Least cost combination of inputs
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Minimization of short-run The production function However much of a commodity a business firm produces, it endeavours to produce it as cheaply as possible. The marginal products are closely related to the marginal rates of substitution previously defined. A single isoquant P, in the figure denotes the desired level of output, but there is a set of iso-cost lines representing various levels of total cost outlay. An isoquant or iso-product map represents various technical possibilities of producing different levels of output. On the other hand, a family of iso- cost line represents the various levels of total cost or outlay, given the prices of two factors.

There is perfect competition in the factor There is perfect competition in the factor market. 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. It is a tool that analysis the qualitative input — output relationship and also represents the technology of a firm or the economy as a whole. A profit maximising entrepreneur will seek to minimise his cost for producing a given output, or to put it in another way, he will maximise his output for a given level of outlay. According to this isoquants are sloping downward i. It will be seen from Fig.

One cannot say exactly at which particular point on the expansion path the entrepreneur will in fact be producing unless one knows either the output which he wants to produce or the size of the cost or outlay it wants to incur. Decreasing costs are characteristic of manufacturing in which heavy, automated machinery is economical for large volumes of output. The discussion will deal first with variable cost. The factor price line is also known as isocost line because it represents various combinations of inputs that may be purchased for the given amount of money allocated. Production theory is extended to deal with two variable inputs by the introduction of isoquants. If the price of labour rises from Rs.

The 500 units of output can be produced by any combination of labour and capital such as R, S, E, T and J lying on the isoquant. This is the point at which and firm is able to produce maximum quantity and at minimum cost. The area within the ridge lines is rational region of production arid beyond that the two regions are irrational. Likewise, if the price of capital changes, the outlay and the price of labour remaining the same, the iso-cost line will shift. In both cases the factors will have to be employed in optimal combination at which the cost of production will be minimum. . Check out Ronald Coase and Guido Calabresi for more.

Cost Function Cost function is defined as the relationship between the cost of the product and the output. Which will be the least-cost combination of factors can be understood from considering Fig. An algorithm that finds the five least-cost sequences for scheduling military personnel through a series of courses where the costs incurred are transportation costs. The first explains the supply curves of the commodities produced in an economy. The producer equates the marginal rate of technical substitution or, the ratio of the marginal physical products of the two factors with the price ratio of the two factors. Suppose, the producer wants to produce six units of output. In order to ascertain this minimum cost we substitute the maximum values of A and B procured above and the given prices of labour and capital i.

This is the second basic finding: in response to any price the profit-maximizing firm will produce and offer the quantity for which the marginal cost equals that price. 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. This, also, is a fundamental theorem of income distribution and one of the most significant theorems in economics. Isoquants nearer to origin represent less quantity of output and vis-a-visa. The slope of the iso-quant reflects the marginal rate of technical substitution. If a producer seeks to minimize the cost of producing a given amount of output the condition of the equilibrium, is that the marginal rate of technical substitution must be equal to the factor price ratio. 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.

Now, if a firm wants to produce a higher level of output as denoted by the equal product curve Q 2, then it will choose the factor combination E 2 which is the least-cost combination for new output. The other two isocost lines shown are interpreted similarly. The same level of output can be produced by various combinations of factor inputs. Given iso-cost line and the series of isoquants isoquant-map , the producer will choose the level of output, where the given iso-cost line is tangent to the highest possible isoquant. Interspacing between them is least at the ends and maximum in the middle. All these and other various combinations are shown in Fig.

It will be seen from fig. An isocost line shows the alternative quantities of two factors viz. This will make sure minimum feasible cost for producing 2000 units of output. Thus the expansion path may be defined as the locus of the points of tangency between the isoquants and the iso-cost lines. Therefore, the entrepreneur will not choose any of the combinations R, S, T and J. As the substitution of one factor for another is carried out more and more, it becomes progressively more difficult unit a point is reached beyond which substitution between factors becomes impossible.

The line joining the minimum cost combinations such as E 1, E 2, E 3, E 4 is called the expansion path because it shows how the factor combination with which the firm produces will alter as the firm expands its level of output. This curve is of fundamental importance for economic analysis, for together with the for the product it determines the market price of the commodity and the amount that will be produced and purchased. Ascertain the volume of labour and capital that the industry must use with respect to optimise output. In other words, the last rupee spent on one factor say, labour is as productive as the last rupee spent on other factor say, capital and producer has no incentive to change the combination of two factors. At any higher market price, the firm will produce the quantity for which marginal cost equals that price.

This is one of the most significant theoretical findings in economics. Isoquants: An isoquant is a locus of points showing all the technically efficient ways of combining factors of production to produce a fixed level of output. On the other hand, the price ratio of the factors is given by the slope of the iso-cost line. Solution Least-cost combination factor needs that the following situation must be met. There are various technical possibilities open to a firm from which it has to choose, that is, there are various combinations of factors which can yield a given level of output and from among which a producer has to select one for production.