# The least cost combination is concerned with which production relationship

### Theory of production | economics | avesisland.info

Here we concerned with production in the narrow sense of physical It is also an economic relation indicating the maximum amount of output that can be Choose the input combination that leads to the lowest cost of producing a fixed level. Least cost combination principle A rational firm/producer seeks maximisation of profit. firm would combine the various factors of production its production function in such a way that with the minimum input and . International Labor Relations. The economic cost of an input is the minimum payment .. Input Substitution (q constant)– Deals with how the optimal combination of from the production function if we remember that at the optimal combination . relationships between.

In stage 1, marginal product exceeds average product. In our example, stage 1 starts when the amount of labour is equal to zero and continues up to the point where 3. 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. From the point of view of economic feasibility the relationships in stage 1 suggest that production should be continued until stage 2 has been reached.

The implication is that the profit-oriented will not will surely seek to expand production all the way through stage 1. In stage 3 total product is itself falling. Thus the rational decision maker will not use more than 5. Beyond this point every extra unit of labour will actually lead to a fall in total output.

Moreover, the elasticity of production is negative in stage 3, thus forcing the same conclusion. Stage 2 and its boundaries are the economically feasible region, i. The exact amount of labour that should be used so as to maximize profits can be determined only after knowing the prices of inputs and outputs. However, it is known to us that the firm will use between 3. Production with Two or More Variable Inputs: We may now extend our analysis to cover more than one variable input.

The principles developed in this section will continue to apply. This implies that we are still dealing with the short run, in which case the law of diminishing returns will apply. Capital inputs are measured vertically and labour inputs are measured horizontally see Fig. For example, 4 machines and 2 workers produce 50 units of output. The operation of law of diminishing returns can also be discerned. When the input of machines is held constant at 4 units, then additional units of labour bring about smaller and smaller additions to output.

Thus, along a given row output increases, but at a decreasing rate. If all inputs are variable, the law of diminishing returns will not apply, and the short run is replaced by a long-run period in which case the decisions to be made by the firm are distinctly different. Production managers of the Metal Box Co. Total product curve is shown in Fig. The law of decreasing returns starts to operate when the seventh man is employed, i.

The average product equation is simply derived by dividing the total product by the variable input X. The second method would be to make use of the MP schedule. Hence the quantity of the variable input that would be employed in this situation may be obtained by making the MP equation equal to 0: The marginal product of the twelfth man is 0.

Production in the Long-Run: We will now consider the more general case of production with two or more variable inputs. To make diagrammatic analysis possible we consider only two variable factors. If we were to change the usage of the fixed input, total, average, and marginal product curves would all shift.

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.

For example, an increase in capital would probably result in an increase in the marginal product of labour over a wide range of labour use. It can be defined as follows: It is also known as production indifference curve.

This is shown by point A on isoquant Q1 in Fig. An additional shovel, at point B, is of no value to a man who can use only one at a time. 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. We see that isoquants for perfect complements are Z-shaped.

Some products can be produced by inputs that can be readily substituted for each other, e. These two items might be perfect substitutes for each other in the generation of heat. Similarly, two nickels will work as well as one dime in operating many vending machines. Alternative foods may fulfil minimum nutrient requirements equally well; for instance, peanut butter and corn meal are both rich in protein, white potatoes and — spinach are good sources of ascorbic acid.

Isoquants for such examples are shown in Fig. In-between these two extreme cases there lie the more common cases where factors are substitutable for each other in varying degrees. In other words, isoquants, like consumption indifference curves, cannot meet or intersect. All the isoquants together constitute an isoquant map In an isoquant map, an isoquant which lies above and to the right of another shows a higher level of output.

Distinguishing between Movements along and Movements among Isoquants: Each of the two isoquants in Fig. At point B, we have more labour and fewer units of capital than at point A. 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. The Marginal Rate of Technical Substitution: As shown in Fig. This negative slope indicates that if the firm reduces the amount of capital employed, more labour has to be used to keep the level of output unchanged.

Thus, the two inputs can be substituted for each other to maintain a specified or fixed level of output. Over the relevant range i. This can be seen in Fig. If capital is reduced from 50 to 40 a decrease of 10 units labour must be increased by only 5 units from 15 to 20 in order to keep the level of output unchanged at units. However, consider a combination where capital is more scarce and labour more abundant. Differently put, the amount of labour that must be added for each unit of capital discharged, keeping output constant, must increase.

The slope of the isoquant measures the rate at which labour can be substituted for capital and vice-versa. It is observed that the isoquant becomes flatter and flatter as the producer moves downward from left to right. In other words, M RTS declines along an isoquant.

The same type of relation holds here, too. Thus, for very small movements along an isoquant, the MRTS is just the ratio of the marginal products of the two inputs. This point may now be proved. The level of output, Q, depends upon the use of the two inputs, L and K. Then, if we add one unit of labour, output would increase by 6 units. Capital must decrease enough to offset the increase in output generated by the increase in labour.

Since the marginal product of capital is 3, two units of capital must be released. Alternatively, if we were to reduce capital by one unit, output would fall by 3 units.

## Theory of production

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. Thus in terms of symbols: In order that the producer stays on the same isoquant it is necessary to set AQ equal to zero. Then solving for the MRTS, we get: Two forces work further to cause marginal product of labour to a fall: Thus, as labour is substituted for capital the marginal product of labour has to fall.

For similar reasons, the marginal product of capital increases as less capital and more labour are used to produce the same level of output. Ridge Lines and the Economic Region of Production: We have postulated convexity of isoquants. 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 ssay capital, that an increase of labour would result in congestion and inefficiency, in which case MP may turn out to be negative.

The definition of production function does not preclude the possibility of negative RTS. 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. The ridge lines OC and OD enclose the area of rational operation, i. But as we noted at the outset, one of the four production decisions a manager must make is: Thus he has to make either of two input choice decisions: Choose the input combination that leads to the lowest cost of producing a fixed level of output i.

The solution to any constrained maximization or minimization problem is choosing the level of each activity whereby the marginal benefits from each activity, per rupee spent, is the same at the margin. 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. Input Prices and Isocosts: The isoquant shows the desire of the producer.

But the desire to produce a commodity is not enough. The firm must have capacity to do so. Usually a firm is supposed to have a fixed amount of money to buy resources. Input prices are determined by the market forces, i. 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.

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. Let us consider a simple example. Now suppose the firm decides to spend Rs. In a more general situation, if a fixed amount C is to be spent, the firm can choose among the combinations given by This equation is illustrated in Fig. If one unit of labour is purchased at Rs. Thus, as the purchase of labour is increased, the purchase of capital has to fall if total cost remains fixed.

The negative of this ratio is the slope of the line. The lines in Fig. In other words, total cost is the same at all points on the line. An increase in outlay, holding factor prices fixed, leads to a parallel rightward shift of the isocost line. There would exist an infinite number of isocost lines, each relating to a different level of cost outlay expenditure. 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: 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.

If w falls relative to r, the isocost line becomes flatter. Production of a Given Output at Minimum Cost: Whatever output a firm chooses to produce, the production manager is desirous of producing it at the lowest possible cost. So the production process has to be organized in the most efficient manner. Point E shows the optimal resource combination, K0units of capital and L0 units of labour.

This is known as the least cost combination i.

Recall that the isoquant shows the desired rate of factor substitution and the isocost line the actual rate of factor substitution. The factor price ratio tells the producer the rate at which one input can actually be substituted for another in the market place.

Recall that MRTS shows the rate at which the producer can substitute between the inputs in production. If the two are not equal, a firm can reduce cost further by altering the factor proportion.

We can analyse the equilibrium condition in an alternative way. Suppose the equilibrium condition did not hold or, specifically, that the producer was at point B in Fig. The firm could therefore reduce its use of labour by Re. Is the firm optimizing the use of its resources? If not, why not? So the firm would be better off by using less labour and more capital. If the firm spend an additional Rs. This approach seems to be more practical than the previous one.

The end result will be the same as before. Such a situation is illustrated in Fig. The isocost line KL shows all possible combinations of the two inputs that can be purchased with a fixed amount of money and a fixed set of factor prices.

Four hypothetical isoquants are shown. And, neither output level Q0 nor level Q1 would be chosen, since higher levels of output can be produced with the fixed cost outlay. At point A, the given isocost line is tangent to the highest attainable isoquant, viz. This point shows the optimal least cost combination of inputs for a fixed level of output.

To examine several optimizing points at a time we use the expansion path. Since we do not assume any change in the factor-price ratio up to this stage, these isocost lines are parallel.

Look at the three optimum points, A, B, and C. Since at each of these: Therefore, the expansion path, OS, is a locus of points along which the MRTS is constant and equal to the factor price ratio. But it is a curve having a special feature: We may accordingly suggest a definition. It shows output expansion effect which is similar to income effect studied in the theory of consumer demand.

On the expansion path, the MRTS remains constant, since the factor-price ratio is constant. The expansion path gives the firm its cost structure. The sum of the quantities of each input used, times the respective input price, gives the minimum cost of producing every level of output. This is turn allows us to relate cost to the level of output produced.

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. 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.

### The Production Process (With Diagram)

This is the second basic finding: Such a conclusion is shown in Figure 3. Marginal cost and price The conclusion that marginal cost tends to equal price is important in that it shows how the quantity of output produced by a firm is influenced by the market price. At any higher market price, the firm will produce the quantity for which marginal cost equals that price. Thus the quantity that the firm will produce in response to any price can be found in Figure 3 by reading the marginal cost curve, and for this reason the marginal cost curve is said to be the short-run supply curve for the firm.

## The Production Process (With Diagram)

The short-run supply curve for a product—that is, the total amount that all the firms producing it will produce in response to any market price—follows immediately, and is seen to be the sum of the short-run supply curves or marginal cost curves, except when the price is below the bottoms of the average variable cost curves for some firms of all the firms in the industry.

This curve is of fundamental importance for economic analysis, for together with the demand curve for the product it determines the market price of the commodity and the amount that will be produced and purchased. One pitfall must, however, be noted. In the demonstration of the supply curves for the firms, and hence of the industry, it was assumed that factor prices were fixed.

Though this is fair enough for a single firm, the fact is that if all firms together attempt to increase their outputs in response to an increase in the price of the product, they are likely to bid up the prices of some or all of the factors of production that they use. In that event the product supply curve as calculated will overstate the increase in output that will be elicited by an increase in price.

A more sophisticated type of supply curve, incorporating induced changes in factor prices, is therefore necessary. Such curves are discussed in the standard literature of this subject.

Marginal product It is now possible to derive the relationship between product prices and factor prices, which is the basis of the theory of income distribution. To this end, the marginal product of a factor is defined as the amount that output would be increased if one more unit of the factor were employed, all other circumstances remaining the same. Algebraically, it may be expressed as the difference between the product of a given amount of the factor and the product when that factor is increased by an additional unit.

The marginal products are closely related to the marginal rates of substitution previously defined. It has already been shown that the marginal rate of substitution also equals the ratio of the prices of the factors, and it therefore follows that the prices or wages of the factors are proportional to their marginal products. This is one of the most significant theoretical findings in economics.

To restate it briefly: This is not a question of social equity but merely a consequence of the efforts of businessmen to produce as cheaply as possible. Further, the marginal products of the factors are closely related to marginal costs and, therefore, to product prices. This, also, is a fundamental theorem of income distribution and one of the most significant theorems in economics.

Its logic can be perceived directly. If the equality is violated for any factor, the businessman can increase his profits either by hiring units of the factor or by laying them off until the equality is satisfied, and presumably the businessman will do so.

The theory of production decisions in the short run, as just outlined, leads to two conclusions of fundamental importance throughout the field of economics about the responses of business firms to the market prices of the commodities they produce and the factors of production they buy or hire: The first explains the supply curves of the commodities produced in an economy. Though the conclusions were deduced within the context of a firm that uses two factors of production, they are clearly applicable in general.

### FARMMANAGEMENTECONOMICSLecture Notes | Tiwari Vishakha - avesisland.info

Maximization of long-run profits Relationship between the short run and the long run The theory of long-run profit-maximizing behaviour rests on the short-run theory that has just been presented but is considerably more complex because of two features: It is of the essence of long-run adjustments that they take place by the addition or dismantling of fixed productive capacity by both established firms and new or recently created firms.

At any one time an established firm with an existing plant will make its short-run decisions by comparing the ruling price of its commodity with cost curves corresponding to that plant.

If the price is so high that the firm is operating on the rising leg of its short-run cost curve, its marginal costs will be high—higher than its average costs—and it will be enjoying operating profits, as shown in Figure 3.

The firm will then consider whether it could increase its profits by enlarging its plant. The effect of plant enlargement is to reduce the variable cost of producing high levels of output by reducing the strain on limited production facilities, at the expense of increasing the level of fixed costs.

In response to any level of output that it expects to continue for some time, the firm will desire and eventually acquire the fixed plant for which the short-run costs of that level of output are as low as possible. This leads to the concept of the long-run cost curve: These result from balancing the fixed costs entailed by any plant against the short-run costs of producing in that plant. The long-run costs of producing y are denoted by LRC y.

The marginal long-run cost is the increase in long-run cost resulting from an increase of one unit in the level of output. It represents a combination of short-run and long-run adjustments to a slight increase in the rate of output. It can be shown that the long-run marginal cost equals the marginal cost as previously defined when the cost-minimizing fixed plant is used. Long-run cost curves Cost curves appropriate for long-run analysis are more varied in shape than short-run cost curves and fall into three broad classes.

In constant-cost industries, average cost is about the same at all levels of output except the very lowest. Constant costs prevail in manufacturing industries in which capacity is expanded by replicating facilities without changing the technique of production, as a cotton mill expands by increasing the number of spindles. In decreasing-cost industries, average cost declines as the rate of output grows, at least until the plant is large enough to supply an appreciable fraction of its market.

Decreasing costs are characteristic of manufacturing in which heavy, automated machinery is economical for large volumes of output. Automobile and steel manufacturing are leading examples. Decreasing costs are inconsistent with competitive conditions, since they permit a few large firms to drive all smaller competitors out of business.

Finally, in increasing-cost industries average costs rise with the volume of output generally because the firm cannot obtain additional fixed capacity that is as efficient as the plant it already has. The most important examples are agriculture and extractive industries. Criticisms of the theory The theory of production has been subject to much criticism.

One objection is that the concept of the production function is not derived from observation or practice. Even the most sophisticated firms do not know the direct functional relationship between their basic raw inputs and their ultimate outputs. This objection can be got around by applying the recently developed techniques of linear programmingwhich employ observable data without recourse to the production function and lead to practically the same conclusions.

On another level the theory has been charged with excessive simplification. It assumes that there are no changes in the rest of the economy while individual firms and industries are making the adjustments described in the theory; it neglects changes in the technique of production; and it pays no attention to the risks and uncertainties that becloud all business decisions.