Question

1. Acme Widget, Inc. has the following production function:
Number of Workers Number of Widgets Produced
1 8
2 15
3 21
4 26
5 30
6 33
Acme can get $5 for each widget it produces. How many workers will it hire if the nominal wage is $38? If it is $27? If it is $22?
2. The marginal product of labour for a certain firm is MPN = 50 – N, where N is the number of labour hours used in production. The price of output is $2 per unit,
a) If the nominal wage is $10/hour, how many hours of labour will be demanded by the firm?
b) If the nominal wage is increased to $12/hour, how many hours of labour will be demanded by the firm?
c) What is the wage elasticity of labour demand for this wage change? (Use the midpoint formula to calculate the arc elasticity.)

Answer 1

Running Head: Acme Widget Inc. Production Function

Acme Widget Inc. Production Function

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Running Head: Acme Widget Inc. Production Function

Acme Widget Inc. Production Function

1. Marginal product is the change in production caused by an increase in one extra worker denoted as MPN. Marginal revenue product is the amount of revenue generated for hiring an additional worker, which is given by multiplying MPN by revenue generated by each unit produced.

i. At nominal wage of $38, Acme Widget should hire only one worker because marginal revenue product is $40. If they decide to hire more than one worker the cost of hiring a new worker will be higher than the revenue generated after hiring the new worker.

ii. At nominal wage of $27, Acme Widget should hire three workers because marginal revenue product is $30. If they decide to hire more than three workers

Running Head: Acme Widget Inc. Production Function

the cost of hiring a new worker will be higher than the revenue generated after hiring the new worker.

iii. At nominal wage of $22, Acme Widget should hire four workers because marginal revenue product is $25. If they decide to hire more than four workers the cost of hiring a new worker will be higher than the revenue generated after hiring the new worker.

2. Marginal product of a firm is MPN=50-N

N is number of hours used for production

Output price is $2 per unit

a. At $10 per hour, how many hours does the firm require?

Marginal revenue should be equals to marginal cost per hour.

Therefore, $10 per hour = MRPN=(50-N)2

10=(50-N)2

10/2=50-N

5=50-N

N=50-5

N=45

The number of hours required by the firm at cost of $10 per hour is 45 hours.

b. At $12 per hour, how many hours does the firm require?

Marginal revenue should be equals to marginal cost per hour.

Therefore, $12 per hour = MRPN=(50-N)2

12=(50-N)2

12/2=50-N

Running Head: Acme Widget Inc. Production Function

6=50-N

N=50-6

N=44

The number of hours required by the firm at cost of $12 per hour is 44 hours.

c. Wage elasticity

Elasticity of demand is given by change in quantity divided by change in price.

$$\begin{array}{l} = (46 - 45) / (12 - 10) \\ = 1 / 2 \\ = 0.5 \\ \end{array}$$

The wage elasticity of labour demand for is inelastic because it is less than 1.

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