Question

please show work.

Company owns 25 jars and 1 worker can make 20 per hour. so, 1 hour labor = 20 jars.

same materials will be used. $9/hr for workers.

Option 1: jar production can be done at plant with workers

Option 2: rent a machine to make jars. 500 per hour.

cost of machine includes everything for $80/hour

1. what is the MPL?

2. what is the MPK?

3. recommended hours of labor and captial?

4. if jars were $.06 each would you think it worth it for production?

what is the production function for jars if L is 1 hour of labor and K is 1 hour?

Answer 1

1.

1 labor hour can give 20 jars in a hour. So,

Marginal Product of labor=MPL=20 per hour

2.

1 machine hour can give 500 jars in a hour. So,

Marginal Product of capital=MPK=500 per hour

3)

Marginal Product of labor per dollar spent=MPL/w=20/9=2.2222

Marginal Product of machine per dollar spent=MPK/r=500/80=6.25

Since machine hour and labor hour are perfect substitute in this case.

We also observe that (MPK/r)>(MPL/w). So, Only machine hours be hired to minimize cost.

4)

Value of MPK at a price of $0.06,

VMPK=Price*MPK=0.06*500=$30

We can see that VMPK<rent of machine ($80). It is not worth to produce.

5)

Let Q be the quantity of jars produced

Q=20*L+500*K

Where L=labor hours and K=machine hours