Question

1. Using the cost minimization model, demonstrate that the firm will substitute away from capital and that its long run costs must rise when the price of capital increases.

2.  Using the cost minimization model, show that the firms long run costs will always be at least as low as the firms short run costs.

Answer 1

1. We know that there are two factors of prouction

• Capital
• Labour

And cost is minimized where

MPL/Wage = MPK/Price of capital

which implies that cost is minimized at the levels of capital and labour  marginal prroduct of labour divided by wage rate is equal to marginal product of capital divided by price of capital

In short run capital is fixed cost , can not be increased or decreased and labour is variable cost and can be changed with the level of output

WHEREAS

In the long run all factors are variable and nothing is fixed as in the long run capital like plant and machinary can also be increased or decreased with change in levels of output.

So if the cost of capital rises , long run cost of production will increase . Manufacturer can can decrease the level of capital employed and substitute it with the labour which will ultimately lead to cost minimization. for the company.

2.

As we can see in above diagram in the short run , firm can operate in any short run average cost curve given the level of capital but in the long run firm can change the size of given level of capital used in the form of plant and machinary etc. and will decide the lowest short run cost curve in order to produce given level of output at minimised cost. In the diagram we can also see that all short run cost curves are tangent to long run cost curves.

Thus the long run average cost curve shows the least possible average cost of producing different level of outputs wwith the change in level of capital employed.