How to calculate total physical product

ECONOMICS

Microeconomics

Costs of Production

Production

Transformation of resources (inputs) into goods and services (output)

Fixed Inputs

Quantity does not change as output changes

For example: capital (K)

Variable Inputs

Quantity changes as output changes

For example: labor (L)

Production Process

LABOR ( L )

CAPITAL ( K )

OUTPUT ( Q )

Production: Short vs Long

Output

Total Physical Product (TPP)

aka Quantity (Q)

Production in the short run

Fixed Inputs + Variable Inputs

Production in the long run

Variable Inputs (no fixed inputs)

Example Production Functions

with K = 1

Output

Total Physical Product (TPP or Q)

The quantity of goods that are produced for a given set of inputs.

For example:

L=3, K=1  330 units

Marginal Physical Product (MPP)

The additional quantity that is produced by increasing the variable input by one unit, holding all other inputs constant.

MPP Example

Total Fixed and Variable Costs

TFC: Total Fixed Cost

Cost associated with fixed inputs (short term production)

Does not vary with the level of output

TVC: Total Variable Cost

Cost associated with variable inputs

Varies with the level of output

TC: Total Cost = TFC + TVC

Total Fixed and Variable Costs

FIXED COST

$400 per unit of capital

VARIABLE COST

$24 per unit of labor

Total Fixed and Variable Costs

FIXED COST

$400 per unit of capital

VARIABLE COST

$24 per unit of labor

Total Cost

FIXED COST

$400 per unit of capital

VARIABLE COST

$24 per unit of labor

Average Productivity

Average Productivity (AP)

=

Q / L

“A study released earlier this year examining stable scheduling practices at Gap Inc. stores found that labor productivity increased 5% and sales rose 7% when managers did things such as keep the days and times of workers’ shifts consistent from week to week.”

Average Costs

AFC: Average Fixed Cost = TFC / Q

AVC: Average Variable Cost = TVC / Q

ATC: Average Total Cost = TC / TPP

= AFC + AVC

Average Fixed Cost = Total Fixed Cost / Quantity

Average Variable Cost = Total Variable Cost / Quantity

ATC = AFC + AVC = 3.33 + 0.20 = 3.53

MARGINAL COST

CHANGE IN TOTAL COST WITH RESPECT TO CHANGE IN OUTPUT

Marginal Cost

Equal to change in total cost divided by change in output:

or…

Equal to wage rate divided by MPP:

Marginal Cost

of 1st unit of labor

Marginal Cost

of 1st unit of labor

MC=?=ATC

1. AFC is falling

2a. When MC < AVC

AVC is falling

2b. When MC > AVC

AVC is rising

1. AFC is falling

2a. When MC < AVC

AVC is falling

2b. When MC > AVC

AVC is rising

3a. When MC < ATC

ATC is falling

3b. When MC > AVC

ATC is rising

Exercise #1 (1 of 3)

At 3 units of labor, what is the marginal physical product?

At 4 units of labor, what is the quantity produced?

Exercise #1 (2 of 3)

At 3 units of labor, the marginal physical product is 35

At 4 units of labor, what is the quantity produced?

Exercise #1 (3 of 3)

At 3 units of labor, the marginal physical product is 35

At 4 units of labor, 60 units are produced

Exercise #2 (1 of 5)

Assume that the cost of labor is $240, and the cost of capital is $1200

At 4 units of labor calculate AFC, AVC, TC, and MC

Exercise #2 (2 of 5)

Cost of labor = $240 per unit

Cost of capital = $1200 per unit

At 4 labor and 2 capital  Q=600 units, MPP=20

Exercise #2 (3 of 5)

Cost of labor = $240 per unit

Cost of capital = $1200 per unit

At 4 labor and 2 capital  Q=600 units, MPP=20

Exercise #2 (4 of 5)

Cost of labor = $240 per unit

Cost of capital = $1200 per unit

At 4 labor and 2 capital  Q=600 units, MPP=20

Exercise #2 (5 of 5)

Cost of labor = $240 per unit

Cost of capital = $1200 per unit

At 4 labor and 2 capital  Q=600 units, MPP=20

Microeconomics

Long Run Costs, Economies of Scale, & Sunk Cost

SRATC = AFC + AVC

MC = ATC

SRATC = min{SRATC}

Q < MCO:

MC < SRATC

and ↓ SRATC

Q > MCO:

MC > SRATC

and ↑ SRATC

Industry Analysis – An Example

4 Firms

Each firm has fixed and variable inputs

Each firm produces quantity that minimizes average total cost (MCO)

Industry output = Sum of firm output: QTY = Q1 + Q2 + Q3 + Q4

In the Long Run

There are no fixed inputs in the production process

NO FIXED INPUTS

NO FIXED COSTS

TOTAL COST = VARIABLE COST

LRATC = Long Run Average Total Cost

The relationship between output (TPP) and average total cost (ATC) when fixed cost has been chosen to minimize average total cost for each level of output.

Economies of Scale

LRATC FALLS => ECONOMIES OF SCALE

Produce more output at lower unit costs

For example, a 5% increase in inputs leads to 8% increase in output

Economies of Scale

Internal Economies of Scale

External Economies of Scale

Technical Economies of Scale

Economies of Scale

Internal Economies of Scale

Specialization of Operations

Production – people become expert performing certain tasks

Administration – management philosophies, sophisticated accounting strategies

Distribution – modernized supply chain, just-in-time strategies

Economies of Scale

Internal Economies of Scale

Specialization of Operations

Production – people become expert performing certain tasks

Administration – management philosophies, sophisticated accounting strategies

Distribution – modernized supply chain, just-in-time strategies

External Economies of Scale

Creation of positive externalities (e.g., Internet) benefits industry or economy

Lower interest rates make it cheaper for firms to invest in new projects

Economies of Scale

Internal Economies of Scale

Specialization of Operations

Production – people become expert performing certain tasks

Administration – management philosophies, sophisticated accounting strategies

Distribution – modernized supply chain, just-in-time strategies

External Economies of Scale

Creation of positive externalities (e.g., Internet) benefits industry or economy

Lower interest rates make it cheaper for firms to invest in new projects

Technical Economies of Scale

Improvements to capital and production processes (e.g., assembly lines)

LRATC Long Run Average Total Cost

Constant Returns to Scale

Average total cost unchanged as production is increased.

A coffee shop with 10 employees can produce 400 cups per day; if they open another coffee shop with 10 employees they can produce another 400 cups.

Smaller firms operating in this region can compete with larger firms

For example, a 5% increase in inputs leads to 5% increase in output

LRATC constant

Diseconomies of Scale

Firms grow to point that causes problems:

Manager coordination of work activities

Timely communication of work directives

Effective monitoring of personnel

Overcrowding effects are often the cause of diseconomies of scale

For example, a 5% increase in inputs leads to 2% decrease in output

LRATC rising

Only relevant in the long run!

A Tale of Three Grinders

$25 $55 $625

#1 #2 #3

#1 Manual

OUTPUT: 50 UNITS

TOTAL COST: $350

#2 Electric

OUTPUT: 150 UNITS

TOTAL COST: $450

#3 Industrial

OUTPUT: 300 UNITS

TOTAL COST: $600

Economies of Scale

Sunk Costs

?

I might as well keep eating because I already bought the food.

?

Well I’m going to keep watching this terrible movie because I have already watched an hour of it already.

?

I might as well continue dating someone bad for me because I’ve already invested so much in them.

SUNK COST

Cost that been paid and cannot be recovered

Decisions that are constrained by consideration of sunk costs are irrational

Thank you!

On your own…

EXERCISE

PK = 240

PL = 16

L

K

Q

0

1

0

1

1

120

2

1

230

3

1

330

4

1

420

5

1

500

6

1

570

7

1

630

8

1

680

9

1

720

L

K

Q

MPP

0

1

0

1

1

120

120

2

1

230

110

3

1

330

100

4

1

420

90

5

1

500

80

6

1

570

70

7

1

630

60

8

1

680

50

9

1

720

40