Question

Suppose that a firm uses labour and capital in production. The wage rate is $10 per unit of labour and the rental cost of capital is $10 per unit. The firm is currently producing 100 units of labour and the rental cost of capital is $10 per unit. the firm is currently producing 100 units of output by using cost minimizing input combination of 50 units of labor and 50 units of capital.

On an isoquant and iso-cost diagram, show than an increase in output from 100 units to 150 units will result in higher short-run total cost, average cost and marginal cost than in the long-run counterparts.

Answer 1

Sol : Isoquant is the cuve or the locus of all such combination which can produce same level of output

         Isocost is the curve showing various combination of two factors which can produced given level of an output with the least cost.

Cost minimising Input combination means that point where isoquant curve is tanget to the isocost curve.

At , Cost minimisation level of output the following diagram :

In the short run , Average cost , Total cost , Marginal cost will be higher than the lomg run because of the following points:

1. In Short Run , it is assumed that one factor of production will be fixed and other will be variable.

2. So, Accordingly capital is fixed and labour is variable factor

3 If , Firm wants to increase its production from the 100 units (that is from least minimum input combination point) to 150 units in the short run , it can be only done by incraesing the labour fatcor.

4. And, in short run there is 3 stages of the production function and when firm is producing 100 units , it is already in Decreasing rate of return , so if the firm appoint the laour more from the point of effie=ciency , it will decrease the productivity per labour and more and more labour have to be apointed which can only incraese the cost of production.

                                       Diagram for short run for increase in Cost due to increase in Production

In the above diagram , cost minimising input combination point is B but when the firm shifted from 100 to 150 units of production. it leads to shifts the isocost curve and isoquant curve . Due to short run , capital remains fixed and more labour has to be employed. . Point A is the point where isoquant curve is not tangent with the isocost curve showing that it is not the least cost input combination point.

But in the long run , where both are the varibale factor (i.e Capital and labour both factor can be increased or decreased . The total cost , average cost and marginal cost are lesser than the short run because of the following diagram :

In the long run due to increase in production units , both factors capital and labour can be increased and due to which isoquant curve shift from IQ1 to IQ2 and isocost curve shifts from IC1 to IC2 (Parallel Shift) and P is the point of the point of optimum combination of units 100 and point Q is showing the new optimum point for units 150.