ms-09 mba assignment july dec 2010 Question 3

3. Briefly describe the Optimal Combination of inputs with the help of an example.

THE OPTIMAL COMBINATION OF INPUTS

            The introduction of this unit one of the decision problems that concerns a production process manager is, which input combination to use. That is, what is the optimal input combination? While all the input combinations are technically efficient, the final decision to employ a particular input combination is purely an economic decision and rests on cost (expenditure). Thus, the production manager can make either of the following two input choice decisions:

1. Choose the input combination that yields the maximum level of output with a given level of expenditure.

2. Choose the input combination that leads to the lowest cost of producing a given level of output.

            Thus, the decision is to minimize cost subject to an output constraint or maximize the output subject to a cost constraint. We will now discuss these two fundamental principles. Before doing this we will introduce the concept isocost, which shows all combinations of inputs that can be used for a given cost.

Iso cost Lines:

            Recall that a universally accepted objective of any firm is to maximise profit. If the firm maximises profit, it will necessarily minimise cost for producing a given level of output or maximise output for a given level of cost. Suppose there are 2 inputs: capital (K) and labour (L) that are variable in the relevant time period. What combination of (K,L) should the firm choose in order to maximise output for a given level of cost? If there are 2 inputs, K,L, then given the price of capital (Pk) and the price of labour (PL), it is possible to determine the alternative combinations of (K,L) that can be purchased for a given level of expenditure. Suppose C is total expenditure, then

            C= PL* L + Pk* K

            If only capital is purchased, then the maximum amount that can be bought is C/Pk shown by point A in figure 7.7. If only labour is purchased, then the maximum amount of labour that can be purchased is C/PL shown by point B in the figure. The 2 points A and B can be joined by a straight line. This straight line is called the isocost line or equal cost line. It shows the alternative combinations of (K,L) that can be purchased for the given expenditure level C. Any point to the right and above the isocost is not attainable as it involves a level of expenditure greater than C and any point to the left and below the isocost such as P is attainable, although it implies the firm is spending less than C.

EXAMPLE:

Consider the following data:

PL = 10, Pk = 20 Total Expenditure = 200.

            Let us first plot the various combinations of K and L that are possible. We consider only the case when the firm spends the entire budget of

200.

            The slope of this isocost is –½. What will happen if labour becomes more expensive say PL increases to 20? Obviously with the same budget the firm can now purchase lesser units of labour. The isocost still meets the Y–axis at point A (because the price of capital is unchanged), but shifts inwards in the direction of the arrow to meet the X-axis at point C. The slope therefore changes to –1.