Theory of Production and the Production Function
The production function relates the quantity of factor inputs used by a business to the to fall. This means that total output will be increasing at a decreasing rate. These include the relationship between the prices of commodities and the prices (or It states the amount of product that can be obtained from each and every The isoquant labelled “” shows all the combinations of the variable inputs that will . The average and marginal cost curves just deduced are the keys to the. The function that explains the relationship between physical inputs and where Q represents the final output and X1 and X2 are inputs or factors of production. In simple terms, we can define Total Product as the total volume or amount of final output This gives the Total product curve a convex shape in the beginning as.
But there are other combinations of variable inputs that could also produce necklace chains per month. If the goldsmiths work more carefully and slowly, they can produce chains from feet of wire; but to produce so many chains more goldsmith-hours will be required, perhaps The other two isoquants shown are interpreted similarly.
It is obvious that many more isoquants, in principle an infinite number, could also be drawn. This diagram is a graphic display of the relationships expressed in the production function. Substitution of factors The isoquants also illustrate an important economic phenomenon: This means that one variable factor can be substituted for others; as a general rule a more lavish use of one variable factor will permit an unchanged amount of output to be produced with fewer units of some or all of the others.
In the example above, labour was literally as good as gold and could be substituted for it. If it were not for factor substitution there would be no room for further decision after y, the number of chains to be produced, had been established. The shape of the isoquants shown, for which there is a good deal of empirical support, is very important. In moving along any one isoquant, the more of one factor that is employed, the less of the other will be needed to maintain the stated output; this is the graphic representation of factor substitutability.
But there is a corollary: In the diagram, if feet of gold wire are indicated by x1 and goldsmith-hours by x2, then the marginal rate of substitution is shown by the steepness the negative of the slope of the isoquant; and it will be seen that it diminishes steadily as x2 increases because it becomes harder and harder to economize on the use of gold simply by taking more care.
The remainder of the analysis rests heavily on the assumption that diminishing marginal rates of substitution are characteristic of the production process generally. The cost data and the technological data can now be brought together. The straight line labelled v2, called the v2-isocost line, shows all the combinations of input that can be purchased for a specified variable cost, v2. The other two isocost lines shown are interpreted similarly. The slope of an isocost line is found by dividing p2 by p1 and depends only on the ratio of the prices of the two factors.
Isoquant diagram for two factors of production, x1 and x2 see text. Three isocost lines are shown, corresponding to variable costs amounting to v1, v2, and v3. If units are to be produced, expenditure of v1 on variable factors will not suffice since the v1-isocost line never reaches the isoquant for units. An expenditure of v3 is more than sufficient; and v2 is the lowest variable cost for which units can be produced.
Cost in Short Run and Long Run (With Diagram)
It may be noted that the cheapest combination for the production of any quantity will be found at the point at which the relevant isoquant is tangent to an isocost line. Thus, since the slope of an isoquant is given by the marginal rate of substitution, any firm trying to produce as cheaply as possible will always purchase or hire factors in quantities such that the marginal rate of substitution will equal the ratio of their prices.
The isoquant—isocost diagram or the corresponding solution by the alternative means of the calculus solves the short-run cost minimization problem by determining the least-cost combination of variable factors that can produce a given output in a given plant.
The variable cost incurred when the least-cost combination of inputs is used in conjunction with a given outfit of fixed equipment is called the variable cost of that quantity of output and denoted VC y. The total cost incurred, variable plus fixed, is the short-run cost of that output, denoted SRC y. Marginal cost Two other concepts now become important.
The average variable cost, written AVC yis the variable cost per unit of output. The marginal variable cost, or simply marginal cost [MC y ] is, roughly, the increase in variable cost incurred when output is increased by one unit; i.
Though for theoretical purposes a more precise definition can be obtained by regarding VC y as a continuous function of output, this is not necessary in the present case. The usual behaviour of average and marginal variable costs in response to changes in the level of output from a given fixed plant is shown in Figure 3. In this figure costs in dollars per unit are measured vertically and output in units per year is shown horizontally.
The figure is drawn for some particular fixed plant, and it can be seen that average costs are fairly high for very low levels of output relative to the size of the plant, largely because there is not enough work to keep a well-balanced work force fully occupied. People are either idle much of the time or shifting, expensively, from job to job. As output increases from a low level, average costs decline to a low plateau. But as the capacity of the plant is approached, the inefficiencies incident on plant congestion force average costs up quite rapidly.
Theory of Production and the Production Function
Overtime may be incurred, outmoded equipment and inexperienced hands may be called into use, there may not be time to take machinery off the line for routine maintenance; or minor breakdowns and delays may disrupt schedules seriously because of inadequate slack and reserves.
Thus the AVC curve has the flat-bottomed U-shape shown. Maximization of short-run profits The average and marginal cost curves just deduced are the keys to the solution of the second-level problem, the determination of the most profitable level of output to produce in a given plant.
The only additional datum needed is the price of the product, say p0. The most profitable amount of output may be found by using these data. If the marginal cost of any given output y is less than the price, sales revenues will increase more than costs if output is increased by one unit or even a few more ; and profits will rise.
Contrariwise, if the marginal cost is greater than the price, profits will be increased by cutting back output by at least one unit. This is the second basic finding: We also see that variable cost first increase at a decreasing rate the slope of STC decreases then increase at an increasing rate the slope of STC increases.
This cost structure is accounted for by the law of Variable Proportions. Average and Marginal Cost: We may first consider average fixed cost AFC. Average fixed cost is total fixed cost divided by output, i. Average fixed cost is relatively high at very low output levels.
However, with gradual increase in output, AFC continues to fall as output increases, approaching zero as output becomes very large. The next important concept is one of average total cost ATC. It is calculated by dividing total cost by output, It is, therefore, the sum of average fixed cost and average variable cost.
It first declines, reaches a minimum at Q3 units of output and subsequently rises. This point can easily be proved. Since AFC declines over the entire range of output. We may finally consider short-run marginal cost SMC. Marginal cost is the change in short-run total cost attributable to an extra unit of output: Thus average variable cost has to fall.
Thus, in this case, AVC must rise. Exactly the same reasoning would apply to show MC crosses ATC at the minimum point of the latter curve. Summary of the Main Points All the important short-run cost relations may now be summed up: The total cost function may be expressed as: Hence the AFC curve is a rectangular hyperbola.Microeconomic Cost Curves (Old Version) MC, ATC, AVC, and AFC
Since business decisions are largely governed by marginal cost, and marginal costs have no relation to fixed cost, it logically follows costs do not affect business decisions. Relation between MC and AC: There is a close relation between MC and AC. This can be proved as follows: When AC is falling, c. On the basis of the relation between MC and AC we can develop a new concept, viz.
It measures the responsiveness of total cost to a small change in the level of output. It can be expressed as: So it is the ratio of MC to AC. From the diagram the following relationships can be discovered. These two concepts will be discussed in the context of market structure and pricing. Column 5 shows that average fixed cost decreases over the entire range of output.
Instead, the long run simply refers to a period of time during which all inputs can be varied. In order to be able to make this decision the manager must have knowledge about the cost of producing each relevant level of output.
We shall now discover how to determine these long-run costs. For the sake of analytical simplicity, we may assume that the firm uses only two variable factors, labour and capital, that cost Rs. The characteristics of a derived expansion path are shown in Columns 1, 2 and 3 of Table In column 1 we see seven output levels and in Columns 2 and 3 we see the optimal combinations of labour and capital respectively for each level of output, at the existing factor prices. These combinations enable us to locate seven points on the expansion path.
The relationship between changes in scale and changes in output are described as returns to scale. It is widely believed that in a typical production activity, when scale of operations is first increased, increasing returns to scale are observed; ultimately, with the exhaustion of all economies, there is constant return to scale; if expansion is carried far enough, returns to scale decrease.
Returns to Scale Table 6. A related point may also be noted in this context. There may be diminishing returns to a factor and increasing returns to scale at the same time. As the size of the firm increases from 2 workers and 1 machine to 6 workers and 3 machines, it experiences increasing returns to scale output increase more than proportionately.
Any further growth in the size of the firm yields decreasing returns to scale because output increases less than proportionately. Increasing Returns to Scale: A situation of increasing returns to scale can be attributed to two considerations indivisibilities of some factors and advantages of specialisation.
The inability to divide certain factor units into smaller units without either complete loss of usefulness in production or partial loss in efficiency results in a relatively low output per unit of input when operations are conducted on a very small scale.
In other words, in some instances it is not possible to adjust all factors in the same proportion upward or downward. Certain types of capital goods, for example, will not perform their function if they are built on too small a scale, since weight is important in their operation.
This is true of various types of capital equipment used in road construction. Similar patterns are found in warehouse construction; doubling the building material will more than double the amount of usable space. With a rectangular building costs of walls will need to increase only 50 per cent for the capacity of the area to double. Indivisibilities are not confined to capital goods. Labour also is not completely divisible.
One operator may be required for each machine, regardless of its size. A freight train requires one engineer, regardless of the tonnage of the train; there is no way of using a fraction of an engineer on a train of light tonnage. Within limits, in small enterprises, employees may be used to perform several different tasks. But as a practical matter, there are severe limitations to such possibilities. A switchboard operator may serve as receptionist and do some stenographic work, but she can scarcely be used at the same time as an elevator operator and window cleaner.
A clerk in a store may be busy only hours a day.
- Theory of production
- Cost in Short Run and Long Run (With Diagram)
Yet he must be paid for the entire day. As an establishment grows, the percentage of labour time not utilised should fall, if management policies are effective. Indivisibilities are also encountered in advertising, research work, and financing.
Advertising on a small scale is relatively less effective than on a much larger scale. Industrial research activities cannot be carried on effectively on a small scale. Indivisibilities are also found in the financing of a business. The cost of floating a bond issue, for example, is to a large extent independent of the size of the issue.
Thus, this method of financing — the cheapest method when large, amounts of capital are to be obtained — is expensive to a firm until it has expanded beyond a certain size. The refusal of many investors to consider the bonds of any except well-known companies increases the difficulty of bond financing by small firms.
Production analysis in a short run
The other and closely related cause of increasing returns to scale is the advantage offered by specialisation. In a very small business, employees must perform a wide variety of tasks.
As the size of enterprise increases, each employee can be used in a relatively specialised job, with a consequent increase in output per worker. The advantages of specialisation of labour have been recognised since the days of Adam Smith. The primary advantages include the greater skill acquired with specialisation, the avoidance of wasted time in shifting from one task to another, and the employment of persons best suited to particular types of work. In managerial activity as well as in other phases of work, advantages of specialisation are encountered.
As a firm grows in size, personnel relations will be conducted by a specialist; traffic management will be in the hands of a full-time traffic expert instead of being performed by a person who also has various other tasks. Specialisation is also possible with capital equipment.
The importance of the phase of increasing returns depends in large measure upon the type of production process involved, hi almost any type, increasing returns are likely to be encountered to some extent when a business expands from a very small initial size because of indivisibilities of labour. If, however, a firm utilises very little capital equipment, and if few advantages of specialisation of labour are derived, increasing returns may very quickly come to an end.
On the other hand, if a firm uses extensive amounts of capital goods of types which cannot be used efficiently on a small scale, there may be very substantial increasing returns extending over a large volume of output.
Thus, increasing returns are very important in steel, cement, and automobile industries, while they are of much less importance in agriculture and retailing. Constant Returns to Scale: A firm will eventually grow to the point at which it is using the best type of capital equipment available and is enjoying full advantages of specialisation of labour.
Beyond this point, further increases in the scale of operations are likely to produce more or less constant returns for a substantial range of output. If the entire scale of operations is double, output will approximately also double. However, constant returns to scale are relevant only for time periods in which adjustment of all factors is possible.
If a firm doubles output in a short period with a fixed physical plant which was previously utilised to normal optimum capacity, returns per unit of the variable factors will decline because of the operation of the Law of Diminishing Returns. But if factors are varied, as may be possible over a long period of time, the law of diminishing returns will not operate. Decreasing Returns to Scale: As a firm continues to expand its scale of operations, beyond a certain point there is apparently a tendency for returns to scale to decrease, and thus a given percentage increase in the quantities of all factors will bring about a less than proportional increase in output.
It is believed, however, on the basis of actual studies, that a long phase of constant returns is usually observed. Decreasing returns to scale for the firm itself are usually attributed to increased problems and complexities of large-scale management.
An increasing percentage of the total labour force will be required in administrative work, in order to provide coordination of the activities of the enterprise and necessary control over the large numbers of employees. Yet these men are far removed from the actual level of operations. One possible cause of such diseconomies seems to be the limited supply of entrepreneurs. The entrepreneurial skills required to manage large enterprises are, it seems, limited in supply so that it is often difficult to match the increase in the supply of other factors with a corresponding increase in the supply of management ability.
With increased size comes loss of personal contact between management and workers, with consequent loss of moral and increase in labour troubles. Distinction between Return Factor and Return to Scale: The law of diminishing marginal physical productivity applies only to the short-run. It describes the additional output that is produced when additional units of a variable input are combined with a particular quantity of a fixed input.
Economies and diseconomies of scale and increasing, constant, and decreasing cost industries are concepts that apply to the long run. Economies and diseconomies of scale refer to an individual firm. Increasing, decreasing, and constant costs refer to an entire industry. The production function shows increasing returns to scale if an equal percentage increases in all inputs results in a more than proportionate increase in output. Suppose a firm uses only two variable factors, say, labour and capital.
Assume that the firm doubles its use of both labour and capital. If, as a result of this, output gets more than doubled, there are increasing returns to scale. If, when inputs are doubled, output is exactly doubled, return to scale are constant. If, finally, doubling of capital and labour causes a less than proportionate increase in output, then decreasing returns to scale are said to be operating. These three cases are illustrated in Fig.
In all the three sections of the diagram we show the short run average and marginal product as variable amounts of labour are employed in two plants. In the short run, the firm of different sizes is restricted to one of the two plants or is supposed to have a fixed plant. This means that its production capacity is fixed. So output changes are associated only with changes in the usage of the variable factor, labour. This is why in the short run we study the return to a factor and in the long run we study the return to scale.
Since in the long run the firm can choose to operate either plant, long-run changes consist of moving from one set of short-run curves to another. This is done by altering the usage of capital. Constant Return to Scale: Suppose the firm is operating at point c or SAP1, at which average product is at a maximum, i. The firm then builds a new plant of double the size of the original plant. Moreover, the quantity of labour employed is also doubled.
As a result output also gets doubled, or, output per unit of factor input remains unchanged. Since output changes in exact proportion to inputs, returns to scale are said to be constant.
This means that average product of input increases. Suppose, as in the previous case, that the firm moves from the smaller plant to the larger plant, thereby doubling its amount of capital. It also uses double the quantity of labour OL2 is exactly twice the quantity of labour OL1. Now average product rises L2h is greater than L1g. If average product per unit of labour rises when labour and capital inputs are doubled, then total product is more than doubled.
This means that the production function is showing increasing returns to scale. In this case, we observe that doubling of the size of the plant and of labour inputs lowers average product from L2n to L2m. Consequently output is less than doubled. There is no contradiction or logical inconsistency between the two relationships.
The following table clarifies the point: Varying outputs resulting from different quantities of labour and capital Table 6. The table enables us to calculate the marginal product of either variable factor labour and capital. It can also be used to identify the nature of returns to scale.
Suppose we want to calculate marginal product of capital.