Question

Suppose a short-run production function is described as Q = 2L – (1/800)L² where L is the number of labors used each hour. The firm’s cost of hiring (additional) labor is $20 per hour, which includes all labor costs. The finished product is sold at a constant price of $40 per unit of Q.

d. Suppose that labor costs remain unchanged but that the price received per unit of output increases to $50. How many labor units (L) will the firm now employ?

I got 640

e. Suppose instead that the price of the product is unchanged at $40, but that the cost of hiring labor increases to $24 per hour. How many labor units (L) will the firm employ?

i got 580

f. In terms of the demand (curve) for labor, how would we visually see (what is the difference between) the changes in parts d and e?

g. Using the production function Q = 2L – (1/800)L². How many units of L would be required to produce 800 units (Q=800). Use the quadratic formula to solve for L.

h. Suppose that management increases the size of its plant, providing each worker with additional capital. What is the most likely impact on the marginal products of its labor input?

Answer 1

Q = 2L – (1/800)L²

Cost of labor = w = 20

P = 40

Marginal Product of labor: dQ/dL = 2 - L/400

In equilibrium p*MPL =w

40*(2 - L/400) = 20

2 - L/400 = 1/2

L/400 = 3/2

L = 600

d)

Now P = 50

In equilibrium p*MPL =w

50*(2 - L/400) = 20

2 - L/400 = 2/5

L/400 = 8/5

L = 640

e)

w = 24

In equilibrium p*MPL =w

40*(2 - L/400) = 24

2 - L/400 = 3/5

L/400 = 7/5

L = 560

f)

The Labor demand curve is is function of real wage. When price of product increases, the p*MPL increases thus the demand curve shifts to the right.

When w increases, there is no change in demand curve of the labor. When w increases, the real wage increases and thus labor demand falls, thus there is a movement along the curve.

g)

Q = 2L – (1/800)L²

Q = 800

800 = 2L – (1/800)L²

640,000 = 1600L - L²

L² - 1600L + 640,000 = 0

L = 800

h)

If each worker is provided with additional capital, the productivity of workers will increase. This will thus increase the marginal product of labor.

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