PRODUCTION OPTIMISATION
Normally, a profit maximising firm is interested to know what combination of factors of production (or inputs) would minimise its cost of production for a given output. This can be known by combining the firmâ€™s production and cost functions, namely isoquants and isocost lines respectively.
Isoquants: Isoquants are similar to indifference curves in the theory of consumer behaviour. An isoquant represents all those combinations of inputs which are capable of producing the same level of output. Since an isoquant curve represents all those combination of inputs which yield an equal quantity of output, the producer is indifferent as to which combination he chooses. Therefore, Isoquants are also called equalproduct curves, production indifference curves or isoproduct curves. The concept of isoquant can be easily understood with the help of the following schedule
Table 2 : Various combinations of X and Y to produce a given level of output
Factor combination  Factor X  Factor Y  MRTS 
A  1  12  
B  2  08  4 
C  3  05  3 
D  4  03  2 
E  5  02  1 
When we plot the various combinations of factor X and factor Y, we get a curve IQ as shown in Figure 2.
Isoquants have properties similar to indifference curves. Isoquants are negatively sloped, convex to the origin due to diminishing marginal rate of technical substitution (MRTS) and are non intersecting. However, there is one important difference between the two: whereas in an indifference curve it is not possible to quantify the level of satisfaction acquired by the consumer, the level of production acquired by the producer is easily quantified. Thus, while isoquant IQ1 represents 100 units, curves IQ2, IQ3 etc. representing higher levels of production can be drawn. While a curve on the right represents a higher level of output, that on the left represents a lower level of output
Isocost or Equalcost Lines: Isocost line, also known as budget line or the budget constraint line, shows the various alternative combinations of two factors which the firm can buy with given outlay. Suppose a firm has Rs. 1,000 to spend on the two factors X and Y. If the price of factor X is Rs. 10 and that of Y is Rs. 20, the firm can spend its outlay on X and Y in various ways. It can spend the entire amount on X and thus buy 100 units of X and zero units of Y or it can spend the entire outlay on Y and buy 50 units of it with zero units of X factor. In between, it can have any combination of X and Y. Whatever be the combination of factors the firm chooses, the total cost to the firm remains the same. In other words, all points on a budget line would cost the firm the same amount.
We can show the isocost line diagrammatically also. The Xaxis shows the units of factor X and Yaxis the units of factor Y. When the entire â‚¹ 1,000 is spent on factor X, we get OB of factor X and when the entire amount is spent on factor Y we get OA of factor Y . The straight line AB which joins points A and B will pass through all combinations of factors X and Y which the firm can buy with outlay of â‚¹ 1,000. The line AB is called isocost line.
Figure 3 shows various isocost lines representing different combinations of factors with different outlays. Isoquants, which represent the technical conditions of production for a product and isocost lines which represent various â€˜levels of cost or outlayâ€™ (given the prices of two factors) can help the firm to optimize its production. It may try to minimise its cost for producing a given level of output or it may try to maximise the output for a given cost or outlay. Suppose the firm has already decided about the level of output to be produced. Then the question is with which factor combination the firm should try to produce the predecided level of output. The firm will try to use the leastcost combination of factors. The least cost combination of factors can be found by superimposing the isoquant that represents the pre decided level of output on the isocost lines. This is shown in Figure 4.
Suppose the rm has decided to produce 1,000 units (represented by isoquant P). These units can be produced by any factor combination lying on P such as A, B, C, D, E, etc. The cost of producing 1,000 units would be minimum at the factor combination represented by point C where the isocost line MM1 is tangent to the given isoquant P. At all other points such as A, B, D, E the cost is more as these points lie on higher isocost lines Compared to MM1. Thus, the factor combination represented by point C is the optimum combination for the producer. It represents the leastcost of producing 1,000 units of output. It is thus clear that the tangency point of the given isoquant with an isocost line represents the least cost combination of factors for producing a given output.
SUMMARY
