**Alfred Marshall Demand, Alfred Marshall Theories Definition**

Marshall's suggestion that the influence of demand on price determination is relatively easy to analyze may well be correct. Yet there were problems with the theory of demand that Marshall was not able to solve satisfactorily. He seemed to recognize these difficulties and avoided them by assumption. His most important contribution to demand theory was his clear formulation of the concept of price elasticity of demand. Price and quantity demanded are inversely related to each other; demand curves slope down and to the right. The degree of relationship between change in price and change in quantity demanded is disclosed by the coefficient of price elasticity. The coefficient of price elasticity is

eD = - percent change in quantity demanded / percent change in prices = (Ap/p) / (Aq/q)

Because price and quantity demanded are inversely related, the computed price elasticity of demand coefficient would be negative. By convention, to express the coefficient as a positive number, a negative sign is added to the right side of the equation. The price of a product times the quantity demanded will equal the total expenditure of the buyers or, alternatively, the total revenues of the seller (p x q = TE = TR). If price decreases by 1 percent and quantity demanded increases by 1 percent, total expenditure, or revenue, will remain unchanged and the coefficient will have a value of 1. If price decreases and total expenditure or revenue increases, the coefficient will have a value greater than 1 and the commodity is said to be price elastic. If the price decreases by a given percentage and quantity demanded increases by a smaller percentage, total expenditure or revenue will decrease, the coefficient will have a value less than 1, and the commodity is said to be price inelastic. Marshall also applied the elasticity concept to the supply side, and in so doing gave economics another extremely useful tool. Although the notion of price elasticity had been suggested in earlier literature, it was Marshall, with his mathematical ability, who was able to express it precisely; he is therefore considered its discoverer.

According to Marshall, individuals desire commodities because of the utility received through their consumption. The form of the utility function used by Marshall was additive; that is, he derived total utility by adding the utilities received from consuming each good. The utility received from consuming good A depends solely on the quantity of A consumed, not on the quantities of other goods consumed. Thus, substitution and complementary relationships are ignored. An additive utility function is given as

U = f1qA + f2qB + f3qc +......+fnqN

The utility function used in contemporary practice explicitly recognizes complementary and substitute relationships and is expressed as

U= f(qA, qB, qC,......, qN)

F. Y. Edgeworth and Irving Fisher, two of Marshall's contemporaries, suggested the more generalized utility function now used. The most important implication of Marshall's use of the additive utility function, which we will discuss shortly, concerns income effects.

Marshall assumed that utility was measurable through the price system. If an individual pays $2 for another unit of good A and $1 for another unit of good

B, then A must give twice the utility of B. He also argued that intergroup comparisons of utility were possible because in group comparisons, personal peculiarities are washed out.

In Marshall's framework, the most important task of the theory of demand is to explain the shape of the demand curve. If a commodity's marginal utility decreases as more of the commodity is consumed, does it follow that individuals will pay lower prices for larger quantities? Are demand curves, then, negatively sloped? Marshall accepted diminishing marginal utility (Gossen's First Law) and formulated the equilibrium condition that would give maximum utility for an individual consuming many commodities (Gossen's Second Law):

MUa/Pa= MUb/Pb=........ MUn/Pna=MUm

In equilibrium, the consumer will spend in such a way that the last dollar spent for any final good will have the same marginal utility as that spent for any other good. The ratios of these marginal utilities to prices will be equal to, and thus disclose, the marginal utility of money. The marginal utility of money is the marginal utility received from the last dollar of expenditure. If saving is considered as a good, then the marginal utility of money is the utility received from the last dollar of income. The marginal utility of a single good is equal to its price times the marginal utility of money:

MUa= Pa * MUm

Let us work through the derivation of a demand curve in order to see some of the problems encountered and Marshall's solution to these problems. If we begin with an individual who is maximizing utility and then lower the price of one good, we can derive the relationship between price and quantity demanded. Using Equations (11.1) and (11.2), we see that lowering the price, PA, of good A will lead to an increase in quantity demanded only under certain conditions. Lowering the price of good A will have two effects. The substitution effect reflects the fact that good A is now relatively cheaper than its substitutes, and so the individual's consumption of good A will increase. The substitution effect will always lead to greater consumption at lower prices and less consumption at higher prices. The income effect produced by price changes is more complex. Lowering the price of good A increases an individual's real income. With the lower price, the individual can buy the same quantity of good A as before and have income left over that can be spent on good A or on other goods. For example, if the price of good A was $ 1 and 10 units were previously purchased, lowering the price of good A to $0.90 increases real income by $1.00. A normal good is one whose consumption increases with increases in income. If good A is a normal good, its demand curve will slope down and to the right. Lowering its price will increase the quantity demanded through both the substitution effect and the income effect.

If good A is an inferior good, other complications occur. An inferior good is one whose consumption decreases with increases in income. Hamburger might well be an inferior good in a consumer's budget. As income increases, the quantity of hamburger consumed will decrease as better cuts of beef replace hamburger. If good A is an inferior good, then a fall in its price will lead to an increase in its consumption because of the substitution effect, but a decrease in its consumption because of the income effect. If the substitution effect is stronger than the income effect, the demand curve will be negatively sloped; but if the income effect is stronger than the substitution effect, the demand curve will be positively sloped. The possibility of upward-sloping demand curves is extremely disturbing to the theory of demand. The theoretical possibility exists, but no empirical information has yet been produced to indicate the actual occurrence of upward-sloping demand curves.

Marshall first stated the general law of demand: "The amount demanded increases with a fall in price, and diminishes with a rise in price."17 He then noted that information gathered by Robert Giffen suggests that the demand curve of poorer individuals for bread may slope up and to the right. In other words, for these individuals, a rise in the price of bread results in a reduction in the consumption of meat and of more expensive foods, and a rise in the consumption of bread. For this reason, inferior goods with a more powerful income effect than substitution effect are referred to as Giffen goods in the theoretical literature. Again, although there is a considerable Body of theoretical literature on the so-called Giffen paradox, no acceptable statistical information showing actual upward-sloping demand curves has been produced.

Let us return to the theoretical problems of deriving demand curves and how Marshall handled them. Because he worked with an additive utility function, he ignored substitution and complementary relationships in his formal mathematical treatment of deriving demand curves—although, characteristically, he did discuss these issues. Marshall simply assumed that the income effect of small price changes is negligible; that is, that the marginal utility of money remains constant for small changes in the price of any single commodity. Thus, if we lower the price of good A in Equation (11.1), quantity demanded increases and the marginal utility of good A decreases until the ratio MUa/Pa is brought into equality with the ratios for other commodities, and all are again equal to the constant marginal utility of money. Marshall's procedure can be studied from another perspective. Using Equation (11.2), a fall in the price of good A (assuming that the marginal utility of money is constant) must lead to an increase in its consumption because of the principle of diminishing marginal utility.

Marshall had two reasons for dismissing these theoretical difficulties by assuming that the marginal utility of money was constant: first, he did not have the theoretical tools to distinguish clearly between the substitution and income effects; second, he claimed that the income effect of minor changes in the price of a good was so small that no harm was done by ignoring it.