The Theory of Consumer Choice

THE BUDGET CONSTRAINT: WHAT THE CONSUMER CAN AFFORD

•The budget constraint shows the limit on the consumption “bundles” that a consumer can afford.

•People consume less than they desire because their spending is constrained, or limited, by their income.

•The budget constraint shows the various combinations of goods the consumer can afford given his or her income and the prices of the two goods.

Any point on the budget constraint line indicates the consumer’s combination between two goods.

            

  Pı Xı + P2 X2 ≤  M

Where  Pı is the price of good Xı

            P2 is the price of good X2

                M is money income of the consumer.

The budget set

The set of bundles available to the consumer is called the budget set. The budget set is

 the collection of all bundles that the consumer can buy with her income at

the prevailing market prices.

The equation of the Budget Line is

Pı Xı + P2 X2 =  M  The line consists of all bundles which

cost exactly equal to M.

                                                                                                                               

Budget Set. Quantity of good 1 is measured

along the horizontal axis and quantity of good 2

is measured along the vertical axis. Any point in

the diagram represents a bundle of the two

goods. The budget set consists of all points on

or below the straight line having the equation

Pı Xı + P2 X2 =  M 

The slope of the budget line

•Pı Xı + P2 X2 =  M  

The slope of the budget constraint line equals the relative price of the two goods, that is, the price of one good compared to the price of the other. i.e.,

  -P1/P2

It measures the rate at which the consumer can trade one good for the other.

Changes in the Budget Set

When the price of either of the goods or the consumer’s income

changes, the set of available bundles is also likely to change. Suppose the

consumer’s income changes from M to M¹ but the prices of the two goods remain

unchanged. Now the equation of the budget line is

Pı Xı + P2 X2 = M¹

1. If only M  increases, Budget line shift to the right.

2. If only M decreases,  Budget line shift to the left.

CHANGE IN PRICE

1. If only P1  increases,  Budget line becomes  steeper.

2. If only P1 decreases, Budget line becomes  flatter.

1. If only P2 increases,  Budget line becomes  flatter.

2. If only P2 decreases,  Budget line becomes  steeper.

Monotonic Preferences

It means “more is better”. Preferences are monotonic if and only if between any two bundles, the consumer prefers the bundle which has more of at least one of the goods and no less of the other good as compared to the other bundle.

Diminishing Rate of Substitution

As the amount of good 1 increases, the rate of substitution between good 2 and good 1 diminishes. Preferences of this kind are called convex preferences.

PREFERENCES: WHAT THE CONSUMER WANTS

A consumer’s preference among consumption bundles may be illustrated with indifference curves.

•An indifference curve is a curve that shows consumption bundles that give the consumer the same level of satisfaction.

                             

                                

                                               

             

                                          

The consumer is indifferent, or equally happy, with the combinations shown at points A, B, and C because they are all on the same curve.

•The Marginal Rate of Substitution

•The slope at any point on an indifference curve is the marginal rate of substitution.

•It is the rate at which a consumer is willing to trade one good for another.

•It is the amount of one good that a consumer requires as compensation to give up one unit of the other good.

                                                                                              

                                                                                   MRS= ∆X2 /∆X1

                                                                              

 Four Properties of Indifference Curves

•Higher indifference curves are    preferred to lower ones.

•Indifference curves are downward  sloping.

•Indifference curves do not cross.

•Indifference curves are bowed inward. i.e., convex to the origin.

•Property 1: Higher indifference curves are preferred to lower ones.

•Consumers usually prefer more of something to less of it.                            

•Higher indifference curves represent  larger quantities of goods than do lower indifference curves.

•Property 2:  Indifference curves are downward sloping.

•A consumer is willing to give up one good only if he or she gets more of the other good in order to remain equally happy.

•If the quantity of one good is reduced, the quantity of the other good must increase.

•For this reason, most indifference curves slope downward.

•Property 3: Indifference curves do not cross.

•Property 4: Indifference curves are bowed inward.

•People are more willing to trade away goods that they have in abundance and less willing to trade away goods of which they have little.

•These differences in a consumer’s marginal substitution rates cause his or her indifference curve to bow inward. i.e., convex to the origin.

Two Extreme Examples of Indifference Curves

•Perfect substitutes

•Perfect complements

•Perfect Substitutes

•Two goods with straight-line indifference curves are perfect substitutes.

•The marginal rate of substitution is a fixed number.

•Perfect Complements

•Two goods with right-angle indifference curves are perfect complements.

OPTIMIZATION: WHAT THE CONSUMER CHOOSES

•Consumers want to get the combination of goods on the highest possible indifference curve.

•However, the consumer must also end up on or below his budget constraint.

The Consumer’s Optimal Choices

•Combining the indifference curve and the budget constraint determines the consumer’s optimal choice.

•Consumer optimum occurs at the point where the highest indifference curve and the budget constraint are tangent (or equal).

•The consumer chooses consumption of the two goods so that the marginal rate of substitution equals the relative price. i.e., point B on the Figure.

.At the consumer’s optimum, the consumer’s valuation of the two goods equals the market’s valuation.

How Changes in Income Affect the Consumer’s Choices

•An increase in income shifts the budget constraint outward.

•The consumer is able to choose a better combination of goods on a higher

   indifference curve.

•Normal versus Inferior Goods

•If a consumer buys more of a good when his or her income rises, the good is called a normal good.

•If a consumer buys less of a good when his or her income rises, the good is called an inferior good.

•A fall in the price of any good rotates the budget constraint outward and changes the slope of the budget constraint.

A Change in Price

Income and Substitution Effects

•A price change has two effects on consumption.

•An income effect

•A substitution effect

•The Income Effect

•The income effect is the change in consumption that results when a price change moves the consumer to a higher or lower indifference curve.

•The Substitution Effect

•The substitution effect is the change in consumption that results when a price change moves the consumer along an indifference curve to a point with a different marginal rate of substitution.

•A price change first causes the consumer to move from one point on an indifference curve to another on the same curve..

Summary

•A consumer’s budget constraint shows the possible combinations of different goods he can buy given his income and the prices of the goods.

•The slope of the budget constraint equals the relative price of the goods.

•The consumer’s indifference curves represent his preferences.

•Points on higher indifference curves are preferred to points on lower indifference curves.

•The slope of an indifference curve at any point is the consumer’s marginal rate of substitution.

•The consumer optimizes by choosing the point on his budget constraint that lies on the highest indifference curve.

•When the price of a good falls, the impact on the consumer’s choices can be broken down into an income effect and a substitution effect.

•The income effect is the change in consumption that arises because a lower price makes the consumer better off.

•The income effect is reflected by the movement from a lower to a higher indifference curve.

•The substitution effect is the change in consumption that arises because a price change encourages greater consumption of the good that has become relatively cheaper.

•The substitution effect is reflected by a movement along an indifference curve to a point with a different slope.