Question

2. Suppose a firm is producing 200 widgets. The firm’s production function is Cobb-

Douglas with decreasing returns to scale. (This means we have normal, convex

isoquants). The firm uses K’ units of capital and L’ units of labor. Initially, the input prices

are w’ and r’. However, an exogenous shock in the labor market causes an increase in

the wage rate, resulting in an increase in input prices from w’ to w’’ where w’<w’’. Using

a graph (of isoquant and isocost lines) and words, describe what happens as a result of

this change in input prices assuming the firm wants to continue producing 200 widgets.

Answer 1

Q = A.K. L ^1-  0<<1

C = w'L + r'K (initially)

Note: A Cobb Douglas Production function shows Constant Returns to Scale.

The point of tangency of the iso-cost line and the isoquants give the optimal labour and capital employed by the firm.

Slope of iso-cost line is (w'/r'). Slope of the isoquants are known as MRTS = (MP_L / MP_K)

Tangency implies MRTS = w'/r'

Now, when an external shock changes w' to w'' and w''<w', the new isocost line has a slope w"/r' < w'<r'.

[C'' = w''.L + r'.K]

This means, the isocost line is now flatter than the initial isocost lines.

The corresponding changes are indicated in the following figure.