute one input for the other (the curvature of the isoquant shows us the extent to which the inputs can be substituted for each other). For example if the utility were producing 120 units of output at point e using 6 units of labor and 2.27 units of network and the price of labor dramatically increased but the cost of capital (associated with the network) fell, managers would be able to produce the same amount of output using less labor: they could instead use 3 units of 68 Water Utility Benchmarking labor and 4.25 units of network. This movement along the isoquant could not be accomplished instantaneously.

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  Microeconomics

  Theory and Applications

  • Edgar K. Browning, Mark A. Zupan(Authors)
  • 2019(Publication Date)
  • Wiley

    (Publisher)

  Thus, a close analogy exists between the consumer’s budget line and a firm’s isocost line. In one respect, however, the analogy breaks down. Con- sumers are usually restricted to operating within a given budget, but firms are not. Firms can expand their use of all inputs and finance the expansion by selling the increased output. The firm’s total cost of operation is not a constant but varies with output, which explains why there are three isocost lines in Figure 8.4a (among the many that could be drawn) and not just one. Least Costly Input Combinations Analyzing isocost lines and isoquants together allows us to determine what combinations of inputs the firm will use to produce various rates of output. We have seen how a firm’s pro- duction function can be represented by isoquants, and three (IQ 3 , IQ 6 , and IQ 9 ) are shown in Figure 8.4b. Suppose that the firm plans to spend exactly TC 2 to hire inputs. From among the input combinations it can use (shown by the middle isocost line), the firm will clearly want to choose the labor–capital combination that yields the greatest output. The firm could employ the input combination at point D, but only three units of output would be produced (since point D is on isoquant IQ 3 ). By using less capital and more labor at point B, the firm can produce six units of output at the same total cost. Indeed, six units of output is the maximum output possible at a total cost of TC 2 , as shown by the fact that higher isoquants like IQ 9 lie entirely above the middle isocost line. To produce the maximum output possible at a given total cost, a firm should operate at a point where an isocost line is tangent to the highest iso- quant attainable: IQ 6 is tangent to the middle isocost line at point B. In the same manner, we see that nine units is the maximum output possible at the higher total cost of TC 3 , where the firm would operate at point C. Similarly, three units is the maximum output possible at a total cost of TC 1 .

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  Business Economics and Managerial Decision Making

  • Trefor Jones(Author)
  • 2004(Publication Date)
  • Wiley

    (Publisher)

  The isoquant map also shows that the production possibilities initially exhibit increasing returns to scale and then decreasing returns to scale. Changes in scale result from movements from one isoquant to another rather than from movements along a particular isoquant. If the ¢rm moves from isoquant Q 1 to isoquant Q 4 ,then the ¢rm is able to increase output from 100 to 400, while increasing capital employed from 50 to 100 and labour employed from 50 to 100. Thus, output increases fourfold, while inputs increase twofold. The ¢rm can therefore bene¢t from increasing returns by operating on isoquant Q 4 . From isoquant Q 4 to isoquant Q 5 output increases by 25%, but the factors employed increase by 50%. Thus, by moving to a higher isoquant the ¢rm incurs decreasing returns to scale. If a ¢rm decides to install a plant to produce 400 units of output with the labour and capital combination at point D, then it is assumed in the short run that the ¢rm cannot vary its capital but can vary its labour input. The short-run situation is illustrated in Figure 7.5, where the ¢rm is constrained to operate along the horizontal line KT. Thus, if the ¢rm is producing 400 units, then it can increase production by employing more labour but cannot vary the ¢xed factor capital. TOTAL, AVERAGE AND MARGINAL PRODUCT CURVES Product curves relate output to factors used and allow information from the production function to be presented in two or, sometimes, three dimensions. The information in Figure 7.5 along the line KT can be plotted in a diagram like Figure 7.6, where output CHAPTER 7 g PRODUCTION AND EFFICIENCY 129 200 150 100 50 Capital A B C D E F 50 100 150 200 Labour Q 6 (600) Q 5 (500) Q 4 (400) Q 3 (300) Q 2 (200) Q 1 (100) Figure 7.4 Isoquants and returns to scale is measured on the vertical axis and the variable factor labour on the horizontal axis. The total product curve plots the output produced on each isoquant, together with the units of labour used.

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  Pricing and Equilibrium

  • Erich Schneider(Author)
  • 2013(Publication Date)
  • Taylor & Francis

    (Publisher)

  This line may be described as the isocost line and obviously Ues further away from the origin the larger are the total costs, C. With given prices for factors the various isocost lines, corresponding to different levels of total costs, run parallel. We are concerned here with the same relationships which we discussed in connexion with the budget lines of a household. We can, therefore, fill in the whole plane v 1, v 2 with a number of parallel isocost lines (Fig. 86). Let us draw in, as is done in Fig. 86, the isoquant T 1 T 2 for a particular level of output, along with the system of isocost lines. Then it is easily seen what the total costs are of each combination of factors lying on the isoquant. The study of Fig. 86 shows that the total costs of the two substitute factors are at a minimum where the isoquant touches an isocost line. In Fig. 86 this minimum cost combination is given by the coordinates of the point T m. We know that the marginal rate of substitution of the first factor for the second, for the combination of factors given by the point T m, is equal to the tan of the angle α (Fig. 86). On the other hand, the tan of the angle α is also equal to the ratio of the factor prices, (1) so that for the minimum cost combination T m the marginal rate of substitution is equal to the ratio of the factor prices. For each level of output there exists a single uniquely determined minimum cost combination. The totality of these minimum cost combinations corresponding to different levels of output, are given, in the case of two substitute factors, by the curve OT m ′ T m ″ (Fig. 87). To each level of output let us allot the corresponding minimum cost combination. Then we obtain the curve which shows the dependence, given the factor prices, of the minimum variable costs on the level of output

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  Health Economics

  An Industrial Organization Perspective

  • Xavier Martinez-Giralt, Pedro Barros(Authors)
  • 2013(Publication Date)
  • Routledge

    (Publisher)

  q. Therefore, for each output level there will be the corresponding efficiency frontier. The collection of all these input combinations (i.e., efficiency frontiers) gives origin to the concept of production function.

  The efficiency frontier defines a boundary for the set of production possibilities associated with each level of output. The graphical representation of the efficiency frontier is termed isoquant, as it describes all the efficient ways to achieve a certain production level. Figure 3.2 (b) shows several isoquants, each corresponding to a different level of production. The further away they are from the origin (that is, the more resources are used in an efficient manner), the higher is the associated volume of production.

  The slope of the isoquants provides information about the relationship between inputs. In particular, it gives information on substitution possibilities across inputs to reach a given level of output. Take as a first example a surgical procedure that requires labor input made up of nurse and physician work in a ratio of 2:1 (say, four nurses and two physicians). If this is a fixed value in the sense that adding one more physician or one more nurse does not allow us to produce more output, but withdrawing one nurse or one physician would make it impossible to do the surgical procedure, we have no substitution possibilities.

  Suppose now that adding one more physician would allow us to use two fewer nurses. If such substitution possibilities exist at a fixed rate, whatever the use of inputs, then perfect substitution possibilities exist. An intermediate case of imperfect substitution can also be envisaged. The isoquants corresponding to these three cases are shown in Figure 3.3

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  Intermediate Microeconomics with Microsoft Excel

  • Humberto Barreto(Author)
  • 2009(Publication Date)
  • Cambridge University Press

    (Publisher)

  The initial solution to the firm’s isoquant side problem focuses attention on the cheapest combination of inputs to produce a given level of output. The canonical graph is quite similar to the standard graph from the Theory of Consumer Behavior, but as Figure 2.2.1.4 shows, there are substantial differences. Perhaps the most important similarity is the continued use of the compar-ison of a price ratio to the slope of a curve in order to determine whether the optimal solution has been found. In the case of the constrained cost min-imization problem, the firm will choose that combination of inputs where w r = TRS . Exercises Open Word and answer the following questions. Save the document and print it when you are done. 1. The Q&A sheet asks you to change r to 30 and use Solver to find the initial solution. Find the initial solution to this same problem via analytical methods and compare the two results. Are they the same? Show your work. 2. The fixed proportions production function, Y = min { α L, β K } is analogous to the perfect complements utility functional form. Suppose α = β = 1, w = 10, r = 50, and q = 100. Find L ∗ , K, ∗ and TC ∗ . Show your work. Use Word’s Drawing Tools to draw a graph of the optimal solution. 3. Given the quasilinear production function, Y = √ L + K , and input prices r = 2 and w = 5, find the cheapest way to produce 1000 units of output. Use analytical methods and show your work. 4. Set up the problem in question 3 in Excel and use Solver to find the optimal solution. Take a screen shot of the solution on your spreadsheet and paste it into your Word document. 5. Can isoquants intersect? Explain why or why not. References The epigraph is from page 1044 of Joseph Schumpeter’s History of Economic Analysis (published in 1954, shortly after his death). This classic traces the intellectual history of economics from Aristotle to the 20th century.

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  Managerial Decision Making

  • J. Bridge, J. C. Dodds(Authors)
  • 2018(Publication Date)
  • Taylor & Francis

    (Publisher)

  As their name suggests these lines show the combination of the two inputs which will result in a given cost. For example, if each unit of K cost the firm £5 and each unit of L cost £3.20, then isocost C = £16,000 could re reached by employing 3,200 units of K or 5,000 units of L or any combination of K and L on the (straight) isocost line connecting these intercepts. The equation of this isocost line is 5k + 3.2l = 16,000. Moving NE from the origin, successive isocost lines represent increasing levels of cost. The equation of isocost line C = £24,000 is 5k + 3.2l = 24,000 having intercepts at k = 4,800 and l = 7,500. The slope of these isocost lines is the same and depends upon the relative prices of the inputs. Figure 3.2 Isocost lines Figure 3.3 The Isocost Line and Isoquants Together For a given cost level, the maximum output the firm can attain can be seen in the two input case by drawing the relevant isocost line in the isoquant diagram as in Figure 3.3. Suppose we take isocost C = £16,000. All points lying on this line by definition represent combinations of factor inputs which add up to £16,000 cost to the firm. The maximum output available for £16,000 total cost can be determined by finding the highest isoquant lying on, or within that isocost line. In Figure 3.3, the isoquant Q 2 = 2,000 is just attainable by using the combination of k and l at the point of tangency T. This gives values of 1,600 for k and 2,500 for l. So the maximum output available from a given outlay on inputs can in theory be identified from the isocost line and isoquants, where as point of tangency will occur at some input-output level. At this point of tangency, the slope of the isocost line (tangent) is equal to the slope of the isoquant. The latter shows the additional amount of input L which would have to be introduced into production to maintain a given level of output when one unit of K is withdrawn from the process

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  The Pure Theory of International Trade and Distortions (Routledge Revivals)

  • Bharat Hazari(Author)
  • 2016(Publication Date)
  • Routledge

    (Publisher)

  Outputs are measured by reference to the origins O 1 and O 2, and any point in the box reflects a certain allocation of capital and labour between the two commodities. Given our assumptions about the nature of production functions, the level of output can be measured by the distances of their isoquants from the respective origins. The diagonal O 1 O 2 measures the overall capital–labour ratio. This diagram plays an important role in the derivation of the production possibility schedule. It has already been stated that each point of a particular isoquant represents the same level of output, and hence the output of each commodity can be measured by the intersection between the isoquant and the diagonal. For example, the output of the first commodity X 1, represented by isoquant x 1 and, is indicated by O 1 a 1 and respectively. Similarly, the points O 2 b 2 and can be interpreted. Given these interpretations of points along the diagonal, a movement away from O 1 towards O 2 represents an increase in the output of the first commodity X 1 and a decline in the output of the second commodity X 2 and vice versa. By introducing the Pareto optimality criterion the contract locus and the production possibility curve can be derived. This criterion states that a production point is efficient if every other feasible reallocation of inputs results in a decrease in the output of at least one commodity. In view of this criterion efficiency in the allocation of the two resources labour and capital can be attained at points such as A and C, where the isoquants of the two commodities are tangential to each other. The locus of all tangency points, the curve O 1 ACO 2, is called the contract curve or the efficiency locus. Figure 1.8 The position of the contract curve in the box depends on the assumption regarding the capital intensity of the two sectors

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