Production &cost

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2.3. THEORY OF PRODUCTION

A N D

C O S T

producers are able to change the quantity of some, but not all

2.3.1. The Short and Long run Production Theories

of the resources they employ. It is a period in which some

The production function describes the relationship between

resources (usually plant) are fixed and some are variable.

inputs and output. In other words it is the process of using the services of different inputs to obtain output. From this

Variable inputs are inputs whose use must change for output to

definition it follows that the production function is the

change. Fixed inputs are those inputs whose use is constant

relationship between any combinations of input services and

regardless of the level of output. For example, in the corn

the maximum output attainable, given the technology.

production fertilizer, seeds, insecticides and gasoline are variable inputs while farm buildings, machinery and truck are

The Period of Production

fixed inputs.

The production period, during which the output level can depend on the condition of the input combinations, is divided

(b) Long run

into two: short run and long run.

In the long run a firm can vary its plant size and firms can enter or leave the industry. A period of time long enough to enable

(a) Short run

producers of a product to change the quantities of all the

In the short run a firm’s plant capacity is assumed to be fixed.

resources they employ. It is a period, in which all the resources

The term short run refers to a period of time in which

and costs are variable and no resources or costs are fixed.

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As more and more of an input are supplied, the effect of this The actual period of time that is required to vary the plant size

addition on production changes and the change is explained by

or to change the quantities of fixed inputs is likely to vary from

three stages.

industry to industry. In sum industries it might take less than a

Stage I – the quantity of output increases more rapidly than the

year while in others it might take a decade or more. Long run

quantity of the input (increasing marginal returns),

time period is considered as a planning period during which the

Stage II – the quantity of output increases less rapidly than the

firm can make a plan whether to change the use of fixed inputs.

quantity of the input (diminishing marginal returns), and Stage III – the quantity of output declines as the quantity of the

The Law of Diminishing Returns

input increases (negative marginal returns)

As successive increments of a variable resource are added to

Among these stages of production Stage II, being the stage

fixed resources, the marginal product of the variable resource

where profit maximization takes place, is the most relevant

will eventually decrease. The law of diminishing returns

one. Observe that not all production processes have all the

indicates that, beyond some point, output will increase by

three stages of production.

diminishing amounts as more units of a variable resource (labor) are added to a fixed resource (capital).

2.3.2. Short run Production Functions  Total, Average and Marginal Products 

The Stages of Production

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Total Product

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The total product shows the relationship between the amounts 300

Table 1: Total, Average and Marginal Schedules Total Product Tones 29 72 123 176 225 264 287 288 261 200

Marginal Product Tones 29 43 51 53 49 39 23 1 -27 -61

Average Product Tones 29 36 41 44 45 44 41 36 29 20

C O S T

The total product curve for corn production

of an input used and how much is produced.

Number of Workers Number 1 2 3 4 5 6 7 8 9 10

A N D

250

Total Product Curve

200

Stages

150 100

I

Stage I

50

Stage II

Stage III

0 1

II

2

3

4

5

6

7

8

9

10

Number of employed workers

III

A unit increase in labor initially has an increasing corn yields

The above table and the figure below show how much corn can

up to the fourth unit of labor, in the first stage of production –

be produced as the variable inputs used, the number of workers

increasing marginal returns. At the fifth point the average

employed, varies when it is used together with the fixed inputs,

product is at its maximum value. Starting from the fifth unit of

land.

labor, as the input increases by one unit, corn production still increases but at a decreasing rate, i.e., each additional increment on labor generates a smaller increase in output than

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the last, this is exhibited in the second stages of production –

maximum value at the end of Stage I of the production

diminishing marginal returns. This continues until output

function. Additional amounts of labor in Stage II still increase

reaches its maximum, i.e., the second stage provides the

corn production, but output is increasing at a decreasing rate.

optimum amount of labor at the eighth unit of labor. Any

This implies that at the second stage the AP falls although

further additional labor unit after this point will result in a

output increases until total product reaches at its maximum at

decline in output, such a movement happens at the third stage

the end of Stage II. Even in Stage III, where increasing more

of production - negative marginal returns.

labor results in a decrease in corn production, the AP continues to fall and becomes smaller and smaller but never has a value



of zero.

Average Product

Average product (AP) is the total output produced per unit of a resource employed (total product divided by the quantity of that employed resource) and indicates the productivity of the input used. The formula is given by AP 

Q Quantity of Output  o Quantity of Variable Input Qi

At low levels of labor unit, as the amount of labor is increased, the corn output per unit of labor also increases and reaches its

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Corn product

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The AP and MP curves

MP 

60

30 20

Important Relationships

AP

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Stage I 2

3

Stage II 4

5

6

(a) Between TP and MP

Stage III 7

8

9

 As MP is increasing TP is also increasing at the increasing

1

rate.

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 As Mp reaches a maximum point TP changes its rate of

Labor input

MP 

Qo  Quantity of Output   Quantity of Variable Input Qi

the input (labor).

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-10 1

C O S T

The MP is the change in the TP (corn) for a one-unit change in

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0

A N D

change.  As MP starts to decline TP still increases but at a decreasing

Marginal Product

The additional output produced when one additional unit of a

rate.

resource is employed (the quantity of all other resources

 As MP becomes zero TP reaches a maximum point

employed remaining constant); equal to the change in total

 As MP becomes negative TP starts to decline

product divided by the change in the quantity of a resource

(b) Between MP and AP

employed.

 When MP > AP, AP is increasing ,i.e. the MP curve (broken line) lies above the AP curve

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 when MP = AP, AP is at its maximum ,i.e., AP crosses MP



 when MP < AP, AP is falling, i.e. MP lies below AP

A N D

C O S T

The monetary values of services of workers, fuel, materials and rent for machineries and equipments on hourly basis are examples of variable cost.



2.4. THEORY OF COSTS

To determine total variable cost for a given amount of output, simply multiply the quantity of each variable input by the price of that input and sum the result

Cost can be defined as the measures of the monetary value of 

inputs used to produce an item over a given period of time.

The curve that plots the total variable cost of producing each level of output is given by the TVC curve

2.4.1. Analysis of Costs in the Short-run

Total Fixed Costs (TFC) 

In the short run the total cost of any output is the sum of fixed

Are costs that remain the same regardless of the level of output

and variable costs (TC = TFC + TVC).



Property taxes, mortgage payments, insurance, interest on borrowed money, managers salary, depreciation and

1. Total Cost

general overhead costs are examples of TFC

Total Variable Cost (TVC) 



Regardless of the amount of output you choose to

is the sum of all variable costs needed to produce a

produce (even if you don’t produce anything) you have

given level of output. It varies with output.

to pay for these items.

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Total Cost (TC) 



Is the total cost of all the inputs used to produce a given level of output

The total cost curve plots the total cost of producing at different levels of output o The TFC is a straight line

Total Cost = Total Fixed Cost + Total Variable Cost (TC)

=

(TFC)

+

o The vertical distance between the TVC and the

(TVC)

TC is a constant o The TVC and TC curves are ‘curvy’,i.e, not straight lines o the shape of TVC curve mirrors that of the Total

Table 2.4. Cost of Productions for different level of Output 0 10 20 30 40 50 60 70 80

TFC 140 140 140 140 140 140 140 140 140

TVC 0 70 110 180 280 450 720 1120 1680

Output TC AFC 140 210 14 250 7 320 4.7 420 3.5 590 2.8 860 2.3 1260 2 1820 1.8

AVC

AC

MC

7 5.5 6 7 9 12 16 21

21 12.5 10.7 10.5 11.8 14.3 18 22.8

7 4 7 10 17 27 40 56

Product Curve TC, TVC & TFC

Total Cost Curve

1800-1600-1400-1200-1000-800--

Total Variable Cost Curve

600-400--

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Total Fixed Cost

200-| 10

| 20

| 30

| 40

| 50

| 60

| 70

| 80

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TC Quantity produced

As the number of outputs produced increases  AFC continuously declines but never becomes zero- showing the spread of overhead costs over the total number of outputs produced  AVC and AC decline first, reach a minimum point ( the AC reaches a minimum before the AVC does) and increases  The gap between AVC and AC becomes narrower and narrower because AFC becomes smaller and smaller 2. Average Cost If we divide total cost values by the quantity produced, we get average cost values. The three kinds of average values are calculated using the following formula AVC 

TVC Quantity produced

AFC 

TFC Quantity produced

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AFC, AVC, and AC

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additional unit, using the following formula. MC 

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AC

20

curve only it possible to calculate MC by, MC 

10 AFC

5 40

50

the change in total var iable cos t the chnage in output

Important points about MC

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the change in total Cost The change in output

In the short run, since the MC depends on the TVC

AVC

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C O S T

one more unit of output. It is calculated on the basis of an

Average Fixed, Variable and Total Cost curves

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A N D

Marginal cost is the extra or additional cost of producing

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a. The marginal cost is the same as the slope of the

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total cost curve. The most accurate estimate of the

Output

marginal cost is the first derivative of the total cost function. MC 

3. Marginal Cost

TC Q

Since the total cost curve is not a straight line, the marginal cost changes along the curve.

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when output increases from 66 to 74 (74.00  66.00)  0.62 (99.3  86.4)

b. The MC curve first decreases, then reaches a minimum and increase afterwards.

when output increases from 74 to 82

c. As indicated, it is possible to estimate the MC by

(82.00  74.00)  0.84 (108.8  99.3)

calculating the average change in cost per unit of added output. This is equivalent to calculating the

Using this approach, calculate the marginal cost as output

slope of straight line segments approximating the

changes from 86.4 units (TC of $66) to 108.8 (TC of $82)

TC curve. Given two total cost values –

Which of the two estimates of marginal cost above do you

( x1 , y1 ) and ( x 2 , y 2 ) – the slope of the line

think would best approximate the true MC at 70 to 71 units? At

between the values is:

74 to 75 unit of output? Why?

Slope  Corn Yield (X) 86.04

Total Cost (Y) 66.00

99.3

74.00

108.8

82.00

y 2  y1 x 2  x1 Marginal Cost (Slope) 0.62* 0.84

The actual slope calculations are:

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AVC

MC

 The law of diminishing returns indicates that, beyond some AC

Average Fixed, Variable and Total Cost curves and Marginal Cost

units of a variable resource (labor) are added to a fixed

AFC

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point, output will increase by diminishing amounts as more

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resource (capital).  In the short run the total cost of any level of output is the

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sum of fixed and variable costs (TC = TFC + TVC)

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 Average fixed, average variable, and average total costs are

0

AFC, AVC, and AC

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fixed, variable, and total costs per unit of output; marginal 20

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40

50

60

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cost is the extra cost of producing 1 more unit of output

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 Average fixed cost declines continuously as output

Output

increases; average-variable-cost and average-total-cost

Note that the MC curve cuts both the AVC and the ATC curves

curves are U-shaped, reflecting increasing and then

at their minimum points.

diminishing returns; the marginal-cost curve falls but then rises, intersecting both the average-variable- and the SUMMARY

average-total-cost curves at their minimum points.

Short-run Production Costs

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 Diseconomies of scale are caused by problems of Long-run Production Costs

coordination and communication which arise in large firms  Minimum efficient scale is the lowest level of output at

 Most firms have U-shaped long-run average-total-cost

which a firm’s long-run average total cost is at a minimum

curves, reflecting economies and then diseconomies of scale (= increase in the average total cost of producing a product as the firm expands the size of its plant – its outputin the long run).  Economies of scale (= reductions in the average total cost of producing a product as the firm expands the size of plant – its output – in the long run; the economies of mass production.) are the consequence of greater specialization ( = the use of the resources of an individual, a firm, a region, or a nation to produce one or a few goods and services.) of labor and management, more efficient capital equipment, and the spreading of start-up costs among more units of output

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