Econ 4531 Prob 2 solutions
Homework #2 – Solutions
1. Union A wants to represent workers in a firm that would hire 20,000 workers if the wage rate is
$12 and would hire 10,000 workers if the wage rate is $15. Union B wants to represent workers in a firm that would hire 30,000 workers if the wage is $20 and would hire 33,000 workers if the wage is $15. Which union is likely to organize?
The union will be more likely to attract the workers’ support when the elasticity of labor demand (in absolute value) is small. The elasticity of labor demand facing union A is given by:
A
%E (20,000 10,000) 20,000
2 .
%w
(12 15) 12
The elasticity of labor demand facing union B is given by:
B
%E (33,000 30,000) 33,000
0.45
%w
(15 20) 15
Union B, therefore, is more likely to organize as |-0.45| < |-2|.
2. Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 6 and r = 4. These prices then shift to w = 4 and r = 2.
(a) In which direction will the substitution effect change the firm’s employment and capital stock?
Prior to the price shift, the absolute value of the slope of the isocost line (w/r) was 1.5. After the price shift, the slope is 2. In other words, labor has become relatively more expensive than capital. As a result, there will be a substitution away from labor and towards capital (the substitution effect).
(b) In which direction will the scale effect change the firm’s employment and capital stock?
Because both prices fall, the marginal cost of production falls, and the firm will want to expand. The scale effect, therefore, increases the demand for both labor and capital (as both are normal inputs).
(c) Can we say conclusively whether the firm will use more or less labor? More or less capital?
The firm will certainly use more capital as the substitution and scale effects reinforce each other in the direction of using more capital. The change in labor
1. Union A wants to represent workers in a firm that would hire 20,000 workers if the wage rate is
$12 and would hire 10,000 workers if the wage rate is $15. Union B wants to represent workers in a firm that would hire 30,000 workers if the wage is $20 and would hire 33,000 workers if the wage is $15. Which union is likely to organize?
The union will be more likely to attract the workers’ support when the elasticity of labor demand (in absolute value) is small. The elasticity of labor demand facing union A is given by:
A
%E (20,000 10,000) 20,000
2 .
%w
(12 15) 12
The elasticity of labor demand facing union B is given by:
B
%E (33,000 30,000) 33,000
0.45
%w
(15 20) 15
Union B, therefore, is more likely to organize as |-0.45| < |-2|.
2. Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 6 and r = 4. These prices then shift to w = 4 and r = 2.
(a) In which direction will the substitution effect change the firm’s employment and capital stock?
Prior to the price shift, the absolute value of the slope of the isocost line (w/r) was 1.5. After the price shift, the slope is 2. In other words, labor has become relatively more expensive than capital. As a result, there will be a substitution away from labor and towards capital (the substitution effect).
(b) In which direction will the scale effect change the firm’s employment and capital stock?
Because both prices fall, the marginal cost of production falls, and the firm will want to expand. The scale effect, therefore, increases the demand for both labor and capital (as both are normal inputs).
(c) Can we say conclusively whether the firm will use more or less labor? More or less capital?
The firm will certainly use more capital as the substitution and scale effects reinforce each other in the direction of using more capital. The change in labor