Given: Let w = price of labor (L) and r = price of capital (K) and (C) is cost.

Suppose w=10; r= 5 and C=$100, referring to the isocost equation,

1.      How many units would the capital be if there is no hired labor?

2.      How many units would the labor be if there is no rented capital?

3.      Show in a graph the isocost line.

4.      Suppose the cost (C) fell to $75, what does this denote for K and L? Show the new isocost line in the same illustration in no. 3.

5.      Suppose the wage increased to 20 and the rent and the cost as given remain the same , what would be the new isocost line? Show graphically.

 

Solution

Given, Total cost (C) = $100, Price of labor (W) = $10, Price of capital (r) = $5

Question 1

If there is no hired labor, than the amount of capital which could be used = 100/5 =20 units.

Question 2

If there is no rented capital, the amount of labor which could be hired = 100/10 = 10 units

Question 3

Isocost line is a line showing different combinations of Capital and labor which cost same to a firm. It is shown as line KL in the figure.

Question 4

Suppose the cost (C) fell to $75, it means that now only less capital (75/5=15 units) and less labour (75/10=7.5 units) can be hired than before. So the isocost line will shift backward or left to K₁L_1.

Question 5

Suppose the wage increased to 20 and the rent and the cost as given remain the same i.e. 5 and 100 respectively. So the amount of Labor will be 100/20 =5 units and the amount of Capital 100/5=20 units. So the new isocost line will be K2L2.

Please see the attached file for the complete solution