191k views
0 votes
Suppose a firm's production function is Q = 4K⁰·⁵ L⁰·⁵. Its level of capital is fixed at 1 unit, the price of labor is PL = 32 per unit, and the price of capital is PK = 400 per unit. Given this information, its short run production function and average product of labor function may be determined. Which of the following is correct?

1) Q = 2L⁰·⁵
2) Q = 4L⁰·⁵
3) APL = 2L⁻⁰·⁵
4) APL = 4L⁻⁰·⁵

User AGupta
by
7.2k points

1 Answer

4 votes

Final Answer:

The correct option 0.5 Q=4L option B.

Step-by-step explanation:

Given the production function

=

4

0.5

0.5

Q=4K

0.5

L

0.5

and the fixed level of capital (

=

1

K=1), we can substitute

=

1

K=1 into the production function to simplify it:

=

4

(

1

)

0.5

0.5

=

4

0.5

Q=4(1)

0.5

L

0.5

=4L

0.5

This implies that the short-run production function is

=

4

0.5

Q=4L

0.5

, and option 2,

=

4

0.5

Q=4L

0.5

, is correct.

To determine the average product of labor (APL), we use the formula

=

APL=

L

Q

. Substituting the short-run production function into this formula:

=

4

0.5

=

4

0.5

APL=

L

4L

0.5

=4L

−0.5

Therefore, the correct expression for the average product of labor is

=

4

0.5

APL=4L

−0.5

, and option 4,

=

4

0.5

APL=4L

−0.5

, is correct.

Understanding these functions is crucial for firms to optimize their production processes and make informed decisions about resource allocation. In this scenario, the short-run production function

=

4

0.5

Q=4L

0.5

highlights the relationship between labor input and output, while the average product of labor function

=

4

0.5

APL=4L

−0.5

provides insights into labor productivity as a function of the variable input

L.

User Jake Brewer
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories