Theories in Demand Analysis

12 months ago

Atiqur Rahman

18 minutes

Introduction

People demand goods and services in an economy to satisfy their needs. All goods & services have wants satisfying capacity which is known as a utility in economics. Utility is a highly subjective concept; it can differ from person to person.

Utility (level of satisfaction) is measured by means of introspection. By demand for goods & services, economists essentially mean willingness as well as ability of the consumer to procure and consume the goods & services.

Thus, demand for a commodity or service is dependent upon (a) its power to satisfy want or desire and (b) the capability of the potential consumer to pay for the good or service.

In a nutshell, therefore, we can state that when desire is backed by willingness and ability to pay for a good or service, then it becomes Demand for the good or service.

Conceptually, demand is nothing but a consumer’s readiness to satisfy desire by paying for goods or services. A desire accompanied by the ability and willingness to pay makes a real or effective demand.

Demand is one of the most significant decisions making variables in the present globalised, liberalized and privatized economy. Under this sort of economy, consumers & producers have a wide choice. There is full freedom for both that is buyers & sellers in the market. Therefore Demand reflects the size and pattern of the market.

The future of a producer depends upon the well-analyzed consumer demand. Even the firm does not want to make a profit as such but wants to devote itself to ‘customer services’ or ‘social responsibilities’. That is also not possible without evaluating the consumer’s tastes, preferences, choices etc. All these things are directly built into the economic concept of demand.

The survival and growth of any business enterprise depend upon the appropriate analysis of demand for its product in the market. Demand analysis has thoughtful significance to management for the day-to-day functioning and expansion of the business. Thus the short-term & long-term decisions of the management are dependent upon the trends in demand for the product. Any rise or fall in demand for the product has to be to find out reasons and revised production plans, technology or change in the advertisement, packaging, quality etc.

The market system works in an orderly manner because it is governed by certain Fundamental Laws of the Market, known as the Law of Demand and Supply. The demand & supply forces determine the price of goods and services in the market. The laws of demand & supply play a very important role in economic analysis.

Thomas Carlyle, the famous 19th-century historian, remarked, “It is easy to make parrot learned in economics; teach a parrot to say demand and supply.”

The most important function of microeconomics is to explain the laws of demand & supply, market mechanism and the working of the price system.

The law of demand states that whenever the price of a product increases, then the demand for that product decreases and vice versa, provided other things remain constant. Here these other things are the Income of the individual, Price of related goods, Tastes & preferences, Population, Advertisement etc.

While studying the law of demand, the direct relationship between price and demand is studied. This is because, under the economic theory price of a product is considered the main determinant of demand in the short run period.

The law of diminishing marginal utility states that marginal utility, or the extra utility obtained from consuming a good, decreases as the quantity consumed increases. In essence, each additional good consumed is less satisfying than the previous one. This law is particularly important for insight into market demand and the law of demand. If each additional unit of a good is less satisfying, then a buyer is willing to pay less. As such, the demand price declines. This inverse law of demand relation between demand price and quantity demanded is a direct implication of the law of diminishing marginal utility.

A more advanced form of consumer demand theory involves the analysis of indifference curves. An indifference curve presents all combinations of two goods that provide an identical amount of utility. Hence a consumer is “indifferent” between consuming any combination of the two goods at any point on the curve. Indifference curve analysis relies on a relative ranking of preferences between two goods rather than the absolute measurement of utility (utils) derived from the consumption of a particular good.

Revealed Preference Theory, pioneered by economist Paul Samuelson, is a method of analyzing choices made by individuals, mostly used for comparing the influence of policies on consumer behaviour. These models assume that the preferences of consumers can be revealed by their purchasing habits.

Revealed preference theory came about because existing theories of consumer demand were based on a diminishing marginal rate of substitution (MRS). This diminishing MRS relied on the assumption that consumers craft consumption decisions to maximize their utility. While utility maximization was not a notorious assumption, the fundamental utility functions could not be calculated with great certainty. Revealed preference theory was a means to reconcile demand theory by defining utility functions by observing behaviour.

Pragmatic Approach to Demand Analysis

There are several economists who questioned the worth of various theories of consumer behaviour. Many economists have understood that the various approaches to utility are theoretically impressive. But it is challenging for economists to relate this theoretic approach to elucidate the intricacy of the real world.

Thus in order to keep away from this problem, many economists have used a pragmatic/practical approach to the theory of demand. Economists have acknowledged the law of demand, which states that there exists a negative relationship between price and quantity demanded. It implies that as price rises, quantity demanded decreases and vice versa.

The economists using the law of demand, formulated the demand functions directly on the basis of market data. They have formulated the demand functions without considering utility theory and the behaviour of the individual consumer.

Individual demand function shows the functional relationship between the demand for a commodity by an individual and its determinants. These determinants are the price of the good, the prices of related goods, the consumer’s income, the consumer’s taste & preference, the environmental factors and the expectations.

The individual demand function is represented as-

Q^d x = f (Px, Pr, Y, T, S, E)

Where,

Px = Pr ice of goods

Pr = Pr ice of related goods

Y = Consumersincome

T = Consumer’s taste and preferences

S = Environmental factors

E = Expectations

The term Q^dx stands for the quantity that the consumer demands of good X. It is determined by many factors, i.e. a multivariate relationship.

The demand function being a multi-variate function, is estimated using econometric methods. Such demand functions show the market behaviour of the consumers, i.e. it is the behaviour of all consumers as a group and not the behaviour of single individuals. In most cases, the demand function refers to a group of commodities, i.e. demand for food, demand for consumer durables, demand for commodities etc.

Economists face serious difficulties while estimating demand functions. The aggregation of individual demand makes the use of index numbers inevitable. The problems with the usage of index numbers are numerous. Besides this, there are several estimation problems which impair the reliability of the demand functions estimated statistically.

One of the major difficulties arises when all the determinants of demand change simultaneously, making it extremely difficult to assess the influence of each factor separately. There has been continuous improvement in econometrics techniques, and demand functions are easily estimated using these techniques.

Constant Elasticity Demand Function:

The constant elasticity demand functions are the functions that are widely used in applied research and have constant elasticity. It can be written in functional form as:

This demand function is known as the constant elasticity of demand function because, in this functional form, the coefficients b,c and d are the price, cross and income elasticity of demand which are assumed to remain constant.

Let us prove that the elasticity of demand remains unchanged under the constant elasticity of demand function.

Proof: Let us first prove that b is the price elasticity of demand which remains constant. In order to prove this, first express the above functional form in logarithm form and then partially differentiate the function.

Constant Elasticity Demand Function Proof

Here it is obvious that if prices and income are changing by the same proportion, say by t percent. This change in income and price will not affect the quantity demanded as t will appear in both the numerator and denominator of the real income and relative price and thus cancel out. There is no change in quantity demanded. It implies that there is no money illusion in consumer behaviour.

Distributed Lag Models of Demand- Dynamic version of Demand Functions:

The dynamic version of the demand function is shown with distributed lag models of demand. The current development in demand theory is the expression of demand function in dynamic form. The reason behind the inclusion of lagged variables is that current purchasing decisions are influenced by the past behaviour of individuals.

Dynamic demand functions include lagged values of income & quantity demanded as a separate variables influencing the demand in any particular period. In order to express the demand function in a dynamic form, we must assume a particular relation between the past and the present.

One of the most vital relationships is that current purchasing behaviour depends upon past levels of demand and past levels of income. We can classify this as demand for durable goods & non-durable goods. If the commodity is durable, then past purchases represent the stock of this commodity which clearly affects the current and future purchases of the product.

On the other hand, if the commodity is non-durable, then past purchases represent the habit of the consumer, which is acquired by purchasing and consuming the commodity in the past. Thus, this clearly affects current and future purchases of the product. These are the factors that are incorporated into the demand function to make it dynamic.

Another major assumption is that the past level of income or demand has a greater influence on present consumption patterns than the more remote ones.

The demand functions which include lagged values of demand or of income are called distributed lagged models. The distributed lagged function can be expressed as:

𝑄_𝑥(𝑡) = 𝑓{𝑃_𝑥(𝑡), 𝑃_{𝑥(𝑡−1)}, … … … , 𝑄_{𝑥(𝑡−1)}, 𝑄_{𝑥(𝑡−2)}, … … … , 𝑌_(𝑡), 𝑌_(𝑡−1), … … }

Here the quantity demanded of good X depends not only on the current period rice and income but also on past levels of demand and prices. The necessity of a dynamic approach has been recognized for the study of certain consumer durable commodities.

The usage of dynamic formulation has been extended to a wide range of commodities by Richard Stone. His work was published in “The Durability of Consumers Durable Goods” in Econometrica in 1960. The generalization of the dynamic demand function was given by Houthakkar and Taylor. They published their work in “Consumer demand in the United States” in 1966.

Nerlove has developed a model which is based on the stock adjustment principle. This model is used extensively in demand functions as well as investment functions. This model was initially used to study demand functions for consumer durables. Recently the extension of the stock adjustment principle to non-durable goods has been done by Houthakkar and Taylor. This extension of the stock adjustment principle is named as ‘habit creation principle’.

Nerlove’s Stock Adjustment Principle:

Nerlove has developed a model which is based on the stock adjustment principle. It is also known as the partial adjustment model. In his work on demand analysis for agriculture and other commodities, Nerlove suggested the partial adjustment model with a constant speed of adjustment to justify the specification of distributed lags. This model is used extensively in demand functions as well as investment functions.

This model is based on some behavioural assumptions:

There exists a desired level of capital stock that an entrepreneur requires to have a smooth production process.
The desired level of capital stock is determined by the variables that are controlling output, such as price and cost.
The model of desired capital stock cannot be estimated because it is unobservable.

The demand function when Nerlove’s stock adjustment model is applied to consumer durables can be written in the form:

𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑚𝑜𝑑𝑒𝑙: 𝑄(𝑡) = 𝑎. 𝑌(𝑡) + 𝑏. 𝑄(𝑡−1)

There is a desired level of durable goods which is given as 𝑄𝑡∗. This desired level of durable goods is determined by the current level of income. This can be written as-

𝑄_𝑡^∗ = 𝑐. 𝑌_(𝑡) …………(1)

It is very difficult for the consumer to acquire the desired level of durables immediately due to limited income, limited credits etc. Thus, the consumers acquire only a part of the desired level in each period. The acquisition of the desired level of durables by consumers is gradual. So, in each period, we come closer to 𝑄_𝑡^∗.

In each period, the consumer purchases a certain quantity 𝑄_(𝑡). The quantity that is purchased by the consumer in the previous period is denoted by 𝑄_(𝑡−1). The actual change in the quantity from the previous period is the difference 𝑄_(𝑡) − 𝑄_(𝑡−1). This change in actual purchases is only a fraction K of the desired change, 𝑄_𝑡^∗ − 𝑄_(𝑡−1). Thus, the actual change is a fraction of desired change and can be written as-

𝐴𝑐𝑡𝑢𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 = 𝐾 (𝐷𝑒𝑠𝑖𝑟𝑒𝑑 𝐶ℎ𝑎𝑛𝑔𝑒)

[𝑄_(𝑡) − 𝑄_(𝑡−1)] = 𝑘[𝑄_𝑡^∗ − 𝑄_(𝑡−1)]……(2)

Where K is the coefficient of stock adjustment. This is the expression of stock adjustment. The value of the coefficient of stock adjustment lies between 0 and 1. Let us substitute equation (1) in the stock adjustment expression we obtain,

[𝑄(𝑡) − 𝑄(𝑡−1)] = 𝑘[𝑐. 𝑌(𝑡)– 𝑄(𝑡−1)]

Rearranging the terms, we get

𝑄_(𝑡) = (𝑘𝑐)𝑌_(𝑡) + (1 − k) 𝑄_(𝑡−1)

Now assume kc=a and (1-k)=b, we obtain the stock adjustment in its final form as:

𝑄(𝑡) = 𝑎. 𝑌(𝑡) + 𝑏. 𝑄(𝑡−1)

Houthakkar’s and Taylor’s Dynamic Model:

The model of Houthakkar and Taylor is based on Nerlove’s formula. They have extended the analysis of stock adjustment to non-durable goods. The current demand for durable goods depends on the stock of such commodities.

On the other hand, the current demand for non-durable goods depends upon the purchases of the commodities in the past. This is so because if the commodity is non-durable, then past purchases represent the habit of the consumer, which is acquired by purchasing and consuming the commodity in the past.

Thus, this clearly affects current and future purchases of the product. This would lead to the habit formation process. The demand function in the case of non-durable goods can be written as:

𝑄_𝑡 = 𝑎 + 𝑏. 𝑃_𝑡 + 𝑐. ∆𝑃_𝑡 + 𝑑. 𝑌_𝑡 + 𝑒. ∆𝑌_𝑡 + 𝑓. 𝑄_𝑡−1

Where,

Q is quantity demanded in period t

𝑃_𝑡 is the price in period t

∆𝑃_𝑡 is the change in price between period t and t-1.

𝑌_𝑡 is the income in period t

∆𝑌_𝑡 is the change in income between period t and t-1.

The demand function can be derived in the following steps. Let us proceed with the demand for a product in a particular period. Demand for a product in a particular period depends upon three factors-price of a product, the stock of the commodity and on the current level of income. This can be expressed as:

𝑄_𝑡 = 𝑔 + ℎ. 𝑃_𝑡 + 𝑖. 𝑆_𝑡 + 𝑗. 𝑌_𝑡

Where,

𝑄_𝑡 is the demand for the product in period t

𝑃_𝑡 is the price in period t

𝑌_𝑡 is the income in period t

𝑆_𝑡 is the stock of durable if the demand function refers to durable goods

𝑆_𝑡 is the stock of non-durable if the demand function refers to non-durable goods

The sign of the coefficient of 𝑆 can be negative or positive. The coefficient of 𝑆 in the case of durables will be negative. This is so because the more quantity the consumer has, the lesser the demand for such commodities. The more the quantity of wooden products and electronic gazettes we have, the lesser the demand for these products. Thus, in the case of durables, the sign of 𝑆 is negative, i.e. possessing a negative relationship.

The coefficient of 𝑆 in the case of durables will be positive. This is because of our habits. The higher our purchases of non-durable goods, the stronger our habit becomes. Thus, in the case of non-durables, the sign of S is positive, i.e. possessing a positive relationship.

The stock, 𝑆 cannot be measured. This is because of two reasons. First, the stock of durable goods is composed of various heterogeneous items. They may be of various ages. For example, the gazette is not of the same age as any electronic equipment. Some products may be so old and need replacement. Some products are new. Some need to be scrapped etc. It is very difficult to measure stock because of this heterogeneity. We want to have stocks which are the sum of depreciated inventories of durable goods. But the appropriate deprecation rates are not known. Second, the stock of non-durables, i.e. the stock of habits, is a psychological variable and cannot be quantified.

As stock cannot be measured so we can eliminate algebraically stocks from the demand function and replace it with other measurable variables by making some reasonable assumptions.

Linear Expenditure System

A linear expenditure system is a model which deals with groups of commodities rather than individual commodities. The addition of all such groups yields total consumer expenditure. Linear expenditure system is widely used in aggregate econometric models where they provide disaggregation of the consumption function as desired.

One of the model earliest models of a linear expenditure system was suggested by Richard Stone in 1954. The linear expenditure system was formulated on the basis of the utility function. The demand function under this model is derived by maximizing the utility function subject to budget constraints.

The approach of this model is the same as like approach of the indifference curve. The indifference curve approach is basically used for handling commodities which are substitutes. On the other hand, a linear expenditure system is applied to a group of commodities between which substitution is not possible.

The utility function is additively showing that the total utility is the sum of utilities derived from various groups of commodities. Additivity implies that the utilities of various groups are independent.

Theories in Demand Analysis

Introduction

Pragmatic Approach to Demand Analysis

Constant Elasticity Demand Function:

Distributed Lag Models of Demand- Dynamic version of Demand Functions:

Nerlove’s Stock Adjustment Principle:

Houthakkar’s and Taylor’s Dynamic Model:

Linear Expenditure System

Read More- Microeconomics

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Introduction

Pragmatic Approach to Demand Analysis

Constant Elasticity Demand Function:

Distributed Lag Models of Demand- Dynamic version of Demand Functions:

Nerlove’s Stock Adjustment Principle:

Houthakkar’s and Taylor’s Dynamic Model:

Linear Expenditure System

Read More- Microeconomics

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