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The Production Function Claudia Garcia-Szekely 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-. Factors of Production

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The Production Function


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the production function

The Production Function

Claudia Garcia-Szekely

©2001Claudia Garcia-Szekely

in this lecture
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
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
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
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
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 run7
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
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
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

the production process

The Production Process

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

©2001Claudia Garcia-Szekely

there are three important ways to measure the productivity of inputs
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
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
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
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

Rise

Run

AP: slope of ray from origin…

Q

AP (of 10 workers) = 15

TP

150 units

Slope = 150/10 = 15

L

10

ap slope of ray from origin16
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 origin17
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 origin18
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: 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

marginal product mp

Marginal Product (MP)

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

mp slope of the production function

Rise

Run

MP: Slope of the Production Function

Slope = 30/3 = 10

Q

MP = 10

TP

160 units

30

130 units

3

L

9

12

choosing the slope of the production function
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
The Slope of the Production Function

Is called THE MARGINAL PRODUCT OF LABOR.

MP

©2001Claudia Garcia-Szekely

the marginal product of labor
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
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
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
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
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
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
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
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
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 l33
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
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
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
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
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
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
Consider a small sandwich shop…

©2001Claudia Garcia-Szekely

slide40

AP

L

MP

©2001Claudia Garcia-Szekely

in the sandwich shop as more employees are added to the fixed inputs eventually mp falls
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