Intermediate Microeconomics

Professor Yongmin Chen

Topic 4. Individual Demand and Market Demand

The Equilibrium of the Consumer: Review

The consumer is in equilibrium, or her consumption choice is optimal, if any of the following is true:

(1) Given the budget constraint, the consumer has chosen the commodity bundle that maximizes her utility.

(2) The commodity bundle the consumer chooses is at the point where her indifference curve is tangent to her budget line.

(3) The consumer's marginal rate of substitution of X for Y is equal to the price of X over the price of Y.

(4) The ratio of the marginal utilities of any two goods is equal to their price ratio.

Effects of Changes in Income

When the consumer's income changes, her optimal choice of consumption will also change. We can analyze this in two steps:

First, a change in income shifts the budget line. If there is an increase in income, the budget line will shift out; and if there is a decrease in income, the budget line will shift in.

Second, after a shift in the budget line, the consumer finds a new consumption bundle at which her indifference curve is tangent to the new budget line.

(See a graphical illustration in class.) This way, we can find out the relationship between the equilibrium quantity purchased of a good and the level of income. This relationship is usually referred to as the Engel curve.

Example. The derivation of the Engel curve for a good.

For most goods, when income is higher, the consumer will purchase more of them. Such goods are called normal goods. In other words, a normal good is one whose Engel curve has a positive slope. The opposite of the normal good is the inferior good. A good is called an inferior good if the consumer will buy less of it with higher income.

Example. An inferior good.

Example. True or false: If a good is an inferior good, consumers will prefer less of it to more of it.

Example. Why should an investor be interested in the Engel curves of goods?

Effects of Changes in Price

When a commodity's price changes, the consumer's optimal choice of consumption will change too. Again, we can analyze this in two steps:

First, a change in a good's price rotates the budget line. If it is a price increase, the budget line will rotate inward; and if it is a price decrease, the budget line will rotate outward.

Second, after the budget line has rotated due to the price change, the consumer finds a new consumption bundle at which her indifference curve is tangent to the new budget line.

(See a graphical illustration in class.) This way, we can find out the relationship between the equilibrium quantity demanded of a good and the level of the good's price. This relationship, of course, is the consumer's demand curve.

Example. The derivation of the demand curve for an individual consumer.

Substitution and Income Effects

The effects of a price change on a consumer can be divided conceptually into two parts: the substitution effect and the income effect. Suppose there is an increase in the price of good X. As a result, the consumer will have a new budget line and will be on a lower level of satisfaction (indifference curve). Now imagine we can give the consumer some money so that she can achieve the same level of satisfaction as before, even though the price has increased. This occurs when we shift the new budget line to the right so that it is tangent to the consumer’s initial indifference curve again. However, since price has increased for good X, the consumer will now want to buy less of it, even if she would have the same level of satisfaction as before due to the imaginary increase in income. This change in the amount of X consumed by the consumer is called the substitution effect. Now if we move from this imaginary point back to the consumer’s actual consumption point after the price change, this would represent a movement that is caused purely by income change, and the change in the amount of consumption of the good associated with this movement is called the income effect. See explanation in class.

The substitution effect is always negative. That is, if the price of good X increases (decreases) and real income is held constant, there will always be a decrease (increase) in the consumption of good X. However, the income effect is less clear. For a normal good, an increase in real income would increase the consumption of the good, and for an inferior good it is to the contrary. Thus for a normal good, the effects of the substitution and income effects go in the same direction, which means that the price and quantity of a normal good is always inversely related (that is to say, the demand curve for a normal good is always downward sloping). If the good is an inferior good, the substitution and income effects will go in the opposite direction. Still, the substitution effect is usually dominating, and thus the demand curve is usually downward sloping even for an inferior good. But for an inferior good it is possible that price and quantity are positively related, and when that occurs, the situation is called the Giffen’s paradox. Since Giffen’s paradox can rarely occur in practice, in our analysis we shall always assume that the demand curve for a good is downward sloping, even if it is an inferior good.

Consumer Surplus

Consider a consumer's decision on buying sugar. Suppose for the first pound of sugar, he is willing to pay 60 cents. He is willing to pay 45 cents to buy one additional pound, and 30 cents to buy still another pound. Therefore, for three pounds of sugar, his total willingness to pay is 135 cents. Now if the price is 30 cents a pound, then he need only pay 90 cents to buy three pounds of sugar. In this case, we say the consumer receives 45 cents consumer surplus. The difference between what the consumer would be willing to pay and what the consumer actually has to pay is called consumer surplus. It is equal to the area under the demand curve and above the price line, from zero quantity to the quantity that is demanded under the price. (See graphical illustrations in class).

Consumer surplus is the basic measure of consumer welfare. It has important implications both for business decisions and public policies.

Example. Why would a shoe store sell you the second pair of shoes for the half price?

Example. Reduction in consumer surplus due to import quotas on sugar.

Deriving the Market Demand

We have seen how individual demand can be derived. To obtain the market quantity demanded for a good at each price, we add up the quantities demanded by all the individuals in the market. That is, the market demand curve for a good is the horizontal summation of the individual demand curves of all the consumers in the market.

Example. Suppose a market has only two consumers, one consumer's demand curve is Q = 10 - p and another consumer's demand curve is Q = 20 - 2p. What is the market demand?

The Sellers' Side of the Market:

From a seller's (a firm's) point of view, demand is important because it determines revenues. Suppose the quantity sold on the market is Q, and price is p, then total revenue is

TV = Qp

Marginal revenue is the additional revenue resulting from the sale of one additional unit.

MR = d(TR)/dQ

That is, marginal revenue is the slope of the total revenue curve.

Example. The graphs of total revenue and marginal revenue.

There is an important relationship between marginal revenue and the price elasticity of demand.

MR = p(1 + 1/h)

Example. Marginal revenue for the linear demand curve: Q = a - bp.

The demand curve a firm faces is often different from the market demand. There are two extreme cases. In the one end, there is only one firm in the market and thus the firm's demand coincides with the market demand. This is the case of monopoly. In the other end, there are many firms in the market and each firm can not influence the market price. This is the case of perfect competition.

Example. The demand curve and the marginal revenue curve of a perfectly competitive firm.

Measurement of Demand Curves

Industry analysts and firms often want to know the demand for particular commodities. There are several ways to undertake this task, and none seems to be perfect.

(1) Market experiments.

(2) Consumer interviews.

(3) Statistical techniques.

The typical problem one runs into in estimating market demand using statistical methods is the identification problem.

Example. Suppose you have collected some observations on prices and quantities purchased. Why might you not be able to estimate demand using only these data? Can you think of a method that, with some additional information, will enable you to estimate demand?

Example. The demand for steel is considered to be price elastic. According to some estimates, it is less than 0.4. Does this mean that the demand for the product of a steel company is also price inelastic? If a steel company produces a quantity at which the demand for its product is price inelastic, is this company maximizing profit?