Question

Create a labeled isoquant diagram to show the impact on the optimal combination of labor and capital if the wage rate rises when labor and capital are substitutes for each other.

Answer 1

In this the wage rate rises and we have to see what will be its impact on optimal labour and capital.

So we see the impact in two steps first we will see the effect because of substitution effect and second we will see the impact because of output effect.

We will keep the output constant first to see the impact along isoquant. So if the output is held constant increase in wage rate will lead to substitution of capital for labour, i.e., firm will reduce labour input and increase capital as shown in the diagram a movement along isoquant from A to B .

The cost minimization condition is marginal rate of technical substitution equal to cost of labour divided by cost of capital. RTS=w/v.

Now , as wage (w) has increased so this condition will be satisfied by movement from A to B .

Now we consider output effect in which we consider change in output. As wage rate has increased it will lead to increase in the marginal cost as a result MC shifts upward to MC^I and level of output reduces.

So isoquant shifts leftward and due to decrease in level of output even less labour is hired.

So, because of both substitution and output effect due to increase in wage rate labour hired is reduced from L₁ to L₂. Capital has increased from K₁to K₂.