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Umme BabaAyush Parekh

Suchit ChauhanArul Collins

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LAW OF VARIABLE PROPORTIONS

&LAW OF RETURNS TO

SCALE

Introduction

What is Economics?• Economics is the study of the • production and consumption of goods• transfer of wealth to produce and obtain those

goods.

• Economics explains how people interact within markets to get what they want or accomplish certain goals.

Macroeconomics

Macroeconomics contains broader view by analyzing the economic activity of an entire country or the international marketplace.

Microeconomics focuses on the actions of individuals and industries, like the dynamics between buyers and sellers, borrowers and lenders.

Types of EconomiesMicroeconomics

Production Function

• A production function is an equation, table or graph, which specifies the maximum quantity of output, which can be obtained, with each set of inputs.

• Prof. Richard H. Leftwich states that production function refers to the relationship between inputs and outputs at a given period.

(Inputs = resources such as land, labor, capital and organization used by a firm

Outputs = goods or services produced by the firm)

• It is written as Q = F(X1, X2… Xn). • Where Q is the maximum quantity of output and X1, X2,… Xn are the

quantities of the various inputs. If there are only two inputs, labor L and capital K, we write the equation as Q = F(L,K).

• The concept of production function stems from the following two things:• 1. It must be considered with reference to a particular period.• 2. It is determined by the state of technology. Any change in technology

may alter output, even when the quantities of inputs remain fixed.

• Total Product : It is the total output or quantity that is produced by a firm using fixed and variable factors at a given point of time.

• Average Product : It is defined as the product produced per unit of variable input employed when fixed inputs are held constant.

Average Product = (Total Product) / (Variable Inputs Employed)

• Marginal Product : It is defined as the change in total product that comes as a result of a one unit increase in the variable input.

Marginal Product = (dTP) / (dVI)(where TP is total product and VI is variable inputs. )

Total, Average & Marginal Product

Lawof

VariableProportions

Prof. Marshall stated, “An increase in the quantity of a variable factor added to fixed factors, at the end results in a less than proportionate increase in the amount of product, given technical conditions.”

Assumptions of the LawOnly one variable factor unit is to be varied

while all other factors should be kept constant

Different inits of variable factor are homogenous

Techniques of production remain constantThe law will hold good only short and a given

periodThere are possibilities of varying the

proportion of factor inputs.

Diminishing returns arise due to the following :-The proportion of variable factors is greater

than the quantity of fixed factors. Hence both AP and MP decline.

Total output diminishes because there is a limit to the full utilization of indivisible factors and introduction of specialization. Hence Output declines.

Imperfect suitability of factor inputs is another cause. Up to certain point substitution is beneficial, once optimum point is reached, the fixed factors cannot be compensated by the variable factor.

Lawof

Returns to Scale

The law of returns to scale examines the relationship between output and the scale of inputs in the long-run when all the inputs are

increased in the same proportion.

All the factors of production (such as land, labor and capital) but organization are variable

The law assumes constant technological state. It means that there is no change in technology during the time considered

The market is perfectly competitive

Outputs or returns are measured in physical terms.

Assumptions

•The law of increasing returns

• The law of constant returns

•The law of decreasing returns

Three Stages of Returns to Scale

Unit Scale of Production Total Returns Marginal Returns

1 1 Labor + 2 Acres of Land 4

4 (Stage I - Increasing Returns)

2 2 Labor + 4 Acres of Land 10 6

3 3 Labor + 6 Acres of Land 18 8

4 4 Labor + 8 Acres of Land 28 10 (Stage II -

Constant Returns)

5 5 Labor + 10 Acres of Land 38 10

6 6 Labor + 12 Acres of Land 48 10

7 7 Labor + 14 Acres of Land 56

8 (Stage III - Decreasing Returns)

8 8 Labor + 16 Acres of Land 62 6

Production function

v/sCost

function

Production function A production function relates

physical output of a production process to physical inputs or factors of production

Cost function The cost-of-production theory

of value is the theory that the price of an object or condition is determined by the sum of the cost of the resources that went into making it. The cost can comprise any of the factors of production (including labor, capital, or land) and taxation.

Total Cost Total cost in economics

includes the total opportunity cost of each factor of production as part of its fixed or variable costs.

The total product (or total physical product) of a variable factor of production identifies what outputs are possible using various levels of the variable input

Total Cost v/s Total ProductTotal Product

Average cost Average cost or unit cost is

equal to total cost divided by the number of goods produced (the output quantity, Q). It is also equal to the sum of average variable costs (total variable costs divided by Q) plus average fixed costs (total fixed costs divided by Q)

Average product is the per unit production of a firm. Conceptually, it is simply the arithmetic mean of total product calculated for each variable input over a whole range of variable input quantities

Average Cost v/s Average Product

Average Product

Marginal cost Marginal cost is the change in the

total cost that arises when the quantity produced has an increment by unit. That is, it is the cost of producing one more unit of a good. In general terms, marginal cost at each level of production includes any additional costs required to produce the next unit

The marginal product of an input (factor of production) is the extra output that can be produced by using one more unit of the input (for instance, the difference in output when a firm's labor usage is increased from five to six units), assuming that the quantities of no other inputs to production change

Marginal cost v/s Marginal product

Marginal product

Summary

Law of Variable Proportions

Short periodOnly one factor is varied The factor ratio remains

changedThere are three stages:

a) Increasing returns to factor. b) Diminishing returns to factor c) Negative returns to factor

Productions is of variable type

Long period All factors varied The factor ratio remains

unchanged There are three stages: a) Increasing returns to

scale b)Decreasing returns to

scale c)Constant returns to scale

Productions is of constant type

Difference between the LawsLaw of Returns to Scale

SHORT RUN• Short run is defined as a period when production

can be increased only with increase in variable factors .

LONG RUN• Long run is defined as a period which allows the firm

to change their sizes and scales to increase output  

SHORT RUN• The short run as the time horizon over which the scale of

operation is fixed and the only available business decision is the number of workers to employ.

• Quantity of labor is variable but quantity of capital and production processes are fixed 

LONG RUN• The long run as time horizon is needed for a producer to

have flexibility over all relevant production decisions• Long run: Quantity of labor, quantity of capital, and

production processes are all variable 

Production Decisions

SHORT RUN• In the short run, firms have already chosen whether to

be in business and at what scale and technology of production.

• The number of firms in an industry is fixed

LONG RUN• In the long run, firms have the flexibility to fully enter

or exit an industry.• The number of firms in an industry is variable since

firms can enter and exit

Market Entry and Exit

SHORT RUN• Firms will produce if the market price at least covers

variable costs, since fixed costs have already been paid and, as such, don't enter the decision-making process.

• Firms' economic profits can be positive, negative or zero.

LONG RUN• Firms will enter a market if the market price is high enough to

result in positive economic profit.• Firms will exit a market if the market price is low enough to result

in negative economic profit.• If all firms have the same costs, firm profits will be zero in the

long run in a competitive market

Market Behavior

Conclusion

It is helpful in understanding clearly the process of production.

The law tells us that the tendency of diminishing returns is found in all sectors of the economy .

The law tells us that any increase in the units of variable factor will lead to increase in the total product at a diminishing rate.

Law of Variable Proportions

This law may not apply universally to all kinds of productive activities .

This law has been found to operate in agricultural production more regularly than in industrial production.

If increasing units of an input are applied to the fixed factors, the marginal returns to the variable input decrease eventually.

Law of Returns to Scale