Short run cost theory

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MICROECONOMICS

SLMtitle.png Short Run Cost Analysis




SLMobj.png Learning Objectives
After reading this chapter, you are expected to learn about:
  • Understand the concept of Short Run Cost function
  • Understand various types of short run cost functions (Linear, quadratic, cubic cost function etc)
  • Understand the pattern of change in Average Fixed Cost and the Variable cost as the Output of a firm increases
  • Understand the pattern of change in the Marginal cost as the output of a firm changes
  • Understand the relationship between Average Cost and Marginal cost in the short run







SLMinto.png Introduction

Cost of production of a good or service determines the profit that will be earned by a company involved in production process or creation of service. In economic theory there are various cost concepts which are discussed and observed. The important cost concepts related to production are following: Fixed cost, Variable cost, Average cost and Marginal cost. The control of a firm over its cost of production and the identification of least cost production point/quantity ensures higher profits for a firm. In this module the pattern of changes short run costs on account of change in the output being generated by a firm is discussed in detail.



SLMsections.png
 Let's Revise Important Cost Concepts


We already know that following are the important cost concepts related to the production process of a firm:

  • Fixed Cost
  • Varibale Cost
  • Average Cost
  • Marginal Cost

please refer to following page Introduction to Cost Concepts to understand various cost concepts in detail. Here we will briefly state again the meaning of above stated cost concepts for better understanding of the module on short run cost analysis.

Fixed Cost is that cost which does not change (that is either goes up or goes down) irrespective of whether the firm is operating or not. For example on account of strike or account of Lockout in Maruti-Suzuki’s Manesar plant the production process stands still. Even when the plant is not operating the Firm still has to bear such expenses which are indirect in nature. For Example Rent of the factory premises, Wages of administrative employees etc. In other Fixed cost is not related direct production/manufacturing expenses.

Variable Cost on the Other hand is directly proportional to the production operations. As the size of production at any business grows, along with that grow the variable expenses. As the name suggests, the variable expenses vary with the business operations. When the firm is not operating on account of Strike/Lockout etc, then the variable cost of the firm is Zero

Average Cost is the cost that is obtained after dividing Total Cost with the number of units produced.

  • Total Cost = Fixed Cost + Variable Cost
  • Average Cost = Total Cost / Units of Good produced

Marginal Cost is the change in the Total cost when an additional unit of good is produced. In other words Marginal Cost is difference between total Cost of producing ‘N + 1’ units of good and ‘N’ units of good.

  • Marginal Cost = [math]TC_{n}-TC_{n-1}[/math]


SLMsections.png
 Short Run and Long Run in Economic Theory


Understanding Short Run and Long Run Concept in Economic Theory

A famous statement made by celebrated economist J.M. Keynes states that "In the Long Run we are all dead". Thus, while undergoing any learning on microeconomic theory it becomes important for us to know that what is meant by the terms Short Run and the Long Run in economic theory.

'Short Run' is the time period in which if a firm wishes to increase its output it can do so by changing only certain variable inputs or factors of production like Labour, Raw material etc while certain other nputs or factors of production like Capital.

Short run is the time period during which if a firm wishes to increase its output then it can do so only by changing the variable factors ( like Labor). Other factors (like capital) remain fixed in the short run or in other words cannot be varied on account of time limitation applicable on the company.

For example let us assume that a company like Maruti-Suzuki in India suddenly experiences spurt or upward movement in the demand of certain category of cars in its product line. The company will therefore try to produce more cars in order to cater to the increased market demand. In the short run the company will be able to increase the amount of production only by varying inputs like labor, raw material etc but the company will not be able to alter the plant size in order to enhance its production facility as such change in production facility may require some time in terms of implementation of such change.

On the other hand in the 'Long Run' everything is variable. Thus if a company wishes to enhance its output it can do so by varying all the factors like labor, raw material, plant size, important machinery and other facilities. In other words in the long run all factors of production or inputs are variable for the company. As per the above example of Maruti-Suzuki in the long run the company will also be in position to increase its plant size or will be in position to start new production facility in order to produce more.

SLMsections.png
 Types of Short Run Cost Functions


Short run cost function of a Company can be of any of the following types:

  • Linear Cost Function
  • Quadratic Cost Function
  • Cubic Cost Function
SLMsections.png
 Linear Cost Function


Linear Cost Function

In case, for a firm or a company, its variable cost changes in the same proportion as the output of the firm, then a straight line or linear relationship is observed between the output generated by the firm and the cost involved in the producing the same. It is possible for us to express this relationship by using the mathematical equation of a straight line. This can be as follows:

[math]TC = a + bQ[/math]

For the above equation following terms mean as follows: TC = Total Cost, a and b are constant. Q is the Quantity Produced.

Here, the constant ‘a’ indicates the value of total cost when the output of the firm is zero. This value of total cost will be equal to the fixed cost of the firm as at this point the variable cost of the firm will be zero as the output of the firm is zero. On the other hand constant ‘b’ indicates the slope of straight line curve depicting the relationship between the cost and the output.

The linear relationship existing between Cost and Output is exprssed in the following table:

Quantity'Q' FC VC TC=FC+VC AFC=FC/Q AVC=VC/Q ATC=TC/Q [math]MC=TC_{n}-TC_{n-1}[/math]
0 10 0 0 0 0 0 0
1 10 2 12 10.0 2 12.0 2
2 10 4 14 5.0 2 7.0 2
3 10 6 16 3.33 2 5.33 2
4 10 8 18 2.5 2 4.5 2
5 10 10 20 2.0 2 4.0 2
6 10 12 22 1.67 2 3.66 2
7 10 14 24 1.43 2 3.42 2
8 10 16 26 1.25 2 3.25 2
9 10 18 28 1.11 2 3.11 2
10 10 20 30 1 2 3.0 2


In the above table 'Q' is the quantity produced
FC is Fixed Cost
VC is Variable Cost
TC is Total Cost (Which is FC + VC)
AFC is Average Fixed Cost obtained by dividing FC with Q
AVC is Average Variable Cost obtained by dividing VC with Q
ATC is Average Total Cost obtained by dividing TC with Q and
MC is Marginal Cost obtained by subtracting the Total Cost of producing 'n' number of goods from the Total Cost of producing 'n = 1' number of goods

The diagrammatic representation of such a straight line cost curve will be as follows:

COC4.jpeg

The diagrammatic representation of the Average Cost and the Marginal Cost for the Linear Cost function will be as follows:

COC3.jpeg

SLMsections.png
 Quadratic Cost Function


Quadratic Cost Function

A Quadratic Cost function can be mathematically depicted as follows:

[math]TC = a+bQ+cQ^{2}[/math]

In the above stated Quadratic equation ‘a' is constant indicating the value of total cost when the output of the firm is zero. The value of total cost in such a case will be equal to the fixed cost of the firm as at this point the variable cost of the firm will be zero. While, the constants ‘b’ and ‘c’, indicate the slope of the quadratic cost function. A Quadratic Cost function can be expressed as follows:


Quantity'Q' FC VC TC=FC+VC AFC=FC/Q AVC=VC/Q ATC=TC/Q [math]MC=TC_{n}-TC_{n-1}[/math]
0 10 0 0 0 0 0 0
1 10 4 14 10.0 4 14.0 4
2 10 10 20 5.0 5.0 10.0 6
3 10 17 27 3.33 5.66 9 7
4 10 26.4 36.4 2.5 6.6 9.1 9.4
5 10 37 47 2.0 7.4 9.4 10.6
6 10 50 60 1.67 8.33 10.0 13
7 10 67 77 1.43 9.57 11 17
8 10 92 102 1.25 11.5 12.75 25
9 10 132 142 1.11 14.66 15.77 40


In the above table 'Q' is the quantity produced
FC is Fixed Cost
VC is Variable Cost
TC is Total Cost (Which is FC + VC)
AFC is Average Fixed Cost obtained by dividing FC with Q
AVC is Average Variable Cost obtained by dividing VC with Q
ATC is Average Total Cost obtained by dividing TC with Q and
MC is Marginal Cost obtained by subtracting the Total Cost of producing 'n' number of goods from the Total Cost of producing 'n = 1' number of goods

The digramtic representation of Quadratic Cost function can be as follows:

COC1.jpeg

The shape of Average cost curve and the Marginal cost curve under the Quadratic Cost function can be as follows:

COC2.jpeg


SLMsections.png
 Cubic Cost Function


Cubic Cost Function

The Cubic Cost function can be mathematically depicted as follows:

[math]TC = a+bQ-cQ^{2}+dQ^{3}[/math]

If the cost function is Cubic then following can be the shape of the TC (Total Cost), FC (Fixed Cost) and the TVC (Total Variable Cost) curves:

Costc2.jpeg

In the above diagram, the shape of the total variable cost curve is like inverse ‘S’. This shape indicates that if more and more of the variable factor is applied to the fixed factor then the output of the firm initially increases at an increasing rate then at a constant rate and finally it starts to diminish. Please refer to the On account of the above the Average Variable cost initially decreases, reaches its minimum and finally it starts to increase again. This also results in the increase in the Total Variable Cost and the Total Cost at a diminishing rate initially, then at a constant rate at finally at an increasing rate

The shape of the ATC (Average Total Cost), MC (Marginal Cost) and AVC (Average Variable Cost) curves under the Cubic Cost function will be as follows:

Costc6.jpeg

The above depicted Cubic Cost Function can also be explained by using the following Cost values as stated in the following table:

Quantity'Q' FC VC TC=FC+VC AFC=FC/Q AVC=VC/Q ATC=TC/Q [math]MC=TC_{n}-TC_{n-1}[/math]
0 10 0 10 0 0 0 0
1 10 4 14 10 4 14 4
2 10 7 17 5 3.5 8.5 3
3 10 9 19 3.33 3 6.33 2
4 10 10 20 2.50 2.50 5 1
5 10 11 21 2 2.2 4.2 1
6 10 14 24 1.67 2.33 4.00 3
7 10 18 28 1.43 2.57 4.00 4
8 10 24 34 1.25 3.00 4.25 6
9 10 32 42 1.11 3.55 4.66 8
10 10 42 52 1.00 4.2 5.2 10

Again, in the above table 'Q' is the quantity produced
FC is Fixed Cost
VC is Variable Cost
TC is Total Cost (Which is FC + VC)
AFC is Average Fixed Cost obtained by dividing FC with Q
AVC is Average Variable Cost obtained by dividing VC with Q
ATC is Average Total Cost obtained by dividing TC with Q and
MC is Marginal Cost obtained by subtracting the Total Cost of producing 'n' number of goods from the Total Cost of producing 'n = 1' number of goods


SLMsum.png Results


Summing Up What We Read

  • Short Run is the time period in which if a firm wishes to increase its output it can do so by changing only certain variable inputs or factors of production like Labour, Raw material etc while certain other nputs or factors of production like Capital.
  • In the long run everything is variable and thus, if a company wishes to enhance its output in the long run then it can do so by varying all the factors like labor, raw material, plant size, important machinery and other facilities. In other words in the long run all factors of production or inputs are variable for the company.
  • Fixed Cost is that cost which does not change (that is either goes up or goes down) irrespective of whether the firm is operating or not.
  • Variable Cost on the Other hand is directly proportional to the production operations. As the size of production at any business grows, along with that grow the variable expenses. As the name suggests, the variable expenses vary with the business operations. When the firm is not operating on account of Strike/Lockout etc, then the variable cost of the firm is Zero
  • Average Cost is the cost that is obtained after dividing Total Cost with the number of units produced.
  • Marginal Cost is the change in the Total cost when an additional unit of good is produced. In other words Marginal Cost is difference between total Cost of producing ‘N + 1’ units of good and ‘N’ units of good.
  • The short run cost function can be of following types:Linear,Quadratic and Cubic.
  • Depending upon the Cost function (that is whether it is Linear, Quadractic or Cubic)is the digramatic representation of the cost curves like AC, MC, AVC, ATC etc



SLMsaq.gif Self-Assessment Questions (SAQs) {{{n}}}
Self Assessment Questions on Introduction to Microeconomics


=Some Objective Questions

Point added for a correct answer:  
Points for a wrong answer:
Ignore the questions' coefficients:

1. Short Run is

the time period in which if a firm wishes to increase its output it can do so by changing only certain variable inputs or factors of production like Labour, Raw material etc while certain other nputs or factors of production like Capital
the time period which is veru short
the time period in which the return on the factors of production is negative

2. Long Run is

the time period which is very long
the time period in which all the factors are variable
the time taken by components like production, consumption, product pricing, demand to adjust themselves as per the market requirements

3. Linear Cost function is

One which assumes that there is no relationship between the Cost and the Output produced by a Firm
One which assumes straight line relationship between Cost and Output Produced by a FirmStudy of economic behavior of an individual firm, industry, household, consumers etc in an economy
under which there is fall in the valuation of a firm in the market

4. Marginal Cost is

Cost of production borne by the Marginal Farmers
Cost of Production of a firm when a firm undergoes Business Cycles
Marginal Cost is the change in the Total cost when an additional unit of good is produced. In other words Marginal Cost is difference between total Cost of producing ‘N + 1’ units of good and ‘N’ units of good.Understanding Consumer Behaviour
All of the above

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True or False Quiz
  • The shape of Average Total Cost curve under Cubic Cost function is
    • 'S' shaped, rising upward mildly from left to right
      • True
    • 'L' shaped, on account of sudden change in Cost
      • False
  • Average Fixed Cost
    • Decreases continously as the Output of the Firm increases
      • True
    • Increases continously as the Output of the Firm increases
      • False




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