Theory of production

Ram Kumar Phuyal, Ph.D.Ram Kumar Phuyal, Ph.D.Microeconomics Microeconomics

Kathmandu UniversityKathmandu University

Theory of ProductionTheory of Production

Contents:

This presentation includes about production function with one and two variable input(s), returns to scale, and short run and long run costs functions.

The Production FunctionThe Production Function

The The production function production function refers to the physical relationship refers to the physical relationship between the inputs or resources of a firm and their between the inputs or resources of a firm and their output of goods and services at a given period of time, output of goods and services at a given period of time, ceteris paribus. ceteris paribus.

The production function is The production function is dependent dependent on different on different time frames. Firms can produce for a brief or lengthy time frames. Firms can produce for a brief or lengthy period of time. period of time.

Firm’s InputsFirm’s Inputs

Inputs - are resources that contribute in the Inputs - are resources that contribute in the production of a commodity. production of a commodity.

Most resources are lumped into three categories: Most resources are lumped into three categories: Land, Land, Labor,Labor, CapitalCapital OrganizationOrganization Raw materials and etc.Raw materials and etc.

Fixed vs. Variable InputsFixed vs. Variable Inputs

Fixed inputs -resources used at a constant amount in Fixed inputs -resources used at a constant amount in the production of a commodity. the production of a commodity.

Variable inputs - resources that can change in quantity Variable inputs - resources that can change in quantity depending on the level of output being produced. depending on the level of output being produced.

The longer planning the period, the distinction between The longer planning the period, the distinction between fixed and variable inputs disappears, i.e., all inputs are fixed and variable inputs disappears, i.e., all inputs are variable in the long run.variable in the long run.

Production Analysis with One Variable InputProduction Analysis with One Variable Input

Total product (Q) Total product (Q) refers to the total amount of output refers to the total amount of output produced in physical units (may refer to, kilograms produced in physical units (may refer to, kilograms of sugar, sacks of rice produced, etc)of sugar, sacks of rice produced, etc)

The The marginal product (MP) marginal product (MP) refers to the rate of change refers to the rate of change in output as an input is changed by one unit, holding in output as an input is changed by one unit, holding all other inputs constant.all other inputs constant.

L

L

TPMP

L

∆=∆

Total vs. Marginal ProductTotal vs. Marginal Product

Total Product (TPx) = total amount of output Total Product (TPx) = total amount of output produced at different levels of inputsproduced at different levels of inputs

Marginal Product (MPx) = rate of change in output as Marginal Product (MPx) = rate of change in output as input X is increased by one unit, input X is increased by one unit, ceteris paribusceteris paribus..

XX

TPMP

X

∆=∆

Production Function of a Rice FarmerProduction Function of a Rice FarmerTable 1.Table 1.

Units of LUnits of L Total Product Total Product

(Q(QLL or TP or TPLL))Marginal Product Marginal Product

(MP(MPL)L)

00 00 --

11 22 22

22 66 44

33 1212 66

44 2020 88

55 2626 66

66 3030 44

77 3232 22

88 3232 00

99 3030 -2-2

1010 2626 -4-4

FIGURE 1. Total product curve. The total product curve shows the behavior of total product with an input (e.g., labor) used in production assuming a certain technological level.

L

QL

QL

2

6

12

20

26

30

32

Labor

Tot

al p

rodu

ct

0 2 4 6 8 1097531

Marginal ProductMarginal Product

The The marginal product marginal product refers to the rate of change in output refers to the rate of change in output as an input is changed by one unit, holding all other inputs as an input is changed by one unit, holding all other inputs constant.constant.

Observe that the marginal product Observe that the marginal product initially increases, reaches a initially increases, reaches a maximum level, and beyond this point, the marginal product declines, maximum level, and beyond this point, the marginal product declines, reaches zero, and subsequently becomes negative.reaches zero, and subsequently becomes negative.

The The law of diminishing returns law of diminishing returns states that "as the use of states that "as the use of an input increases (with other inputs fixed), a point will an input increases (with other inputs fixed), a point will eventually be reached at which the resulting additions to eventually be reached at which the resulting additions to output decrease" output decrease"

Total and Marginal ProductTotal and Marginal Product

-10

-5

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7 8 9

TPL

MPL

FIGURE 2.

Law of Diminishing Marginal Law of Diminishing Marginal ReturnsReturns

As more and more of an input is added As more and more of an input is added (given a fixed amount of other inputs)(given a fixed amount of other inputs), total , total output may increase; however, as the output may increase; however, as the additions to total output will tend to additions to total output will tend to diminish.diminish.

Counter-intuitive proof: if the law of Counter-intuitive proof: if the law of diminishing returns does not hold, the diminishing returns does not hold, the world’s supply of food can be produced in world’s supply of food can be produced in a hectare of land.a hectare of land.

Average Product (AP)Average Product (AP)

Average product is a concept commonly Average product is a concept commonly associated with efficiency. associated with efficiency.

The The average product average product measures the total output per measures the total output per unit of input used. unit of input used. The "productivity" of an input is usually The "productivity" of an input is usually

expressed in terms of its average product. expressed in terms of its average product. The greater the value of average product, the The greater the value of average product, the

higher the efficiency in physical terms. higher the efficiency in physical terms. Formula:Formula: L

L

TPAP

L=

TABLE 2. Average product of labor.

Labor (L)Total product of

labor (TPL)Average product of

labor (APL)

0 0 0

1 2 2

2 6 3

3 12 4

4 20 5

5 26 5.2

6 30 5

7 32 4.5

8 32 4

9 30 3.3

10 26 2.6

Rise = Y

Run = L0L

Y

The slope of the line from the origin is a measure of the AVERAGE

Y

L1 L2

a b

riseSlope =

run

Y

L=

FIGURE 3.

Labor

Q

QL

0

Total Product

a

bc

d

The average product at b is highest.

AP at c is less than at a.

AP at d is less than at c.

FIGURE 4.

L

L

Q

TPL

Highest Slope of Line from Origin

Max APL

Inflection point

Max MPL

0 L1 L2 L3

FIGURE 5.

Relationship between Average and Relationship between Average and Marginal CurvesMarginal Curves

When the marginal is less than the average, the When the marginal is less than the average, the average decreases.average decreases.

When the marginal is equal to the average, the When the marginal is equal to the average, the average does not change (it is either at maximum average does not change (it is either at maximum or minimum)or minimum)

When the marginal is greater than the average, When the marginal is greater than the average, the average increasesthe average increases

Relationship between Average and Marginal Relationship between Average and Marginal Curves: Example of Econ 11 ScoresCurves: Example of Econ 11 Scores

When the marginal score (new exam) is less When the marginal score (new exam) is less than your average score, the average than your average score, the average decreases.decreases.

When the marginal score (new exam) is equal When the marginal score (new exam) is equal to the average score, the average does not to the average score, the average does not change. change.

When the marginal score (new exam) is When the marginal score (new exam) is greater than your average score, the average greater than your average score, the average increases.increases.

L

Q

Max APL Max MPL

0 L1L2 L3

MPL

APL

At Max AP, MP=AP

FIGURE 5.

AP, MP

L

AP,MP

0 L1L2 L3

MPL

APL

Stage IMP>AP

AP increasing

Stage IIMP<AP

AP decreasingMP still positive

Stage IIIMP<0

AP decreasing

L

TP

0 L1 L2 L3

TPL

FIGURE 6.

Three Stages of ProductionThree Stages of Production

In Stage I In Stage I APAPLL is increasing so MP>AP. is increasing so MP>AP.

All the product curves are increasingAll the product curves are increasing Stage I stops where Stage I stops where APAPLL reaches its maximum at reaches its maximum at

point point A. A. MP peaks and then declines at point MP peaks and then declines at point C C and beyond, and beyond,

so the law of diminishing returns begins to manifest so the law of diminishing returns begins to manifest at this stageat this stage

Three Stages of ProductionThree Stages of Production

Stage IIStage II starts where the starts where the APAPLL of the input begins to decline. of the input begins to decline. QQLL still continues to increase, although at a still continues to increase, although at a

decreasing rate, and in fact reaches a maximumdecreasing rate, and in fact reaches a maximum Marginal product is continuously declining and Marginal product is continuously declining and

reaches zero at point reaches zero at point D, D, as additional labor inputs as additional labor inputs are employed.are employed.

Three Stages of ProductionThree Stages of Production

Stage III starts where the Stage III starts where the MPL MPL has turned has turned negative. negative. all product curves are decreasing. all product curves are decreasing. total output starts falling even as the input is total output starts falling even as the input is

increased increased