Economics
Isocost Line
An isocost line represents all the combinations of inputs that a firm can purchase for a given total cost. It shows the trade-off between the cost of labor and capital, with different points on the line representing different combinations of inputs that yield the same total cost. Isocost lines are used to analyze production decisions and input choices in the short run.
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11 Key excerpts on "Isocost Line"
eBook - PDFMicroeconomics
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 .
eBook - PDFManagerial Economics
Problem-Solving in a Digital World
- Nick Wilkinson(Author)
- 2022(Publication Date)
- Cambridge University Press(Publisher)
6.5.4 Determining the Optimal Combination of Inputs The isoquants that have been considered in the previous analysis have all assumed that the firm was producing with technical efficiency, which, as we have seen, means that the outputs involved were assumed to be the maximum that could be produced from the combinations of inputs employed. However, for each isoquant there is only one combination of inputs that is economically efficient, meaning minimizing cost, given a set of input prices. The determin- ation of this input combination requires information regarding both the production func- tion, determining the relevant isoquant, and the prices of the inputs employed. Obviously, this involves moving into the aspects of cost analysis, the subject of the next chapter, but there is a difference of perspective. At this point it is assumed that there is a target level of output that is given. The next chapter focuses more on relationships between costs and output with output treated as a variable. 298 6 Production Theory (a) Isocost Lines The prices of the inputs can be used to compute an Isocost Line. This line shows the different combinations of inputs that can be employed given a certain level of cost outlay. We can now see that an Isocost Line corresponds to the concept of a budget line in consumer theory. Thus, the slope of the Isocost Line is given by the ratio of the input prices P L /P K . Likewise, we can derive the firm’s optimal position in the same sort of way that we derived the consumer’s optimal position. Let us at this point review the concept of the consumer’s optimal position or equilibrium, since it will shed light on the similarities and differences between the optimization procedures involved. In consumer theory, the objective was to maximize total utility subject to a budget constraint. The objective that we are now considering in production theory is to minimize cost subject to an output constraint, meaning that we have to produce a certain output.
eBook - ePubHealth Economics
An Industrial Organization Perspective
- Xavier Martinez-Giralt, Pedro Barros(Authors)
- 2013(Publication Date)
- Routledge(Publisher)
The production function is silent about which point of the efficiency frontier is best. From a technological point of view, all points of the production function that reach the same output level are equal. To choose a point, additional criteria have to be introduced. A natural criterion to impose is to choose the combination of inputs (in the efficiency frontier) that have the least cost in achieving the desired output level. This criterion leads to the introduction of input prices in the choice process.Let wj be the price per unit of input mj . Total cost is then defined by w1 m1 + w2 m2 . The choice of inputs is then guided by the minimization of total cost subject to the constraint of being able to produce a certain level of output. The solution to this choice problem is known as the cost function. Formally, it is described byThe cost function incorporates the information from the production function and from input prices to obtain the least cost of producing an output level. Assuming that input prices are fixed (exogenous to the production entity), total cost can be represented in the (m1 , m2 ) space by a line. Isocost Lines represent combinations of inputs m1 and m2 that at prices w1 and w2 respectively yield the same total cost. The closer they are to the origin, the lower is the cost. So, in graphical terms, the problem can be stated as finding the point of the lowest Isocost Line that still reaches the level of output.The usual properties of the cost function are,- non-negative in q, m : C(q; m1 , m2 ) ≥ 0;
- non-decreasing in mj , ∀ j : ∂C/∂mj ≥ 0;
- non-decreasing in q : ∂C/∂q ≥ 0;
- homogeneous of degree 1 in mj , ∀ j : C(q; θ m1 ,θ m2 ) = θ C(q; m1, m2). This means that when all inputs vary in the same proportion θ
eBook - ePub- Richard Jones(Author)
- 2021(Publication Date)
- Routledge(Publisher)
Chapter 3 The Theory of CostsI. Cost Theory
It is frequently assumed that the problem of selecting the optimum input combination has been solved, and subsequent analysis is carried out in terms of revenues and costs expressed as a function of the rate of output. In this way the principles of production established in Chapter 2 lay the foundations for an analysis of costs. The knowledge of the production function enables the isoquant map to be drawn. Isocost Lines can be added to this map, and the efficient output level and input combination can be established. Each level of output will be associated with a total cost of production. Costs can therefore be related functionally to the rate of output in the form of a cost function or schedule.A typical cost schedule is represented in Table 3.1 . Some terms need to be defined. Column 2 contains total fixed cost (TFC); by definition, this does not vary with output and must be met irrespective of the level of output produced. Thus in Figure 3.1 it is shown as a horizontal line. Column 3 contains total variable cost (TVC). In column 4 the addition of the two preceding figures gives total cost (TC). The curves TC and TVC move together in Figure 3.1 ; that is, the slopes of the two curves are everywhere equal and at each point they are separated by a vertical distance determined by TFCFigure 3.1Table 3.1A typical cost scheduleUnits of output Total fixed cost Total variable cost Total cost Average fixed cost Average variable cost Average total cost Marginal cost 1 100 20.0 120 100.0 20.0 120.0 - 2 100 35.0 135 50.0 17.0 67.5 15.0 3 100 40.0 140 33.3 13.3 47.0 10.0 4 100 50.0 150 25.0 12.5 39.0 10.0 5 100 60.0 160 20.0 12.0 32.0 10.0 6 100 70.0 170 16.7 11.7 28.3 10.0 7 100 80.0 180 14.3 11.4 25.7 10.0 8 100 91.3 191.3 12.5 11.3 23.9 11.3 9 100 104.0 204 11.1 11.5 22.6 13.0 10 100 120.0 220 10.0 12.0 22.0 
eBook - PDFStudies in Economics and Political Science
13 Volume Set
- Various(Author)
- 2022(Publication Date)
- Taylor & Francis(Publisher)
cit., pp. 156-9. CHAPTER 3 The Theory of Costs I. COST THEORY It is frequently assumed that the problem of selecting the optimum input combination has been solved, and subsequent analysis is car- ried out in terms of revenues and costs expressed as a function of the rate of output. In this way the principles of production established in Chapter 2 lay the foundations for an analysis of costs. The knowl- edge of the production function enables the isoquant map to be drawn. Isocost Lines can be added to this map, and the efficient out- put level and input combination can be established. Each level of output will be associated with a total cost of production. Costs can therefore be related functionally to the rate of output in the form of a cost function or schedule. A typical cost schedule is represented in Table 3.1. Some terms 500- 400- 30O Costs 200H Total Variable Cost Total Fixed Cost 10 15 Output 20 Total Cost Figure 3.1
eBook - PDFIntermediate Microeconomics
An Intuitive Approach with Calculus
- Thomas Nechyba(Author)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
For instance, we could give the producer only €250 to work with, which would put us on the light brown isocost curve, but this would still be more than the producer needs to produce 100 units of output. We could keep reducing the producers hypothetical budget until we get to the light blue isocost curve that represents all input combinations that cost exactly €200. This isocost curve contains exactly 1 input bundle – bundle A with 5 hours of labour and 10 units of capital – that can produce 100 units of output. Any less of a hypothetical budget would imply that the producer would not be able to buy sufficiently many inputs to produce 100 units of output. The input bundle A represents the least cost way of producing 100 units of output when input prices are €20 for labour and €10 for capital . The production plan ( ℓ , k , x ) 5 (5, 10, 100) represented by A is the economically efficient way to produce 100 output units given these input prices. Since the slope of the isoquant must equal the slope of the iso-cost at this cost-minimizing input bundle, we can conclude that: Cost minimization implies 2 TRS 5 MP / MP k 5 w r . (12.4) Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 296 CHAPTER 12 PRODUCTION WITH MULTIPLE INPUTS since the least cost input bundle for producing 100 units of output at input prices w 5 20 and r 5 10 involves using 5 labour hours costing a total of €100, and 10 units of capital costing an additional €100, the total cost of producing 100 units of output is €200 (point A 9 ).
eBook - PDF- H. Blomqvist, M. Lundahl(Authors)
- 2002(Publication Date)
- Palgrave Macmillan(Publisher)
The flatter the slope of pp, the more expensive is labour, relatively speaking, and the more units of capital are needed to `buy' a given amount of labour. A line such as pp is also known as a budget line. The budget line is an Isocost Line that may be expressed by the equation C wL rK (2:12) The equation shows the different combinations of labour and capital that give rise to the same cost. If we differentiate (2.12) and put the differential equal to zero, at given factor prices, we obtain: dC wdL rdK 0 (2:13) 18 The Distorted Economy or dL r (2:14) dK w that is, the slope of the factor price line. The total cost, C, does not affect the slope but determines the distance between the budget line and the origin. Each point on an isoquant denotes a given factor combination and differ- ent factor combinations can be used to produce the same quantity of the commodity. Which production technique will be chosen is given by the relative factor prices of the economy. (As we will soon see, how much we want to produce does not matter.) For each given cost level it pays to produce as much as is technically possible. The maximum point is found where the Isocost Line is tangent to an isoquant. (It is also possible to produce at any other point on the Isocost Line, but all other points lie on lower isoquants than does the point of tangency.) If, on the other hand, the goal is to produce a given quantity, the cheapest way of doing this is given by the point of tangency between the corresponding isoquant and an Isocost Line. In the above reasoning producers are assumed to maximize their profits (i.e., they raise production factors up to the point where the value of their marginal products equals what they are paid ): w PQ L (2:15) r PQ K (2:16) where P is the price of the commodities. If P is eliminated from (2.15) and (2.16) we find that r Q K (2:17) w Q L that is, the slope of the factor price line (budget line) must coincide with that of the isoquant.
- Humberto Barreto(Author)
- 2009(Publication Date)
- Cambridge University Press(Publisher)
Understanding points off the cost function. be off the demand curve. We learned that points to the left or right of the inverse demand curve (with price on the y axis) mean that the consumer is not optimizing, i.e., the consumer is not choosing a point of tangency between the indifference curve and budget constraint. We can conduct the same kind of inquiry with the cost function, asking this question: What does it mean to be off the cost curve? Unlike the inverse demand curve, where the exogenous variable is on the y axis, the cost function is graphed with the exogenous variable, out-put, on the x axis. Thus, points off the curve are interpreted vertically above or below the cost function. More specifically, what does it mean if a point is above the cost curve? Figure 2.2.3.1 helps us answer this question. On the left is the familiar iso-quant/isocost graph. The cheapest way to produce q 0 units of output is with the L and K combination at the point labeled TC ∗ . The graph on the right of Figure 2.2.3.1 shows that TC ∗ is a point on the cost function at an output of q 0. Point Z, a point above the cost function, reveals that the firm is producing the level of output q0 at a total cost above the minimum total cost. Then we can deduce that the firm is choosing an input mix that is not cost minimizing. Point Z on the graph on the left of Figure 2.2.3.1 must lie on an isocost above the tangent isocost. We do not know exactly where point Z is on the graph on the left (so we do not know if there is technical or allocative inefficiency), but we do know it has to be somewhere on the isocost that has a total cost the same as the cost of producing point Z (on the graph on the right). Point Y on the right side of Figure 2.2.3.1 is below the cost function. How can this point be generated by the graph on the left? It cannot. There is an isocost with a total cost equal to that at point Y, but it is below the isoquant and, therefore, unattainable.
eBook - PDF- Kumar, K Nirmal Ravi(Authors)
- 2021(Publication Date)
- Daya Publishing House(Publisher)
In both This ebook is exclusively for this university only. Cannot be resold/distributed. cases the factors will have to be employed in optimal combination at which the total cost incurred will be minimum. a. Cost minimization for a given Level of Output Here, the farmer tries to minimize the cost to produce a given level of output in the production programme. Let us suppose, the money with the farmer is Rs. 60 and he has to allocate this money between the two resources viz., manure (Rs. 5/unit) and fertilizer (Rs. 6/unit) and assume that, the farmer wishes to produce 100 units of output (100Y). The earlier discussion on isoquant and iso-cost line reveals two important aspects viz., the isoquant infers ‘what combination of resources the farmer is willing to buy’ and the iso-cost line guides the farmer, ‘what the farmer is able to buy’, so as to attain the LCC of resources. So, when the isoquant and the iso-cost line are combined, we find the quantities of each resource the farmer is both willing and able to buy, so as to produce a desired level of output. So, the isoquant and iso-cost line for a given level of output helps the farmer to find out the combination of resources that will lead to LCC of resources. So, the LCC refers to the point of cost minimization in the production programme at a particular combination of resources, given outlay with the farmer and prices of the resources in the market. Figure 2.27 : Farmer’s Equilibrium – Iso-cost Line Tangent to Isoquant (Cost minimization for This ebook is exclusively for this university only. Cannot be resold/distributed. a given output). From the Figure 2.27, it is clear that, the iso-cost line PL is tangent to the isoquant of 100Y at point ‘A’ and this indicates that, by allocating OQ M units of manure and OQ F units of fertilizer, the cost is minimum in the production programme. It is also important that, the farmer can allocate any combination of resources below PL iso-cost line, but 100Y cannot be achieved.
eBook - PDF- David Besanko, Ronald Braeutigam(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Let’s summarize the results of our comparative statics analysis: • When the firm has smooth isoquants with a diminishing marginal rate of techni- cal substitution, and is initially using positive quantities of an input, an increase in the price of that input (holding output and other input prices fixed) will cause the cost-minimizing quantity of that input to go down. • When the firm is initially using a zero quantity of the input or the firm has a fixed-proportions production function (as in Figure 7.6), an increase in the price of the input will leave the cost-minimizing input quantity unchanged. Note that these results imply that an increase in the input price can never cause the cost-minimizing quantity of the input to go up. K, capital services per year L, labor services per year B A Slope of Isocost Line C 2 = –2 Slope of Isocost Line C 1 = –1 Q 0 isoquant C 2 C 1 K 1 0 K 2 L 2 L 1 FIGURE 7.5 Comparative Statics Analysis of Cost-Minimization Problem with Respect to the Price of Labor The price of capital r = 1 and the quantity of output Q 0 are held constant. When the price of labor is w = 1, the Isocost Line is C 1 and the ideal input combination is at point A (L 1 , K 1 ). When the price of labor is w = 2, the Isocost Line is C 2 and the ideal input combination is at point B (L 2 , K 2 ). Increasing the price of labor causes the firm to substitute capital for labor. CHAPTER 7 COSTS AND COST MINIMIZATION 280 K, capital services per year L, labor services per year Q 0 isoquant 1 1 Slope of Isocost Line C 2 = –2 Slope of Isocost Line C 1 = –1 C 1 A C 2 FIGURE 7.6 Comparative Statics Analysis of the Cost-Minimization Problem with Respect to the Price of Labor for a Fixed-Proportions Production Function The price of capital r = 1, and the quantity of output Q 0 are held constant. When the price of labor w = 1, the Isocost Line is C 1 and the ideal input combination is at point A (L = 1, K = 1).
eBook - PDFIntermediate Microeconomics
A Tool-Building Approach
- Samiran Banerjee(Author)
- 2021(Publication Date)
- Routledge(Publisher)
Given the output and the input prices, we first find these conditional in-put demands graphically, and then using constrained optimization. The for-mer provides the intuition for the necessary mathematical conditions which are derived more rigorously using the latter. These conditions are subse-quently used to derive cost functions for different production functions, in-cluding the linear, Leontief, quasilinear, and Cobb-Douglas technologies in section 8.3. Costs 139 x 1 x 2 0 x 1 -x 2 -q -B A -C -C/w 1 C * -C/w 2 Figure 8.1 Cost minimization 8.2.1 Interior solutions Graphical derivation Suppose the given technology is q = f ( x 1 , x 2 ) and the output level desired is q ¯. In Figure 8.1, the isoquant that yields q ¯ is shown in orange. The objective is to find the input combination on this isoquant that is cheapest. If ( w 1 , w 2 ) are the fixed per-unit input prices, the total cost C of any input bundle ( x 1 , x 2 ) is given by C = w 1 x 1 + w 2 x 2 . (8.1) For an arbitrary outlay C ¯ , equation (8.1) shows input combinations that cost C ¯ and is called an isocost , the line shown in blue. The isocost is the analog to a consumer’s budget line from Chapter 2; its slope is given by the input price ratio − w 1 / w 2 and the blue arrows indicate the direction in which costs are decreasing . Lower lev els of cost out lay re sult in par al lel iso costs that lie to the south west. Figure 8.1 shows that the input combination A can produce the output level q ¯ for a cost of C ¯ , but B = ( x ¯ 1 , x ¯ 2 ) produces q ¯ for a lower cost of C ≈ . In fact, any outlay lower than C ≈ would make the output q ¯ unattainable since that isocost would no longer touch the isoquant, so B is the cost-minimizing input combination. Therefore, the cost-minimizing input combination for any given level of out put is one where the iso quant is tan gent to the iso cost, � 140 Chapter 8 i.e., − TRS = − w 1 / w 2 , or TRS ( ¯ x 1 , ¯ x 2 ) = w 1 w 2 .
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