Waste less time on Facebook — follow Brilliant.
×

Microeconomic Theory - Production Function

Consider a simple production function with only one factor of production L, where L is Labor and Q is the total output.

Q=18L\(^{2}\) -L\(^{3}\)

If L =0, Q= 0. If L=1, Q=17. If L=2, Q=64. If L=3, Q= 135 and so forth....

The Marginal Product of Labor, MPL, is defined as the change in output that results from employing an added unit of labor. If that is the case, we can easily calculate the MPL given the production function Q.

When L goes from 0 to 1, Q went from 0 to 17. When L goes from 1 to 2, Q went up by 64 as shown previously. Therefore, the MPL when Labor=2 is (64-17/1-0)= 47. You can also do the same when you add the third labor, or when L=3. The corresponding MPL is (135-64)/(3-2)= 71.

We can also compute MPL as the first derivative of the Production Function Q where Q is Q=18L\(^{2}\) -L\(^{3}\) Therefore, dQ/dL= 36L - 3L\(^{2}\)

So, when L = 1, plug this into dQ/dL and we get 33. When L=2, dQ/dL= 36(2)-3(2)\(^{2}\)= 60.

See associated production function table here.

Question: Why do the results differ ( 17 against 33 and 47 against 60 and so forth) when we calculated MPL manually versus using the first derive function of Q?

Note by Venture Hi
3 years, 7 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

There are no comments in this discussion.

×

Problem Loading...

Note Loading...

Set Loading...