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## The Production Function

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### The Production Process

### Marginal Product (MP)

In This Lecture

We build a model to describe a “generic” production process.

- The most common characteristics in production processes
- Translate those characteristics into a “model” – a set of equations and graphs-.

©2001Claudia Garcia-Szekely

Factors of Production

- To produce, an entrepreneur uses factors of production.
- Factors of production are:
- Labor (workers)
- Land (a farm)
- Capital (equipment, buildings)

©2001Claudia Garcia-Szekely

The Concept of Plant

- A “plant” is the factory (space) where production takes place and
- All the equipment necessary to produce
- In other words is everything needed to produce, except workers and raw materials.

©2001Claudia Garcia-Szekely

Short Run vs. Long Run

- The short run is defined as the period of time when the plant size is fixed.
- The long run is defined as the time period necessary to change the plant.
- The duration of the long run (and thus that of the short run) depends on the nature of the production process…

©2001Claudia Garcia-Szekely

The Nature of production

- For a coffee shop: the long run is the time it takes to expand the coffee shop.
- For a steel mill: the long run is the time it takes to expand the plant – to build an addition, add the new equipment-
- The long run can be as short as a few weeks or as long as several months, depending on what is involved in expanding capacity to produce.

©2001Claudia Garcia-Szekely

Short Run vs. Long Run

- In the short run, at least one factor of production is fixed (unchangeable)
- In the long run, all factors of production can be changed… are “variable”

©2001Claudia Garcia-Szekely

Firms plan in the Long Run

- At any point in time, a firm is restricted by (committed to) a specific plant size…
- Firms never operate (produce) in the long run.
- The long run is the planninghorizon…when all inputs are variable until you commit to a specific plant size.

©2001Claudia Garcia-Szekely

In the Short Run

- Plant size is fixed.
- This means that production is restricted to the capacity that you have in place at the moment.
- To increase production, the only adjustment possible is to hire more workers or more labor hours (longer shifts).

©2001Claudia Garcia-Szekely

Describes the relationship between inputs (Labor) and output (Q).

©2001Claudia Garcia-Szekely

There are three important ways to measure the productivity of inputs:

- Total product (TP)
- Average product (AP)
- Marginal product (MP)

©2001Claudia Garcia-Szekely

The Production Function (TP)

- This function represents the relationship between the number of workers and the TOTAL number of units of output produced holding all other factors of production (the plant size) constant.
- For a coffee shop, output would be measured in “number of coffee cups a day”
- For a steel mill, output would be measured in “tons of steel produced a day”

©2001Claudia Garcia-Szekely

The Production Function: Output increases with L

Q

27

25

20

Units Produced

8

Units of Labor

L

1

2

3

4

©2001Claudia Garcia-Szekely

Average Product (AP)

- This function represents the average amount of output produced by each unit of labor.
- Output per unit of input

©2001Claudia Garcia-Szekely

AP: slope of ray from origin…

Q

What happens to the

Slope of the ray as L

Increases up to Lo?

AP Increases up to L0

The ray gets steeper:

The slope increases

L

Lo

L increases

AP: slope of ray from origin…

What happens to the

Slope of the ray as L

Increases past Lo?

Q

AP Decreases after to L0

The ray gets flatter:

The slope decreases

L

Lo

L increases

AP: Slope of ray from origin…

Q

Q

AP (slope of ray)

Decreases after L0

AP (slope of ray)

Increases up to L0

Lo

Lo

AP: Increases, reaches a maximum and decreases.

AP

AP (slope of ray)

Decreases after L0

AP (slope of ray)

Increases up to L0

L

Lo

©2001Claudia Garcia-Szekely

The additional output that can be produced by adding one more unit of labor, holding everything else constant.

MP = DQ/DL

The slope of the Total Product Function

©2001Claudia Garcia-Szekely

Choosing the Slope of the Production Function…

To choose the slope we must consider the following:

- The Slope of the Production Function is:

(Rise) DQ / (Run) DL

- How does production (Q) CHANGES when a new worker (L) is hired?

©2001Claudia Garcia-Szekely

The Slope of the Production Function

Is called THE MARGINAL PRODUCT OF LABOR.

MP

©2001Claudia Garcia-Szekely

The Marginal Product of Labor

- Measures the change in output that occurs when one more worker is hired.
- Short hand for Marginal Product of Labor : MP

©2001Claudia Garcia-Szekely

What happens to output as we hire more and more workers?

- Remember that the plant size is fixed.
- That means that you will be hiring more workers to SHARE the EXISTING EQUIPMENT and the EXISTING SPACE.

©2001Claudia Garcia-Szekely

A Coffee Shop

- The plant will be the store, the tables, the coffee machines, etc.
- When you add your first three workers,
- One will make the coffee, the second will be the waiter and the third will manage the register.

©2001Claudia Garcia-Szekely

If you add a fourth worker

- With two waiters, more customers can be served…
- Output would probably increase a lot as you add more and more workers AT THE BEGINNING.
- Eventually, adding new workers would begin to be counterproductive…
- Workers will now need to wait to use the equipment…

©2001Claudia Garcia-Szekely

The most likely scenario

- For most production processes,
- Adding the first workers will be favorable to production as specialization increases productivity.
- Eventually, adding more and more workers to a FIXED PLANT size would result in decreases in productivity due to “crowded conditions”.

©2001Claudia Garcia-Szekely

Diminishing Marginal Product

Is the reduction in incremental output that occurs as more and more workers are added

©2001Claudia Garcia-Szekely

The Law of Diminishing Marginal Product.

- As more of a variable input (labor) is added to a fixed input (plant), additions to output get smaller and smaller..

Note that adding workers increases output but the increases become smaller and smaller as more workers are hired.

©2001Claudia Garcia-Szekely

Negative MP

- Diminishing Returns to labor (Decreasing MP) might turn into “reductions” in output (Negative Marginal Product).

©2001Claudia Garcia-Szekely

Choosing a Graph to show Diminishing Marginal Product

To draw the production function we must choose a graph that shows:

- The more workers we have the more output would be produced.

For this, we need to draw and INCREASING FUNCTION.

©2001Claudia Garcia-Szekely

The Production Function: Output increases with L

Q

27

25

20

Units Produced

8

Units of Labor

L

1

2

3

4

©2001Claudia Garcia-Szekely

Drawing a Typical Production Function

- As we add more and more workers, additions to output - may increase at the beginning but - eventually decrease.

For this, we need to draw a function with a slope that increases at the beginning, reaches a maximum and then decreases.

©2001Claudia Garcia-Szekely

The slope of the TP increases reaches a max and decreases

Q

2

27

25

5

MP

20

Slope = 12 / 1

12

Slope = 5 / 1

Slope = 8 / 1

8

1

1

1

Slope = 2 / 1

8

L

1

2

3

4

1

©2001Claudia Garcia-Szekely

The AP and MP…

TP

Slope of ray is max

Changes concavity

L

MP is max

AP is max

MP,AP

AP

MP

L

©2001Claudia Garcia-Szekely

Relationship between MP and AP

MP

AP

MP = AP when AP is max

MP above AP

AP decreasing

AP increasing

AP

MP below AP

MP

©2001Claudia Garcia-Szekely

The Relationship between AP and MP

- If MP (10) > AP (9), then the Average Product increases.
- If MP (11) < AP (12), then the AP will decrease.
- If MP = AP, then the AP is not increasing or decreasing: it is at the maximum point.

©2001Claudia Garcia-Szekely

Consider a small sandwich shop…

©2001Claudia Garcia-Szekely

In the sandwich shop, as more employees are added to the fixed inputs, eventually MP falls.

Diminishing Returns set in after the second worker

AP

MP

©2001Claudia Garcia-Szekely

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