Production Function
& Cost Analysis
Production is the process that transforms input into output
Production Function
A production function indicates the output Q that a firm produces for every specific combination of inputs like land, labour, capital and management.
Let there be only two types of inputs:
Labour (L) and
Capital (K); then
Q = f (L,K) Assumptions
Is assumed that the state of technology is given.
The function describes maximum output feasible for
a given set of inputs. 2
Production Function
Production Function is of two types: Shot Run and Long Run
Short Run: It is the period during which at least one of the factors of production is available in a fixed quantity.
During this period production can be increased or decreased by changes in other inputs only.
Long Run: It is the period during which all the factors of production are variable.
During this period, production can be increased or decreased through a change in any one or more of the inputs.
Law of Variable Proportion
Also called as Law of Diminishing Returns
It states that as the use of an input increases (with another input fixed) a point will be eventually reached at which any resulting addition leads to decrease of output.
For example, when there are many workers some workers become ineffective and the marginal product of labour falls.
Average Product = Q/L
Marginal Product = Q/ L 4
Law of Variable Proportion
Law of Variable Proportion
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Law of Variable Proportion
If MP > AP, AP increases
When MP < AP, AP decreases
The shape of short run production
function is such that it is first convex
from below and then concave from
below.
Law of Variable Proportion
Three States of Law of Diminishing Returns:
Increasing Return to the Variable Factor: This is the very first stage, in which, when additional units of labour are employed, the total output increases more proportionality, so marginal product rises.
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Law of Variable Proportion
Diminishing Return to Variable Factor: In the second stage, the total output increases but with less than proportionate increases in labour. So, MP falls.
Negative Return to Variable Factor: In this stage, MP<
0
and the total product is falling.This is technically inefficient stage of production and a rational firm will not operate in this stage.
Production Function in the Long Run
In the long run all inputs are variable ISOQUANTS (equal product curves)
Isoquants show all possible combinations of inputs that yield the same output.
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Q1 = 90
L K
3 8
4 6
5 4
8 3
Q2 = 120
L K
6 12
7 10
9 9
10 7
Marginal Rate of Technical Substitution (MRTS)
MRTS is the amount by which the inputs of capital can be reduced when one extra unit of labour is used so that output remains constant.
The amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant.
L MRTS K
Change in labour inputs inputs capital
in Change
Properties of Isoquants
They are downward sloping
Higher isoquants represents higher output
They do not intersect each other
They are convex from below
Isoquants are also known as Iso-Product curve, Equal-product curve or Production indifference curve.
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Special Types of Isoquants
1. Linear Isoquants: Isoquant under
perfect substitution between labour
and capital. Eg. Handicraft
Special Types of Isoquants
2. Right Angled Isoquants: Isoquants under zero substitutability between labour and capital. These are also termed as Leontief Isoquant.
Eg. One hammer for one person
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Return to Scale
It provides the measure of the direction of change in total factor productivity when all factors of production change in the same direction and same proportion.
Increasing Return to Scale: If output more than doubles, when inputs are doubled.
Constant Return to Scale: If output doubles, when inputs are doubled.
Decreasing Return to Scale: If output less than double, when all inputs are doubled.
Return to Scale
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Return to Scale
If an industry is characterised by increasing return to scale, there will be a tendency for expanding the size of the firm, and thus, the industry will be dominated by large size firms.
Quite opposite would prevail in industries where decreasing return to scale is observed.
Firms of all sizes would survive equally well in industries characterised by constant return to scale.
Economies of Scope
It exists in terms of relative cost of producing a variety of goods and services in one firm versus producing them separately in two or more firms.
Total Cost, TC (Qa, Qb) < TC (Qa) + TC (Qb)
Degree of Economies of Scope (SC)
SC >
0
Economies of Scope SC < 0 Diseconomies of Scope
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SC = [C(Q1) + C(Q2) – C(Q1, Q2)] / C(Q1,Q2)
Economies of Scale
It exist if the firm achieves saving in unit cost as it increases production of a given good or service.
LAC – Long Run Average Cost LMC – Long Run Marginal Cost
1. When LMC < LAC, then LAC decreases resulting in Economies of Scale
2. When LMC > LAC, then LAC increases resulting in Diseconomies of Scale
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Reasons for Economies of Scale
1. Due to large plant
Specialization
Indivisibility
Productivity
Equipment Maintenance
2. Due to large firm
Quantity discounts
Fund Raising
Sales Promotion
Research &
Development
Management
Economies of Scale
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1. Due to Large Plant
i) Specialization: Adam Smith said that division of labour improves productivity – through need for a limited training, learning by doing, saving of time, reduction in period idleness, need for lesser equipment, etc. The bigger plants are able to bring desired level of specialization.
Economies of Scale
1. Due to Large Plant
ii) Indivisibility: In a large plant, fixed costs like cost of machinery, equipments, etc gets spread over a large number of products, thus, reducing the long run average cost.
Economies of Scale
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1. Due to Large Plant
iii) Productivity: The relative productivity is more for large plants because a machine that costs twice as much than a smaller one will have productivity more than twice.
iv) Maintenance: Large plants need to carry relatively less repairs and spare parts.
Economies of Scale
2. Due to Large Firm
i) Quantity Discounts: On bulk purchases the firm gets more discounts.
ii) Research & Development: These involve substantial investments which can be done by large firms only and hence lead to improvement in quality and innovation.
Economies of Scale
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2. Due to Large Firm
iii) Fund Raising: Large firms get credit
at favourable rates. Also, floating cost
of equity capital and debentures per
unit of funds raised vary inversely
with the size of debt/capital raised.
Economies of Scale
2. Due to Large Firm
iv) Sales Promotion: Large firms manage to get space and time in various advertising media, which are favourable. Also, average cost per potential customer may be less because fixed cost of advertisement will spread.
v) Management: Large firms enjoy the benefits of top caliber management personnel, which are denied to small firms.
Reasons for Diseconomies of Scale
1. Due to large plant
Transportation cost
Imperfections in labour market
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2. Due to large firm
Coordination and control
Diseconomies of Scale
1. Due to large plant
i) Transportation cost: If the raw material is spatially well spread, then, the transportation cost of raw material will be more in a large plant wherever located than in a number of small plants well dispersed geographically.
Moreover, transportation cost of a large plant is more in case of distribution of output to customers.
Diseconomies of Scale
1. Due to large plant
ii) Imperfections in Labour Market: There is a high degree of immobility among workers and hence huge costs are involved in terms of transport and residential accommodation. Small plants due to their small size are able to get workers at lower wages than large plants.
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Diseconomies of Scale
2. Due to large firm size
i) Coordination and Control: Coordination and communication problems in large firms leads to framing of rule and so bureaucracy starts, which results in hampering creativity and innovation.
Cost Concepts
Cost may be defined as the sacrifice which has already occurred or has potential of occurring in future with an objective to achieve a specific purpose measured in monetary terms.
Determinants of Cost are:
Price of inputs;
Technology
Productivity of inputs
Level of output
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Kinds of Cost
Accounting costs (only money costs)
Real costs (including social and psychological costs)
Opportunity costs (foregone)
Explicit and Implicit Costs
Explicit costs are input costs that require a direct outlay of money by the firm.
Implicit costs are input costs that do not require an outlay of money by the firm.
Economists versus Accountants
Revenue
Total
opportunity costs
How an Economist Views a Firm
How an Accountant Views a Firm
Revenue Economic
profit
Implicit costs
Explicit
costs Explicit
costs
Accounting profit
Costs in the Short Run
In the short run, at least one of the factor of production in fixed.
Costs in the short run are classified as:
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Term Symbol Definition Equation
Fixed Cost FC Cost that is independent of output level
Variable Cost VC Cost that varies with output level
Total Cost TC Cost of all inputs TC = FC + VC Average Fixed
Cost
AFC Total fixed cost per unit of output AFC = TFC/TP
Average
Variable Cost
AVC Total variable cost per unit of output
AVC = TVC/TP
Average Total Cost
ATC Total cost per unit of output ATC = AFC + AVC
Marginal Cost
MC Change in total cost resulting from one unit increase in total output
MC = TC/ TP
1
Output 2 FC
3 VC
4 TC (2+3)
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AFC (2/1)
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AVC (3/1)
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ATC (4/1)
8 MC
0 50 0 50 - - - -
1 50 50 100 50 50 100 50
2 50 78 128 25 39 64 28
3 50 98 148 16.7 32.7 49.3 20
4 50 112 162 12.5 28 40.5 14
5 50 130 180 10 26 36 18
6 50 150 200 8.3 25 33.3 20
7 50 175 225 7.1 25 32.1 25
8 50 204 254 6.3 25.5 31.8 29
9 50 242 292 5.6 26.9 32.4 38
10 50 300 350 5.0 30 35 58
11 50 385 435 4.5 35 39.5 85
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Characteristics of Cost Curves in Short Run
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The FC curve is horizontal.
The VC curve starts from origin, is concave from below in the beginning and is convex from below after a certain level of output.
The TC curve starts from a point above the origin and then follows the shape of VC curve. The TC and VC curves are parallel.
The AFC curve falls continuously but never touches the output axis.
As TP increases, difference between ATC and AVC also decreases because of decreasing AFC.
Characteristics of Cost Curves in Short Run
The output at which MC is minimum (Q1) is less than the output at which AVC is minimum (Q2), which in turn, is less than the output at which ATC is minimum.
MC curve intersects AVC and ATC at their minimum points. MC, AVC and ATC curves are U-shaped.
When MC < AVC or ATC then both AVC and ATC falls
When MC > AVC or ATC then both AVC and ATC rises
COSTS IN THE LONG RUN
Because many costs are fixed in the
short run but variable in the long run, a
firm’s long-run cost curves differ from
its short-run cost curves.
Quantity 0
Average Total
Cost
1,200
$12,000
1,000 10,000
Economies of scale
ATC in short run with small factory
ATC in short run with medium factory
ATC in short run with
large factory ATC in long run
Diseconomies of
scale Constant
returns to scale
