PRODUCTION FUNCTION AND LAW OF VARIABLE PROPORTIONS

Production Function:

Definition:

A given output can be produced with many different combinations of factors of production (land, labor, capita! and organization) or inputs. The output, thus, is a function of inputs. The functional relationship that exists between physical inputs and physical output of a firm is called production function.

Formula:

In abstract term, it is written in the form of formula:

Q = f (x¹, x², ......., xⁿ)

Q is the maximum quantity of output and x¹, x², xⁿ are quantities of various inputs. The functional relationship between inputs and output is governed by the laws of returns.

The laws of returns are categorized into two types.

(i) The law of variable proportion seeking to analyze production in the short period.

(ii) The law of returns to scale seeking to analyze production in the long period.

Law of Variable Proportions/Law of Non Proportional Returns/Law of Diminishing Returns:

 

(Short Run Analysis of Production):

Definition:

There were three laws of returns mentioned in the history of economic thought up till Alfred Marshall's time. These laws were the laws of increasing returns, diminishing returns and constant returns. Dr. Marshall was of the view that the law of diminishing returns applies to agriculture and the law of increasing returns to industry. Much time was wasted in discussion of this issue. However, it was later on recognized that there are not three laws of production. It is only one law of production which has three phases, increasing, diminishing and negative production. This general law of production was named as the Law of Variable Proportions or the Law of Non-Proportional Returns.

The Law of Variable Proportions which is the new name of the famous law of Diminishing Returns has been defined by Stigler in the following words:

"As equal increments of one input are added, the inputs of other productive services being held constant, beyond a certain point, the resulting increments of produce will decrease i.e., the marginal product will diminish".

According to Samuelson:

"An increase in some inputs relative to other fixed inputs will in a given state of technology cause output to increase, but after a point, the extra output resulting from the same addition of extra inputs will become less".

  

Assumptions:

The law of variable proportions also called the law of diminishing returns holds good under the following assumptions:

                       

(i) Short run. The law assumes short run situation. The time is too short for a firm to change the quantity of fixed factors. All the, resources apart from this one variable, are held unchanged in quantity and quality.

(ii) Constant technology. The law assumes that the technique of production remains unchanged during production.

(iii) Homogeneous factors. Each factor unit in assumed to he identical in amount and quality.

Explanation and Example:

The law of variable proportions is, now explained with the help of table and graph.

Schedule:

Fixed Inputs (Land Capital)	Variable Resource (labor)	Total Produce (TP Quintals)	Marginal        Product                (MP Quintals)		Average Product (AP Quintals)
30 30	1 2	10 25	10  15	Increasing marginal return	10 12.5
30 30 30 30 30	3 4 5 6 7	37 47 55 60 63	12 10 8 5 3	Diminishing marginal returns	12.3 11.8 11.0 10.0 9.0
3030	89	6362	0-1	Negative marginal returns	7.96.8

In the table above, it is assumed that a farmer has only 30 acres of land for cultivation. The investment on it in the form of tubewells, machinery etc., (capital) is also fixed. Thus land and capital with the farmer is fixed and labor is the variable resource.

As the farmer increases units of labor from one to two to the amount of other fixed resources (land and capital), the marginal as well as average product increases. The total product also increase at an increasing rate from 10 to 25 quintals. It is the stage of increasing returns.

The stage of increasing returns with the employment of more labor does not last long. It is shown in the table that with the employment of 3rd labor at the farm, the marginal product and the average product (AP) both fall but marginal product (MP) falls more speedily than the average product AP). The fall in MP and AP continues as more men are put on the farm.

The decrease, however, remains positive up to the 7th labor employed. On the employment of 7th worker, the total production remains constant at 63 quintals. The marginal product is zero. if more men are employed the marginal product becomes negative. It is the stage of negative returns. We here find the behavior of marginal product (MP). it shows three stages. In the first stage, it increases, in the 2nd it continues to fall and in the 3rd stage it becomes negative.                  

Three Stages of the Law:

There are three phases or stages of production, as determined by the law of variable proportions:

(i) Increasing returns.

(ii) Diminishing returns.

(iii) Negative returns.

Diagram/Graph:

These stages can be explained with the help of graph below:

(i) Stage of Increasing Returns. The first stage of the law of variable proportions is generally called the stage of increasing returns. In this stage as a variable resource (labor) is added to fixed inputs of other resources, the total product increases up to a point at an increasing rate as is shown in figure 11.1.

The total product from the origin to the point K on the slope of the total product curve increases at an increasing rate. From point K onward, during the stage II, the total product no doubt goes on rising but its slope is declining. This means that from point K onward, the total product increases at a diminishing rate. In the first stage, marginal product curve of a variable factor rises in a part and then falls. The average product curve rises throughout .and remains below the MP curve. 

                        

Causes of Initial Increasing Returns:

The phase of increasing returns starts when the quantity of a fixed factor is abundant relative to the quantity of the variable factor. As more and more units of the variable factor are added to the constant quantity of the fixed factor, it is more intensively and effectively used. This causes the production to increase at a rapid rate. Another reason of increasing returns is that the fixed factor initially taken is indivisible. As more units of the variable factor are employed to work on it, output increases greatly due to fuller and effective utilization of the variable factor.

(ii) Stage of Diminishing Returns. This is the most important stage in the production function. In stage 2, the total production continues to increase at a diminishing rate until it reaches its maximum point (H) where the 2nd stage ends. In this stage both the

marginal product (MP) and average product of the variable factor are diminishing but are positive.  

Causes of Diminishing Returns:

The 2nd phase of the law occurs when the fixed factor becomes inadequate relative to the quantity of the variable factor. As more and more units of a variable factor are employed, the marginal and average product decline. Another reason of diminishing returns in the production function is that the fixed indivisible factor is being worked too hard. It is being used in non-optima! proportion with the variable factor, Mrs. J. Robinson still goes deeper and says that the diminishing returns occur because the factors of production are imperfect substitutes of one another.

(iii) Stage of Negative Returns. In the 3rd stage, the total production declines. The TP, curve slopes downward (From point H onward). The MP curve falls to zero at point L² and then is negative. It goes below the X axis with the increase in the use of variable factor (labor).

Causes of Negative Returns:

The 3rd phases of the law starts when the number of a variable, factor becomes, too excessive relative, to the fixed factors, A producer cannot operate in this stage because total production declines with the employment of additional labor.

a rational producer will always seek to produce in stage 2 where MP and AP of the variable factor are diminishing. At which particular point, the producer will decide to produce depends upon the price of the factor he has to pay. The producer will employ the variable factor (say labor) up to the point where the marginal product of the labor equals the given wage rate in the labor market.

Importance:

The law of variable proportions has vast general applicability. Briefly:

(i) It is helpful in understanding clearly the process of production. It explains the input output relations. We can find out by-how much the total product will increase as a result of an increase in the inputs.

(ii) The law tells us that the tendency of diminishing returns is found in all sectors of the economy which may be agriculture or industry.

(iii) 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. The elasticity of the substitution of the variable factor for the fixed factor is not infinite.

From the law of variable proportions, it may not be understood that there is no hope for raising the standard of living of mankind. The fact, however, is that we can suspend the operation of diminishing returns by continually improving the technique of production through the progress in science and technology

Demand forecasting is the activity of estimating the quantity of a product or service that consumers will purchase. Demand forecasting involves techniques including both informal methods, such as educated guesses, and quantitative methods, such as the use of historical sales data or current data from test markets. Demand forecasting may be used in making pricing decisions, in assessing future capacity requirements, or in making decisions on whether to enter a new market.

Necessity for forecasting demand

Often forecasting demand is confused with forecasting sales. But, failing to forecast demand ignores two important phenomena. There is a lot of debate in demand-planning literature about how to measure and represent historical demand, since the historical demand forms the basis of forecasting. The main question is whether we should use the history of outbound shipments or customer orders or a combination of the two as proxy for the demand.

Stock effects

The effects that inventory levels have on sales. In the extreme case of stock-outs, demand coming into your store is not converted to sales due to a lack of availability. Demand is also untapped when sales for an item are decreased due to a poor display location, or because the desired sizes are no longer available. For example, when a consumer electronics retailer does not display a particular flat-screen TV, sales for that model are typically lower than the sales for models on display. And in fashion retailing, once the stock level of a particular sweater falls to the point where standard sizes are no longer available, sales of that item are diminished.

Market response effect

The effect of market events that are within and beyond a retailer’s control. Demand for an item will likely rise if a competitor increases the price or if you promote the item in your weekly circular. The resulting sales a change in demand as a result of consumers responding to stimuli that potentially drive additional sales. Regardless of the stimuli, these forces need to be factored into planning and managed within the demand forecast.

In this case demand forecasting uses techniques in causal modeling. Demand forecast modeling considers the size of the market and the dynamics of market share versus competitors and its effect on firm demand over a period of time. In the manufacturer to retailer model, promotional events are an important causal factor in influencing demand. These promotions can be modeled with intervention models or use a consensus to aggregate intelligence using internal collaboration with the Sales and Marketing functions.

Methods

No demand forecasting method is 100% accurate. Combined forecasts improve accuracy and reduce the likelihood of large errors. Reference class forecasting was developed to reduce error and increase accuracy in forecasting, including in demand forecasting.

Methods that rely on qualitative assessment

Forecasting demand based on expert opinion. Some of the types in this method are,

• Unaided judgment
• Prediction market
• Delphi technique
• Game theory
• Judgmental bootstrapping
• Simulated interaction
• Intentions and expectations surveys
• Conjoint analysis

Methods that rely on quantitative data

• Discrete Event Simulation
• Extrapolation
• Reference class forecasting
• Quantitative analogies
• Rule-based forecasting
• Neural networks
• Data mining
• Causal models
• Segmentation

Ex post studies of demand forecasts

Ex post studies compare actual with predicted outcomes of forecasts. Such studies generally find demand forecasts to be highly inaccurate. For instance, a statistically valid study of demand forecasts in 210 large public works projects, led by Oxford University professor Bent Flyvbjerg, found that for rail projects the average demand (passenger) forecast was overestimated by a full 106 percent. For roads, half of all demand (vehicle) forecasts were wrong by more than 20 percent; a fourth of forecasts were wrong by more than 40 percent

Elasticity of Demand

Meaning of Price Elasticity of Demand:

The law of demand is straight forward. It tells us when the price of a good rises, its quantity demanded will fall, all other things held constant. The law dose not indicate as to how much the quantity demanded will fall with the rise in price or how much responsive demand is to a rise price. The economists here use and measure the quantity demanded to a change in price by the concept of elasticity of demand.

What is Price Elasticity of Demand?

Definition:

Price elasticity of demand measures the degree of responsiveness of the quantity demanded of a good to a change in its price. It is also defined as:

"The ratio of proportionate change in quantity demanded caused by a given proportionate change in price".

Formula For Calculation:

Price elasticity of demand is computed by dividing the percentage change in quantity demanded of a good by the percentage change in its price.

Symbolically price elasticity of demand is expressed as under:

E_d =  Percentage Change in Quantity Demanded

 Percentage Change in Price

Simple formula for calculating the price elasticity of demand:

 E_d    =     %∆Q

               %∆P

Here:

E_d stands for price elasticity of demand.

Q stands for original quantity.

P stands for original price.

∆ stands for a small change.

Example:

The price elasticity of demand tells us the relative amount by which the quantity demanded will change in response to a change in the price of a particular good. For example, if there is a 10% rise in the price of a tea and it leads to reduction in its demanded by 20%, the price elasticity of demand will be:

E_d = -20

                                                               +10

E_d = -2.0

Degrees of Elasticity of Demand:

We have stated demand for a product is sensitive or responsive to price change. The variation in demand is, however, not uniform with a change in price. In case of some products, a small change in price leads to a relatively larger change in quantity demanded.

Elastic and Inelastic Demand:

For example, a decline of 1% in price leads to 8% increase in the quantity demanded of a commodity. In such a case, the demand is said to elastic. There are other products where the quantity demanded is relatively unresponsive to price changes. A decline of 8% in price, for example, gives rise to 1% increase in quantity demanded.Demand here is said to be inelastic.

The terms elastic and inelastic demand do not indicate the degree of responsiveness and unresponsiveness of the quantity demanded to a change in price.

The economists therefore, group various degrees of elasticity of demand into five categories.

(1) Perfectly Elastic Demand:

A demand is perfectly elastic when a small increase in the price of a good its quantity to zero. Perfect elasticity implies that individual producers can sell all they want at a ruling price but cannot charge a higher price. If any producer tries to charge even one penny more, no one would buy his product.

People would prefer to buy from another producer who sells the good at the prevailing market price of $4 per unit. A perfect elastic demand curve is illustrated in fig. 6.1.

Diagram:

It shows that the demand curve DD^/ is a horizontal line which indicates that the quantity demanded is extremely (infinitely) response to price. Even a slight rise in price (say $4.02), drops the quantity demanded of a good to zero. The curve DD^/ is infinitely elastic. This elasticity of demand as such is equal to infinity.

(2) Perfectly Inelastic Demand:

When the quantity demanded of a good dose not change at all to whatever change in price, the demand is said to be perfectly inelastic or the elasticity of demand is zero.

For example, a 30% rise or fall in price leads to no change in the quantity demanded of a good.

E_d = 0

       30%

E_d = 0

In figure 6.2 a rise in price from OA to OC or fall in price from OC to OA causes no change (zero responsiveness) in the amount demanded.

E_d = 0

       Δp

E_d = 0

(3) Unitary Elasticity of Demand:

When the quantity demanded of a good changes by exactly the same percentage as price, the demand is said to has a unitary elasticity.

For example, a 30% change in price leads to 30% change quantity demand =        30% / 30% = 1.

One or a one percent change in price causes a response of exactly a one percent change in the quantity demand.

In this figure (6.3) DD^/ demand curve with unitary elasticity shows that as the price falls from OA to OC, the quantity demanded increases from OB to OD. On DD^/demand curve, the percentage change in price brings about an exactly equal percentage in quantity at all points a, b. The demand curve of elasticity is, therefore, a rectangular hyperbola.

E_d = %∆q

      %∆p

 E_d = 1

(4) Elastic Demand:

If a one percent change in price causes greater than a one percent change in quantity demanded of a good, the demand is said to be elastic.

Alternatively, we can say that the elasticity of demand is greater than. For example, if price of a good change by 10% and it brings a 20% change in demand, the price elasticity is greater than one.

E_d = 20%

      10%

 E_d = 2

In figure (6.4) DD^/ curve is relatively elastic along its entire length. As the price falls from OA to OC, the demand of the good extends from OB to ON i.e., the increase in quantity demanded is more than proportionate to the fall in price.

E_d  = %∆q

        %∆p

E_d > 1

(5) Inelastic Demand:

When a change in price causes a less than a proportionate change in quantity demand, demand is said to be inelastic.

The elasticity of a good is here less than I or less than unity. For example, a 30% change in price leads to 10% change in quantity demanded of a good, then:

E_d = 10%

       30%

E_d = 1

        3

E_d < 1

In figure (6.5) DD^/ demand curve is relatively inelastic. As the price fall from OA to OC, the quantity demanded of the good increases from OB to ON units. The increase in the quantity demanded is here less than proportionate to the fall in price.

Note: It may here note that the slope of a demand curve is not a reliable indicator of elasticity. A flat slope of a demand curve must not mean elastic demand. Similarly, a steep slope on demand curve must not necessarily mean inelastic demand.

The reason is that the slope is expressed in terms of units of the problem. If we change the units of problem, we can get a different slope of the demand curve. The elasticity, on the other hand, is the percentage change in quantity demanded to the corresponding percentage change in price.

Measurement of Price Elasticity of Demand:

There are three methods of measuring price elasticity of demand:

(1) Total Expenditure Method.

(2) Geometrical Method or Point Elasticity Method.

(3) Arc Method.

These three methods are now discussed in brief:

(1) Total Expenditure Method/Total Revenue Method:

Definition, Schedule and Diagram:

The price elasticity can be measured by noting the changes in total expenditure brought about by changes in price and quantity demanded.

(i) When with a percentage fall in price, the quantity demanded increases so

much that it results in the increase in total expenditure, the demand is

said to be elastic (E_d > 1).

For Example:

Price Per Unit ($)	Quantity Demanded	Total Expenditure ($)
20	10 Pens	200.0
10	30 Pens	300.0

The figure (6.6) shows that at price of $20 per pen, the quantity demanded is ten pens, the total expenditure OABC ($200). When the price falls down to $10, the quantity demanded of pens is thirty. The total expenditure is OEFG ($300).

Since OEFG is greater than OABC, it implies that change in quantity demanded is proportionately more than the change in price. Hence the demand is elastic (more than one) E_d > 1.

(ii) When a percentage fall in price raises the quantity demanded so much as to

leave the total expenditure unchanged, the elasticity of demand is said to be

unitary (E_d = 1).

For Example:

Price Per Pen ($)	Quantity Demanded	Total Expenditure ($)
10	30	300
5	60	300

The figure (6.7) shows that at price of $10 per pen, the total expenditure is OABC ($300). At a lower price of $5, the total expenditure is OEFG ($300).

Since OABC = OEFG, it implies that the change in quantity demanded is proportionately equal to change in price. So the price elasticity of demand is equal to one, i.e., E_d = 1.

(iii) When a percentage fall in price raises the quantity demanded of a good so as to cause the total expenditure to decrease, the demand is said to be inelastic or less than one, i.e., E_d < 1.

For Example:

Price Per Pen ($)	Quantity Demanded	Total Expenditure ($)
5	60	300
2	100	200

In the fig (6.8) at a price of $5 per pen the quantity demanded is 50 pens. The total expenditure is OABC ($300). At a lower price of $2, the quantity demanded is 100 pens.

The total expenditure is OEFG ($200). Since OEFG is smaller than OABC, this implies that the change in quantity demanded is proportionately less than the change in price. Hence price elasticity of demand is less than one or inelastic.

Note:

As the demand curve slopes downward, therefore, the coefficient of price elasticity of demand is always negative. The economists for convenience sake, omit the negative sign and express the price elasticity of demand by positive number.

(2) Geometric Method/Point Elasticity Method:

"The measurement of elasticity at a point of the demand curve is called point elasticity".

The point elasticity of demand method is used as a measure of the change in the quantity demanded in response to a very small changes in price. The point elasticity of demand is defined as:

"The proportionate change in the quantity demanded resulting from a very small proportionate change in price".

Measurement of Geometric/Point Elasticity Method:

(i) Measurement of Elasticity on a Linear Demand Curve:

The price elasticity of demand can also be measured at any point on the demand curve. If the demand curve is linear (straight line), it has a unitary elasticity at the mid point. The total revenue is maximum at this point.

Any point above the midpoint has an elasticity greater than 1, (E_d > 1). Here, price reduction leads to an increase in the total revenue (expenditure). Below the midpoint elasticity is less than 1. (E_d < 1). Price reduction leads to reduction in the total revenue of the firm.

Graph/Diagram:

The formula applied for measuring the elasticity at any point on the straight line demand curve is:

E_d    =     %∆q    X     p

              %∆p           q

The elasticity at each point on the demand curve can be traced with the help of point method as:

E_d = Lower Segment

                                                      Upper Segment

In the figure (6.9) AG is the linear demand curve (1). Elasticity of demand at its mid point D is equal to unity. At any point to the right of D, the elasticity is less than unity (E_d < 1) and to the left of D, the elasticity is greater than unity (E_d > 1).

(1) Elasticity of demand at point D = DG = 400 = 1 (Unity).

                                                     DA     400

(2) Elasticity of demand at point E = GE = 200 = 0.33 (<1).

                                                     EA    600

(3) Elasticity of Demand at point C = GC = 600 = 3 (>1).

                                                      CA    200

(4) Elasticity of Demand at point C is infinity.

(5) At point G, the elasticity of demand is zero.

Summing up, the elasticity of demand is different at each point along a linear demand curve. At high prices, demand is elastic. At low prices, it is inelastic. At the midpoint, it is unit elastic.

(ii) Measurement of Elasticity on a Non Linear Demand Curve:

If the demand curve is non linear, then elasticity at a point can be measured by drawing a tangent at the particular point. This is explained with the help of a figure given below:

In figure 6.10, the elasticity on DD^/ demand curve is measured at point C by drawing a tangent. At point C:

E_d = BM = BC = 400 = 2 (>1).

        MO    CA    200

Here elasticity is greater than unity. Point C lies above the midpoint of the demand curve DD^/. In case the demand curve is a rectangular hyperbola, the change in price will have no effect on the total amount spent on the product. As such, the demand curve will have a unitary elasticity at all points.

(3) Arc Elasticity:

Normally the elasticity varies along the length of the demand curve. If we are to measure elasticity between any two points on the demand curve, then the Arc Elasticity Method, is used. Arc elasticity is a measure of average elasticity between any two points on the demand curve. It is defined as:

"The average elasticity of a range of points on a demand curve".

Formula:

Arc elasticity is calculated by using the following formula:

-

E_d = ∆q X P¹ + P²

                                                        ∆p    q¹ + q²

Here:

∆q denotes change in quantity.

∆p denotes change in price.

q¹ signifies initial quantity.

q² denotes new quantity.

P¹ stands for initial price.

P² denotes new price.

Graphic Presentation of Measuring Elasticity Using the Arc Method:

In this fig. (6.11), it is shown that at a price of $10, the quantity of demanded of apples is 5 kg. per day. When its price falls from $10 to $5, the quantity demanded increases to 12 Kgs of apples per day. The arc elasticity of AB part of demand curve DD^/ can be calculated as under:

E_d = ∆q X P¹ + P²

                                                        ∆p    q¹ + q²

E_d = 7 X 10 + 5 = 7 X 15 = 7 X 15 = 21 = 1.23

        5     5 + 12   5    17    5    17    17

The arc elasticity is more than unity.

Types of Elasticity of Demand:

The quantity of a commodity demanded per unit of time depends upon various factors such as the price of a commodity, the money income of the prices of related goods, the tastes of the people, etc., etc.

Whenever there is a change in any of the variables stated above, it brings about a change in the quantity of the commodity purchased over a specified period of time. The elasticity of demand measures the responsiveness of quantity demanded to a change in any one of the above factors by keeping other factors constant. When the relative responsiveness or sensitiveness of the quantity demanded is measured to changes, in its price, the elasticity is said be price elasticity of demand.

When the change in demand is the result of the given change in income, it is named as income elasticity of demand. Sometimes, a change in the price of one good causes a change in the demand for the other. The elasticity here is called cross electricity of demand. The three main types of elasticity of demand are now discussed in brief.

(1) Price Elasticity of Demand:

Definition and Explanation:

The concept of price elasticity of demand is commonly used in economic literature.Price elasticity of demand is the degree of responsiveness of quantity demanded of a good to a change in its price. Precisely, it is defined as:

"The ratio of proportionate change in the quantity demanded of a good caused by a given proportionate change in price".

Formula:

The formula for measuring price elasticity of demand is:

Price Elasticity of Demand = Percentage in Quantity Demand

                                       Percentage Change in Price

                                                         E_d = Δq X P

                                                                Δp    Q

Example:

Let us suppose that price of a good falls from $10 per unit to $9 per unit in a day. The decline in price causes the quantity of the good demanded to increase from 125 units to 150 units per day. The price elasticity using the simplified formula will be:

E_d = Δq X P

                                                            Δp    Q

Δq = 150 - 125 = 25

Δp = 10 - 9 = 1

Original Quantity = 125

Original Price = 10

E_d = 25 / 1 x 10 / 125 = 2

The elasticity coefficient is greater than one. Therefore the demand for the good is elastic.

Types:

The concept of price elasticity of demand can be used to divide the goods in to three groups.

(i) Elastic. When the percent change in quantity of a good is greater than the percent change in its price, the demand is said to be elastic. When elasticity of demand is greater than one, a fall in price increases the total revenue (expenditure) and a rise in price lowers the total revenue (expenditure).

(ii) Unitary Elasticity. When the percentage change in the quantity of a good demanded equals percentage in its price, the price elasticity of demand is said to have unitary elasticity. When elasticity of demand is equal to one or unitary, a rise or fall in price leaves total revenue unchanged.

(iii) Inelastic. When the percent change in quantity of a good demanded is less than the percentage change in its price, the demand is called inelastic. When elasticity of demand is inelastic or less than one, a fall in price decreases total revenue and a rise in its price increases total revenue.

(2) Income Elasticity of Demand:

Definition and Explanation:

Income is an important variable affecting the demand for a good. When there is a change in the level of income of a consumer, there is a change in the quantity demanded of a good, other factors remaining the same. The degree of change or responsiveness of quantity demanded of a good to a change in the income of a consumer is called income elasticity of demand. Income elasticity of demand can be defined as:

"The ratio of percentage change in the quantity of a good purchased, per unit of time to a percentage change in the income of a consumer".

Formula:

The formula for measuring the income elasticity of demand is the percentage change in demand for a good divided by the percentage change in income. Putting this in symbol gives.

                             

E_y = Percentage Change in Demand

       Percentage Change in Income

Simplified formula:

E_y = Δq X P

                                                            Δp    Q

Example:

A simple example will show how income elasticity of demand can be calculated. Let us assume that the income of a person is $4000 per month and he purchases six CD's per month. Let us assume that the monthly income of the consumer increase to $6000 and the quantity demanded of CD's per month rises to eight. The elasticity of demand for CD's will be calculated as under:

Δq  =  8 - 6 = 2                                   

Δp = $6000 - $4000 = $2000

Original quantity demanded = 6

Original income = $4000

E_y = Δq / Δp x P / Q = 2 / 200 x 4000 / 6 = 0.66

The income elasticity is 0.66 which is less than one.

Types:

When the income of a person increases, his demand for goods also changes depending upon whether the good is a normal good or an inferior good. For normal goods, the value of elasticity is greater than zero but less than one. Goods with an income elasticity of less than 1 are called inferior goods. For example, people buy more food as their income rises but the % increase in its demand is less than the % increase in income.

             

(3) Cross Elasticity of Demand:

Definition and Explanation:

The concept of cross elasticity of demand is used for measuring the responsiveness of quantity demanded of a good to changes in the price of related goods. Cross elasticity of demand is defined as:

"The percentage change in the demand of one good as a result of the percentage change in the price of another good".

Formula:

The formula for measuring, cross, elasticity of demand is:

E_xy = % Change in Quantity Demanded of Good X

          % Change in Price of Good Y

               

The numerical value of cross elasticity depends on whether the two goods in question are substitutes, complements or unrelated.

Types and Example:

(i) Substitute Goods. When two goods are substitute of each other, such as coke and Pepsi, an increase in the price of one good will lead to an increase in demand for the other good. The numerical value of goods is positive.

For example there are two goods. Coke and Pepsi which are close substitutes. If there is increase in the price of Pepsi called good y by 10% and it increases the demand for Coke called good X by 5%, the cross elasticity of demand would be:

E_xy = %Δq_x / %Δp_y =  0.2

Since E_xy is positive (E > 0), therefore, Coke and Pepsi are close substitutes.

(ii) Complementary Goods. However, in case of complementary goods such as car and petrol, cricket bat and ball, a rise in the price of one good say cricket bat by 7% will bring a fall in the demand for the balls (say by 6%). The cross elasticity of demand which are complementary to each other is, therefore, 6% / 7% = 0.85 (negative).

    

(iii) Unrelated Goods. The two goods which a re unrelated to each other, say apples and pens, if the price of apple rises in the market, it is unlikely to result in a change in quantity demanded of pens. The elasticity is zero of unrelated goods.

Factors Determining Price Elasticity of Demand:

The price elasticity of demand is not the same for all commodities. It may be or low depending upon number of factor. These factors which influence price elasticity of demand, in brief, are as under:

        

(i) Nature of Commodities. In developing countries of the world, the per capitalincome of the people is generally low. They spend a greater amount of their income on the purchase of necessaries of life such as wheat, milk, course cloth etc. They have to purchase these commodities whatever be their price. The demand for goods of necessities is, therefore, less elastic or inelastic. The demand for luxury goods, on the other hand is greatly elastic.

For example, if the price of burger falls, its demand in the cities will go up.

(ii) Availability of Substitutes. If a good has greater number of close substitutes available in the market, the demand for the good will be greatly elastic.

For examples, if the price of Coca Cola rises in the market, people will switch over to the consumption of Pepsi Cola, which is its close substitute. So the demand for Coca Cola is elastic.

(iii) Proportion of the Income Spent on the Good. If the proportion of income spent on the purchase of a good is very small, the demand for such a good will be inelastic.

For example, if the price of a box of matches or salt rises by 50%, it will not affect the consumers demand for these goods. The demand for salt, maker box therefore will be inelastic. On the other hand, if the price of a car rises from $6 lakh to $9 lakh and it takes a greater portion of the income of the consumers, its demand would fall. The demand for car is, therefore, elastic.

(iv) Time. The period of time plays an important role in shaping the demand curve. In the short run, when the consumption of a good cannot be postponed, its demand will be less elastic. In the long run if the rise price persists, people will find out methods to reduce the consumption of goods. So the demand for a good in the, long run is elastic, other things remaining constant.

For example if the price of electricity goes up, it is very difficult to cut back its consumption in the short run. However, if the rise in price persists, people will plan substitution gas heater, fluorescent bulbs etc. so that they use less^electricity. So the electricity of demand will be greater (E_d = > 1) in the long run than in the short run.

(5) Number of Uses of a Good. If a good can be put to a number of uses, its demand is greater elastic (E_d > 1).

For example, if the price of coal falls, its quantity demanded will rise considerably because demand will be coming from households, industries railways etc.

(6) Addition. If a product is habit forming say for example, cigarette, the rise in its price would not induce much change in demand. The demand for habit forming good is, therefore, less elastic.

(7) Joint Demand. If two goods are Jointly demand, then the elasticity of demand depends upon the elasticity of demand of the other Jointly demanded good.

For example, with the rise in price of cars, its demand is slightly affected, then the demand for petrol will also be less elastic.

Importance of Elasticity of Demand:

(1) Theoretical Importance:

The concept of elasticity of demand is very useful as it has got both theoretical and practical advantages. As regards its importance in the academic interest, the concept, is very helpful in the theory of value. In the words of Keynes:

"The concept of elasticity is so important that in the provision of terminology and apparatus to aid thought, I do not think, Marshall did any greater service than by the explicit introduction of the idea of the elasticity".

(2) Practical Importance:

(i) Importance in taxation policy. As regards its practical advantages, the concept has immense importance in the sphere of government finance. When a finance minister levies a tax on a certain commodity, he has to see whether the demand for that commodity is elastic or inelastic.

If the demand is inelastic, he can increase the tax and thus can collect larger revenue. But if the demand of a commodity is elastic, he is not in a position to increase the rate of a tax. If he does so, the demand for that commodity will be, calculated and the total revenue reduced.

(ii) Price discrimination by monopolist. If the monopolist finds that the demand for his commodities is inelastic, he will at once fix the price at a higher level in order to maximize his net profit. In case of elastic demand, he will lower the price in order to increase, his sale and derive the maximum net profit. Thus we find that the monopolists also get practical advantages from the concept of elasticity.

    

(iii) Price discrimination in cases of joint supply. The concept of elasticity is of great practical advantage where the separate, costs of Joint products cannot be measured. Here again the prices are fixed on the principle. "What the traffic will bear" as is being done in the railway rates and fares.

(iv) Importance to businessmen. The concept of elasticity is of great importance to businessmen. When the demand of a good is elastic, they increases sale by towering its price. In case the demand' is inelastic, they are then in a position to charge higher price for a commodity.

(v) Help to trade unions. The trade unions can raise the wages of the labor in an industry where the demand of the product is relatively inelastic. On the other hand, if the demand, for product is relatively elastic, the trade unions cannot press for higher wages.

(vi) Use in international trade. The term of trade between two countries are based on the elasticity of demand of the traded goods.

(vii) Determination of rate of foreign exchange. The rate of foreign exchange is also considered on the elasticity of imports and exports of a country. 

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(viii) Guideline to the producers. The concept of elasticity provides a guideline to the producers for the amount to be spent on advertisement. If the demand for a commodity is elastic, the producers shall have to spend large sums of money on advertisements for increasing the sales.

(ix) Use in factor pricing. The factors of production which have inelastic demand can obtain a higher price in the market then those which have elastic demand. This concept explains the reason of variation in factor pricing.