tons, liters, kgs.) Modern methods, however, are still based on the same premise as the original Bessemer Process, which uses oxygen to lower the carbon content in iron. Hire additional workers as demand increases, Employment costs for advertising, travel, interviewing, training, and others, Shift premium costs if additional shift is added, Skilled workers may not be available when needed, Cost of severance pay & increases in unemployment insurance costs, The company must have adequate capital investment in equipment for the peak work force level, Produce in earlier period and hold until product is needed, Service operations cannot hold service inventory, Offer to deliver the product or service later, when capacity is available, Delay in receipt of revenue, at minimum; company may lose customers, Manufacturing companies with perishable products often use this method, Exert special marketing efforts to shift the demand to slack period, Advertising costs, discounts, other promotional programs, Work additional work hours without changing the workforce size, The time available for maintenance work without interrupting production is reduced, Staff for high production levels so that overtime is not necessary, Excess personnel wages during period of slack demand, Work force may be used for deferred maintenance during periods of low demand, Continuing company overhead; subcontractor's overhead and profits, The capacity of other firms can be utilized, but there is less control of schedules and quality levels, Revise make-or-buy decisions to purchase items when capacity is fully loaded, Waste of company skills, tooling and equipment unutilized in slack periods, These methods require capital investments sufficient for the peak production rate, that will be underutilized in slack periods. Thus in order either to maximize output sub­ject to a given cost or to minimize cost subject to a given output, the production manager must employ factors in such amounts as to equate the MRTS with the factor price ratio. Soft drinks are enormously popular beverages consisting primarily of carbonated water, sugar, and flavorings. (4), Now suppose that we double the inputs to 4, 2 and 6, respectively. Thus, the original production function is characterized by con­stant returns to scale (λ =α). If λ= α, the production function is characterized by constant return to scale. This is shown by point A on isoquant Q1 in Fig. This is the case throughout stage 1 in as much as the aver­age product of labour is a measure of its efficiency. An intuitive understanding of the concepts of increasing, constant and decreasing returns to scale can be developed by looking at Fig. These three points may be proved mathematically. Fig. Our mission is to provide an online platform to help students to discuss anything and everything about Economics. The following three points are worth not­ing in this context: 1. When the decision is being considered about which manufacturing pro… Environmental factors capture the broader context in which groups operate, such as reward structure, st… Both inputs and outputs are expressed as flows per period of time. Thus, along a given row output increases, but at a decreasing rate. In fact, the theory of production is just an ap­plication of the constrained optimization technique. Put differently, production at least cost requires that the MRTS of capital for labour be equal to the ratio of the price of labour to the price of capital. That is, the pro­duction process demands more than a doubling of all inputs in order to exactly double the level of out­put. In process manufacturing, the basic inputs (natural resources, raw materials) are broken down into one or more outputs (products). (d) What is the maximum output capability per period? All the three stages together constitute what is broadly called the Law of Variable Propor­tions. These cocoa beans will then be imported or exported to other countries and be transformed into different type of chocolate products (Allen, 1994). The short run is defined as the period of time in which at least one input is fixed. In Fig. The next major activity involves the identification of the alternatives that the firm may employ to meet production forecasts as well as the constraints and costs involved. Production is a process whereby some goods and services, called inputs are transformed into other goods and services called output. This is turn allows us to relate cost to the level of output produced. Thus he has to make either of two input choice decisions: 1. We have noted, in the case of constant returns to scale, if inputs are increased by a given proportion, output rises by the same proportion, that is, αn= a. The informa­tion in this column is illustrated graphically in Fig. The concept makes it clear that 20% increase in output will not always necessitate a 20% increase in labour usage. These new optimal combinations indicate that the firm substi­tutes capital for labour to produce each level of out­put when the price of labour rises relative to the price of capital. Here we concerned with production in the narrow sense of physical trans­formation, with particular reference to economic problems connected with production in the factory. to an elasticity of production measure. A production function is usually defined as a schedule (or table, or mathematical equation) show­ing the maximum amount of output that can be produced from a fixed amount of resources, given the existing technology or the art of production. The labour input value of 3.75 units corresponds to the “peak” of the APL, curve, i.e., maximum APL, and is also a cut-off or critical point for elasticity of production. So output is a function of labour alone. The expansion path gives the firm its cost structure. If combinations A or B are chosen, at the cost outlay represented by K”L”, the producer can reduce costs by moving along Q0 to point E. Point E shows the optimal resource combination, K0units of capital and L0 units of labour. 13.2 is 5-shaped. In this production process, the manager is concerned with efficiency – technical and economic – in the use of these inputs. In the radio example, both average product and the marginal product concept refer to labour (L), the only variable factor of production. Since α can be factored out of Eq. Steel manufacturers use heat to transform iron and other materials into steel. Production is a process in which economic resources or inputs (com­posed of natural resources like land, labour and cap­ital equipment) are combined by entrepreneurs to create economic goods and services (also referred to as … When L equals 2, however, the marginal product of labour (shown in Table 13.1) is 28 units (or aver­age MPL = 2.8 units). 13.10 that output level will be produced at the cost represented by isocost line K’ L’. Economies of scope exist for multiple products when the cost of joint production is less than the cost of producing each output separately. Choose the input combination that leads to the lowest cost of producing a fixed level of output (i.e., cost minimization subject to output constraint). It will be evident that both optimization problems lead to the same rule for the allocation of inputs and the choice of technology. In Fig. If the initial values of K and L are 1 and 2, respectively, then total output is 14. As production systems will involve increasing levels of automation, informatics, robotics, sensors, mobile devices, etc., it’s important to remember that human skills will remain essential for many tasks, making the marriage between humans and machines critical to success. As we move from A to B along the iso­quant for 100 units of output, the only change is in the capital labour ratio. Share Your PPT File. Increasing returns to scale if n > 1, in which case αn > α (output goes up proportionately more than the increase in input usage). If the relative factor prices change, the slope of the isocost line must change, If w rises relative to r, the isocost line becomes steeper. Output has quadrupled, indicating a production function exhibiting increasing returns to scale (λ > α). A build­ing or a blast furnace cannot be discharged (even though its use may fall to zero). While analysing the process of production, eco­nomists find it convenient to classify inputs into two categories: fixed or variable. 13.15. The sum of the quantities of each input used, times the respective input price, gives the minimum cost of producing every level of output. With a given state of technology, the attainable level of output depends largely, but not entirely, upon the quantities of the various inputs employed in the pro­duction process. For example, it is quite possible that when the extra unit of labour is employed, the production process will become more specialized, thereby en­abling both workers to be more efficient or produc­tive. The end result will be the same as before. •  Do the production schedules permit adequate planning of purchases and inventory levels? The process of production is concerned with transforming a set range of inputs, depending on the product, into those outputs that are required by the market (demand). As a firm expands the scale of its operation, oppor­tunities for increased specialization in the use of re­source inputs normally occur. Suppose for a firm using two inputs K and L, MPL = 5, PL = Rs. At point B, we have more labour and fewer units of capital than at point A. Thus, in general, when L and K are allowed to vary marginally, the change in Q resulting from the change in the two inputs is the marginal product of L times the amount of change in L plus the marginal product of K times its change. It is so because in a competitive world the production managers will be compelled to use the technology that is most cost effective.In this context one may draw a distinction be­tween efficiency and effectiveness. The elasticity of production has greater practi­cal implications for production managers who are being asked to raise and lower output on a periodic basis. It is, in reality, a state­ment concerning the physical relationship between different amounts of a variable input and the result­ing output. The slope of the isoquant indicates the substi­tutions that, if made, will leave output unchanged. In traditional economics, the term ‘production’ is used in a broad sense. Input – an input is what you what you put into a production process to achieve an into a production process to achieve an output. The ques­tion to be answered about returns to scale is: How much do we have to increase the two inputs, capital and labour, in order to keep on doubling the rate of output from Q0 to Q1, Q2 to Q2, and Q2 to Q3. Thus it is clear that any desired level of output can be produced by a number of different combina­tions of inputs. 2,000 lies above the line for C = Rs. Clearly, a movement from A to B would result in a reduction of both L and K. And since inputs are to be paid, an entrepreneur would prefer point B to point A, as he is assumed to behave rationally. Various inputs are normally used in production. The human resources function, which recruits and develops the organization’s staff as well as looking after their welfare. We can analyse the equilibrium condition in an alternative way. Privacy Policy3. Alternatively, the average marginal product or marginal product per unit of labour input can be calculated over an input range by simply relating the absolute change in output (∆Q) to the absolute change in the variable (factor) input (∆L). The second method would be to make use of the MP schedule. (d) The maximum output capacity in the short term can be obtained in two alternative ways. •  Can the status of any order or work in progress be readily determined? When the input of machines is held constant at 4 units, then additional units of labour bring about smaller and smaller additions to output. The production function refers to the relationship between the input of factor services and the output of the resultant product. And it presupposes positive marginal product of L and K. But MP of L may become negative if the application of L is so large relative to quantities of other input(s), say capital, that an increase of labour would result in congestion and inefficiency, in which case MP may turn out to be negative. Alternatively, if we were to reduce capital by one unit, output would fall by 3 units. Production may also refer to the goods being produced. Each stage is important from the stand­point of efficient resource utilization (as shown in Fig. In the long run, it is assumed that all fac­tors are variable. Stage 2 and its boundaries are the economically feasible region, i.e., the area within which the rational producer will choose to operate. Whatever output a firm chooses to produce, the production manager is desirous of producing it at the lowest possible cost. Finally, if Q1 is less than 200 units (say, 180) the production function is said to exhibit decreasing returns to scale. This approach seems to be more practical than the previous one. If Rs. Thus, we observe that the production process is time-specific. This is alleviated through detail-oriented planning processes. We have postulated convexity of isoquants. For instance, six hours of labour input and six hours of machine usage may mean six workers each using one machine for one hour (process A), or one worker using one machine for six hours (process B). The long-run, in other words, refers to that time in the future when out­put changes can be accomplished in the most cost- effective manner. Thus, as capital is reduced and labour is in­creased along an isoquant, the amount of capital that can be released for each unit of labour added gradually diminishes. The transformation process typically uses common resources such as labour, capital (for machinery and equipment, … By contrast, the long-run refers to the period of time (or planning horizon) in which all inputs are ca­pable of continuous variation. Other articles where Production is discussed: production system: Underlying principles: All production systems, when viewed at the most abstract level, might be said to be “transformation processes”—processes that transform resources into useful goods and services. In short, the production function is a catalogue of a firm’s output possibilities. Because output is mea­sured per unit of time, inputs must also be measured in terms of services provided for each time period. In this case the distance along the ray between any two successive isoquants remains unchanged, suggesting a proportionate increase in both inputs and output. These data include the following: •  Operations / manufacturing Information, •  Sales, marketing and distribution Information. This hap­pens when output is 115.6 units and labour input is 5.6 units. Suppose that we start with the following production function: Furthermore, suppose that we multiply each in­put by a constant a. We know that along any ray from the origin, the ratio of the two inputs remains constant. Thus, the elasticity of substitution, as defined by Sir John Hicks, is a measure of the relative change in the factor proportion divided by the relative change in factor-price ratio. In our example, stage 1 starts when the amount of labour is equal to zero and continues up to the point where 3.75 units of labour are employed. This can be seen in Fig. Consider oil. Thus, the average product for one unit of labour is 16.5 radios and for two units of labour 21 radios. When analysing production with more than one variable input, it is not possible simply to use av­erage and marginal product curves because these curves are derived holding the use of all other in­puts constant (fixed) and allowing the use of only one input to vary. The operation of law of diminishing returns can also be discerned. Then returns to scale (RTS) would become negative, as at point A of Fig. For example, if 2 units of labour and 5 units of capital are necessary to produce 100 units of output, 200 units of output require 4 of the labour and 10 of capital, 300 units require 6 of labour and 15 of capital, and so on. The expansion path shows the way in which fac­tor proportions change in response to output changes, with the factor-price ratio remaining unchanged. The reason that Castle and Cooke processes and packages Dole pineapple products in Hawaii is more than likely because of low energy costs. Then, if we add one unit of labour, output would increase by 6 units. The principles developed in this section will continue to apply. In man­agerial economics, however, the term is used in a narrow sense to refer to the processes of physical transformation of resources, such as the transforma­tion of iron ore into steel or the production and as­sembly of components into a finished car. In reality, the outputs are the start­ing point of the operation inasmuch as they must be considered in the light of the market possibili­ties. From Table 13.2 we discover the important re­sult that up to 3.75 units of labour (L), the elasticity of production exceeds 1, indicating that output is in­creasing faster than input usage. A process is an action that transforms given inputs into outputs under certain constraints or restrictions and with the aid of some mechanisms. Finally, in traditional economics it is assumed that the techniques of production are ‘given’. Total cost (outlay) is simply the sum of the cost of K units of capital at r rupees per unit and of L units of labour at w rupees per unit. In any discussion of short run production function, capital is taken to be the fixed input. The basic inputs, like natural resources, raw materials, or human resources, are either combined to create the output or transformed into the output. In this case the marginal product of an addi­tional rupee worth of labour is less than the marginal product of an additional rupee worth of capital. Input - the information entered into a computer system, examples include: typed text, mouse clicks, etc.. We may now proceed a step further. Inputs reflect the resources that groups have at their disposal and are generally divided into three categories: individual-level factors, group-level factors, and environmental factors. For example, buildings, major pieces of machinery, and manage­rial personnel are inputs that generally cannot be varied quickly. There would exist an infinite number of isocost lines, each relating to a different level of cost outlay (expenditure). However, while all inputs are in fact variable in practice, the cost of immediate variation in the use of a particular input is often so great that such an input is not varied. Thus, as labour is substi­tuted for capital the marginal product of capital in­creases. This defi­nition surely includes other and equally vital forms of transformation such as that of location, whereby the finished car is moved from the factory to the showroom of the dealer from whom it can be pur­chased. Recall that MRTS shows the rate at which the producer can substitute between the inputs in production. It results from a change in factor prices. In fact, the former is derived from the latter. Suppose that, at a point on the isoquant, the marginal prod­uct of capital (MPk) is 3 and the marginal product of labour (MPL) is 6. Chocolate is a product that requires complex procedures to produce. If Q1 is greater than 200 units (say, 215), there is increasing return to scale. More generally, if all inputs are increased by a factor a and output gets multiplied by a factor of αn then a firm experiences: 1. This implies that a 1% increase in the ratio of the price of labour to the price of cap­ital causes a 1% increase in the capital-labour ratio. By following the same logic it is pos­sible to establish that if the inequality is reversed, such as the case at point A, the firm would con­tinue to substitute labour for capital until the equal­ity holds. Over the relevant range (i.e., economic region) of productions the MRTS diminishes. We have noted earlier that the production func­tion shows the maximum amount of output that can be produced from specified levels of input usage. It shows output expansion effect which is similar to income effect (studied in the theory of consumer demand). Thus differentiating total product (TP) with respect of X gives us the MP equation: The average product equation is simply derived by dividing the total product by the variable input X. Human factors and technology. If not, why not? When 3.75 units of labour are combined with the fixed factors of production, the elasticity of production is equal to exactly 1, indicating that production is increasing at a rate at which labour usage is increas­ing. Therefore, in the short-run, output is basically a function of the quantum (us­age) of the variable factors, i.e., changes in output must be accomplished exclusively by changes in the use of the variable inputs. In other words, isoquants, like consumption indifference curves, cannot meet or intersect. 100) and labour receives a wage of Rs. If λ> α, the production function exhibits increasing returns to scale. This is quite obvious that if no labour input is used, output will be zero, despite the fact that fixed factors of production are available. Various types of labour services as well as certain raw and processed materials could be placed in this category. If λ< α, the production function exhibits decreasing returns to scale. For continuous changes in L and Q, the elastic­ity of production can be expressed as. Combining these two conditions as labour is substituted for capital, MPL decreases and MPk increases; so MPL /MPk will diminish. In other words, 3M enjoys a commanding competitive advantage by controlling the transformation processes that turn raw material inputs into the high value-added Magic Tape product. Thus, constant returns in panel (b) leads to linear total cost curve in panel (b’) – constant cost per unit. Now suppose the firm decides to spend Rs.1, 500 per month for capital and labour. The isoquant shows the desire of the producer. Fifth Edition. This production plan needs to be translated into a master production schedule so as to schedule the items for completion promptly, according to promised delivery dates; to avoid the overloading or under loading of the production facility; and so that production capacity is efficiently utilized and low production costs result. Panel (b) illustrate the case of constant returns to scale. 3. Isoquants for such examples are shown in Fig. In the case of two variable inputs, changing the use of one input is likely to cause a shift in the marginal and average product curves of the other input. Production converts inputs into outputs by changing the inputs in some way. For example, suppose the estimated production function is. To ensure this, the profit-maximizing firm has to choose that input combination for which the marginal product divided by input price is the same for all inputs used. 13.3. First, by reading the relevant figure from the graph or ob­taining the data from the prepared table. How can you monitor effectiveness of your production plans? Thus, over the range from one to two units of labour, average marginal product is 25.5 units. The distinc­tion is not based on any time period but is made on the basis of the possibility of factor substitution. From this we drive the proposition that the short run costs are partly fixed and partly variable; in the long run all costs are variable. The minus sign is added in order to make MRTS a positive number, since ∆K/∆L, the slope of the isoquant, is already negative (because addi­tional use of any factor always at the expense of the other). The most basic form of the short run production function was presented in Equation (1) or (1)’ and contains one variable input. Capital inputs are measured vertically and labour inputs are measured horizontally (see Fig. We see that isoquants for perfect complements are Z-shaped. It forms the foundation for the theory of supply, which, is one of the basic concepts in the deter­mination of prices. To accomplish this objec­tive, the production process must not only be tech­nically efficient but economically efficient, as well. In a like manner the terms input, economic resource, or factor of pro­duction represented by L or K, is used to denote the resources used in the production process. In the theory of consumer demand we noted that MRS is the ratio of the two marginal utilities. Then solving for the MRTS, we get: The M RTS diminishes as the producer moves along an isoquant from left to right. were w and r are, respectively the prices of labour (PL) and capital (PK). If we were to change the usage of the fixed input, total, average, and marginal product curves would all shift. Thus the equation becomes 1500 = 100A’ + 250L . 13.15, increasing returns to scale is illustrated. In terms of the above production function we get: To test production functions for returns to scale, all that is necessary is to compare the value of There are various variables that might account to the value of λ: 1. Now, suppose the price of labour (or wage rate) increases relative to the price of capital (or the rate of interest). 13.2 show that at the early stage of the production pro­cess output increases at an increasing rate as the first few units of labour are added; at the second stage it continues to increase but at a decreasing rate as more and more workers are employed. If both inputs were doubled (α = 2), output would increase to 56(λ = 4). This equation states that for the firm to be em­ploying the least cost combination of inputs K and L, the additional output obtainable from spending an extra rupee on input L must equal the additional output obtainable from spending another rupee on input K. If this relationship did not hold, the firm would gain by purchasing less of the input with a lower additional output per additional rupee expen­diture, and more of the input with a greater additional output per extra rupee expenditure. This is called the input (factor) sub­stitution effect. As noted by Bails and Peppers, “a construc­tion firm may be able to utilize more fully larger and more efficient equipment, than would a smaller construction firm. Iso­quants I and II are only two of an infinite number of isoquants that could possibly be shown in the di­agram. Three Stages of Production and Decision Making: Production with Two or More Variable Inputs: Ridge Lines and the Economic Region of Production: Production of a Given Output at Minimum Cost: Production of Maximum Output with a Given Level of Cost: Testing Production Functions for Returns to Scale. 13.4). In a like manner, an additional worker where there is only one shovel at point C can produce no more holes, assuming shovels are essential for digging and that a worker can work continuously without relief. The definition of production function does not preclude the possibility of negative RTS. Human reproduction is any form of sexual reproduction resulting in human fertilization.It typically involves sexual intercourse between a man and a woman. Here we look at a producer who is a competitor in the input market facing given market-determined input prices; so we treat the input prices as fixed. To be able to perform the aggregate planning process, the following information should be available to this production planning team. For exam­ple, consider first the expansion path OS shown in Fig. Since the marginal product of capital is 3, two units of capital must be released. The most probable explanation for decreasing returns to scale is that there are lim­its to the effective management of larger and larger production units. The factor price ratio tells the producer the rate at which one input can actually be substituted for another in the market place. We may now turn to the fundamental issue of the properties of the short run production function and the implications of these properties for practicing managers against this backdrop. At fixed input prices, r and w for capital and labour, it is possible to purchase with a fixed outlay C, any combination of capital and labour given by the following linear equation: This is the equation for an isocost line whose intercept (C/r) is the amount of capital that may be purchased if no labour is bought and whose slope is the negative of the factor-price ratio (w/r). For any combination along an isoquant, if the usage level of either input is reduced and of the other is held constant, output will fall. 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