MBA 7003 1.1 Basic Conditions Demand

1.1 Demand

Utility Function

Utility

Indifference Curve

Income Consumption & Engels Curves

Price Consumption & Demand Curves

Elasticity

Symbolic Summary of Demand

Industrial Organization begins with Basic Conditions of Demand and Supply. Demand comes from consumers (final and intermediary) while Supply is generated by producers using factors of production and technology. Supply and Demand are the two side of the economic equation.

Demand in economics refers to the willingness of a consumer to pay a given price for a given quantity of a good or service. This reflects the taste of the consumer, i.e., one’s wants, needs and desires subject to a budget constraint – income and prices – assuming the price of other goods and services remain fixed.

Modern economics began with Demand or consumer theory which was then extended to Supply or producer theory and finally to their interaction in different types of Markets. Or as the great American criminal entrepreneur Al Capone said: If there is a Demand there will be a Supply! In this section we will examine the Consumption/Utility Function of the individual consumer. We will then derive the Income Consumption Curve from which the Engels Curve (income demand curve) will be derived. We will then derive the Price Consumption Curve from which we will then derive the Demand Curve itself.

The standard model of market economics rests on the philosophical base laid down by Jeremy Bentham (1748 -1832). His was the last great philosophy of the European Enlightenment (Schumpeter 1954). All is sensation; there is no god. Human beings seek pleasure and avoid pain. Bentham, in his felicitous calculus’ or the calculus of human happiness, proposed a unit measure of pleasure and pain –the utile – the sovereign ruler of the state. Utilitarianism is the generic term but Bentham’s brand is ethical hedonism –ethical pursuit of pleasure. It was in the 1870s that Bentham’s felicitous calculus was married to Newton’s calculus of motion permitting erection of the standard model of market economics.

This atom-like unit, the utile, exhibits distinct characteristics. First, and for Economics most important, the willingness of a person to pay a money price for a good or service measures how many utiles of happiness they expect to receive in exchange. This is reification – making concrete (money) something that is abstract (happiness). Furthermore, it is assumed that goods are infinitely divisible.

Second, total utility is the satisfaction of consuming a total quantity of a good or service.

Third, marginal utility is the additional utility yielded by consuming one more unit of that good or service.

Fourth, diminishing utility means that at some level of consumption an additional unit yields less satisfaction than the preceding unit, i.e. total utility increases but eventually at a decreasing rate. Furthermore, diminishing marginal utility eventually turns negative becoming pain not pleasure, too much of a good thing;

Fifth, diminishing marginal utility means a person does not consume just one good. One does not live by bread alone. Assuming rationality, a person chooses that combination of two or more goods and services that maximizes total utility. This is calculatory rationality meaning every choice is a calculation of the number and nature of utiles, a.k.a., happiness or pleasure.

Furthermore, in theory, the consumer is assumed rational, i.e., one chooses between alternative commodity combinations to maximize utility assuming:

i - perfect knowledge, that is, the consumer is aware of all alternative commodity combinations, their prices and resulting utility;

ii - competence, that is, a consumer is capable of evaluating the alternatives; and,

iii – taste of a consumer is transitive or consistent, that is, if a consumer likes A as much as B and B as much as C then one likes C as much as A.

It is also assumed that the consumer is only able to order commodity combinations by level of utility, 1st, 2nd, 3rd etc. This is called ordinal measurement or rank ordering. Thus in consumption one does not specify the actual numeric level or utility known as cardinal measurement.

Putting all these definitions and assumptions together we generate the consumption function as:

U is continuous meaning there are infinite combinations yielding the same level of utility. Put another way, U is a dense set;

a number assigned to commodity combinations such as U5 indicates only that it is preferable to combinations with a lower number, e.g., U4 and inferior to U6. In other words, we can rank order preferences but any U# has no cardinal meaning; and,

U is defined for a specified timeframe that is long enough to allow substitution between commodity combinations but short enough to insure constancy of taste

For any level of utility say U’ = f (x, y) there is a locus of commodity combinations which graphically form an indifference curve. All combinations on that curve have the same level of utility meaning the consumer is ‘indifferent’ to any point on the curve. The indifference curve is also called a preference or utility curve.

Usually an indifference curve is ‘convex’ in shape reflecting that an increase in x can only be obtained by a reduction in y, and vice versa (B&P 4th Ed Fig. 9.3; 5th ED Fig. 8.3; 7th Ed. Fig. 9.3; R&L 13th Ed Fig. 6A-1 & A2). The amount of Y that must be given up to get more X while maintaining the same level of utility is called the marginal rate of substitution, i.e.,

As noted above ‘f’ in the equation U = f (x, y) is the taste function which is different for each consumer. Thus each consumer will have a uniquely shaped indifference curve and different MRS. When we plot all possible levels of U we get a set of curves forming a consumer’s indifference map. The transitivity assumption ensures the curves do not intersect but rather rise higher and higher.

Before considering the Budget Constraint it is appropriate to consider the nature of goods purchased by a consumer and how they are able to pay their prices. Commodities are called ‘goods’ because they satisfy human want, needs and desires.

Goods can be classified in different ways. First, there are complementary and substitute goods. Complementary goods are one that are consumed together, e.g., hamburgers and French fries or IPods and IPod docking stations. Substitute goods are alternatives to one another, e.g., a bicycle is a substitute for a car in transportation. There are near and distant substitutes for most goods, e.g., a car or a truck are near substitutes while a car and a bicycle are distant substitutes.

Second, there are normal and inferior goods. A normal good is one the consumption of which increases as income increases. An inferior good is one the consumption of which decreases as income increases. An example of an inferior good is cheap wine. As one’s income increases consumption of cheap wine tends to decline.

Third, there are conspicuous consumption or Veblen goods (named after economist Thorstein Veblen) and normal consumption goods. Veblen goods are rare and their consumption goes up as price goes up in distinction from normal goods whose consumption goes down as price goes up. Conspicuous consumption goods are bought to demonstrate to others that one can afford such luxuries.

To buy a good a consumer must pay its price. Further to Bentham’s assumption, the money price one is willing to pay for a good or service equals the satisfaction or utility one believes can be extracted from that good.

To pay a price, however, one must have income. Income is earned through work which in the standard model is disutility, i.e., pain. One does not work for enjoyment (if one does one earns ‘psychic’ income) but rather for the monetary income used to buy goods and thereby derived satisfaction.

While a consumer wants to rise as high up the indifference map as possible, one is constrained by income (I) and the price of x and y. Thus for a given level of income and prices a budget line or constraint can be drawn. This constraint shows all combinations that can be purchased that exhaust income, i.e.,

One cannot consume above the constraint and, in this model, it is irrational to consume below (keeping cash on hand) because utility is derived only from consuming goods & services.

The maximum amount of X or Y one can afford (with a given income and prices) is shown by the intercepts of the budget line and respective axes. The slope of the budget line (rise over run) is the inverse of the price ratio, i.e.,

The slope itself is Py/Px expressed as 1/(Px/Py). This formulation is a ‘convention’ or tradition in economics. It represents the relative price of X and Y, i.e., how many units of X can be bought with one unit of Y at current prices, e.g., $2/$1= a relative price of 2.

If income varies while prices remain fixed then a new higher budget line becomes available to the consumer parallel to the original. In other words higher income relaxes the constraint on one’s happiness. If, on the other hand, the price of X (or Y) decreases the slope of the budget line and therefore the price ratio changes. For example if Px goes down then the intercept which measures the maximum amount of x a consumer can afford increases even if income remains constant.

The combination of x and y that maximizes a consumer’s utility is the one on the budget line tangent or just touching the highest attainable indifference curve (P&B 4th Fig. 9.4; 5th 8.4; 7th Ed Fig. 9.4; R&L 13th Ed Fig. 6A-1). This is the ‘best affordable point’ (P&B 4th Fig. 9.6; 5th 8.6; 7th Ed Fig. 9.6; R&L 13th Ed Fig. 6A-4) and satisfies the following conditions:

that is the slope of the indifference curve or Marginal Rate of Substitution equals the slope of the Budget Line or the inverse of the price ratio (Px/Py) and at this point the ‘rationale’ consumer equates the MU per dollar of each commodity consumed or

dollar-for dollar the additional utility from an additional unit of X is equal dollar-for-dollar to the additional satisfaction from one more unit of Y (P&B 4th Fig. 8.3; 5th Fig. 7.3; 7th Ed not displayed; R&L 13th Ed not displayed).

Consumers will remain at this point, i.e., be in equilibrium, as long as taste, income and prices remain fixed. This is the initial equilibrium. It is a condition which once achieved continues indefinitely unless one of the variables is altered (P&B 4th Ed Fig. 4.8; 7th Ed Fig. 3.7; R&L 13th Ed not displayed). For our purposes there are two types:

a) stable equilibrium: which refers to a condition which once achieved continues indefinitely unless there is a change in some underlying conditions. Changes in economic conditions will be followed by reestablishment of the original equilibrium. Example: a ball resting at the bottom of a cup; shake it and the ball moves; stop shaking and it returns to the bottom of the cup; and,

b) unstable equilibrium: which refers to a condition which once achieved will continue indefinitely unless one of the variables changes but the system will not return to the original equilibrium. Example: a ball resting on the top of an overturned cup - shake it and the ball falls off never to return to the same place.

An increase in income shifts the intercepts of the budget line but leaves its slope constant - assuming constant prices. The locus of tangents of budget lines with indifference curves forms the income-consumption curve, i.e., the set of commodity combinations (x, y) consumed as income increases - assuming constant prices and taste (R&L 13th Ed Fig 6A-5).

From the income-consumption curve we can derive the amount of a given commodity (x) purchased at different levels of income. This forms the Engel Curve (M&Y Fig. 4.2; R&L 13th Ed not displayed) which, in effect, is the income demand curve for a good or service. The shape of the curve depends on the type of commodity. A normal good will have a positively sloped Engel Curve reflecting the fact that as income rises, consumption rises. An inferior good will have a negatively sloped Engel Curve reflecting that as income increases consumption decreases. An example is Kraft Dinner. For a poor student it is a cheap source of pasta and cheese but when the student becomes a well-paid junior executive of a Fortune 500 company it is no longer preferred.

In business it is critical to know if one’s product is a normal or inferior good. If consumer income rises then sales of a normal good will increase. In a recession, however, with falling consumer income sales of a normal good decrease while sales of an inferior good increase.

If the price of one commodity (X) changes a new set of combinations (X, Y) is created between the changing tangents of the budget line and indifference curves forming the price-consumption curve for the commodity. The price-consumption curve shows how much of both commodities are purchased if its price changes - assuming constant income and prices for all other goods (R&L 13th Ed Fig 6A-6).

The demand curve for a commodity (X) can be derived from the price-consumption curve showing how much of that commodity is purchased at different prices - assuming constant income and constant prices for the other good (Y). The shape of the demand curve (X) depends on taste, income and the type of commodity - assuming constant prices for the other good (Y) (P&B 4th Ed. Fig. 9.7; 5th Ed. Fig. 8.7; 7th Ed Fig. 9.7; R&L 13th Ed Fig 6A-7). The Law of Demand generally holds: the higher the price, lower the demand; lower the price, higher the Demand. Why? The Law of Diminishing Marginal Utility.

It is important to note that the change in price of one good or service (assuming income and prices of other goods remain fixed) has two effects. For example, as the price of one good (X) declines it becomes cheaper relative to Y. In equilibrium we have seen that consumers equates the marginal utility per dollar of each good, i.e., MUx/Px = MUy/Py. If the price of X goes down while the price of Y remains constant then dollar for dollar the consumer can get more utility by substituting x for the now more expensive y. This is called the substitution effect. This effect holds for both normal and inferior goods.

In addition, if the price of x goes down the consumer can now afford to buy the same amount but have money income left over. In effect income goes up allowing the purchase of more of both X and Y. This is called the income effect.

The substitution effect is always negative, that is if the price of a commodity (X) goes up, the quantity consumed goes down. The income effect can be positive or negative. For 'normal' goods, an increase in income results in an increase in consumption. If the quantity decreases when income increases the commodity is an 'inferior' good. In most cases, if the price of an inferior good decreases consumption will still increase if income rises.

Elasticity refers to the sensitivity of one variable to a one percentage change in another. Economic theory recognizes three principal types:

a) income elasticity of demand with prices constant refers to the percentage change in the quantity of a commodity demanded compared to a one percent change in income. If income goes up 1% what happens to demand? If it too goes up 1% there is unitary elasticity. If demand goes up more than 1% there is elastic demand; if it goes up less than 1% then there is inelastic income demand for the good or service (P&B 4th Ed, Fig 5.8; 7th Ed not displayed; R&L 13th Ed not displayed);

b) price elasticity of demand refers to the percentage change in the quantity of a commodity demanded compared to a one percentage change in its price. The amount demanded can increase:

i) more than proportionately, i.e. elasticity is greater than one - at the extreme a horizontal demand or supply curve is perfectly elastic - a small increase in price results in a large change in the quantity demanded or supplied;

ii) proportionately, i.e. elasticity is equal to one (unitary elasticity); or,

iii less than proportionately. i.e. elasticity is less than one (inelastic) - at the extreme, a vertical demand or supply curve is perfectly inelastic - any change in price results in no change in the amount of the commodity demanded or supplied (P&B 4th Ed. Fig. 5.8; 7th Ed Fig 4.3; R&L 13th ED. Fig. 4-2 & 4-3); and,

c) elasticity of substitution or cross-elasticity in the consumption of one commodity substituted for another by a consumer in response to a change in their relative prices (P&B 4th Ed Fig. 5.7; 7th Ed Fig. 4.6; R&L 13th Ed not displayed).

In conclusion, consumption is the use of a product whereby utility is destroyed. Put another way it is ‘negative production’. Producers put utility into a good or service to satisfy human wants, needs and desires then consumers extract it. Income is payment for work used to buy goods and services to obtain utility. Work is the physical or intellectual effort made to earn income to purchase products and thereby obtain utility. Price is the dollar and cents cost of a product which is assumed to represent the utility a consumer can derive from it.