Section 3 Chapter 4 & 5

1. Section 3Chapter 4 & 5

2. Consumer choice A model of individual behavior is used to answer questions about individual decision making. Such a model is based on the following premises: a. individual tastes and preferences determine the amount of pleasure people derive from the amount of good and services they consume b. consumers face constraints or limits on their choices c. consumers maximize their well being or pleasure from consumption, subject to the constraint they face Main problem of the consumer: allocate his/her money to buy a bundle(combination) of goods 4.1 Preferences Assumption: consumers have a set of preferences that they use to choose between goods The preferences are illustrated by the indifference curves. Properties of consumers’ preferences Completeness – when facinga choice between any 2 bundles of goods, a consumer can rank them so that only and only one of the following is true: a) the consumer prefers the first bundle to the second one b) the consumer prefers the second bundle to the first one c) the consumer is indifferent between them It rules out the possibility that the consumer cannot decide which bundle is preferable. Notation if a consumer strictly prefers good x to good y, we write xy if a consumer weakly prefers x to y, we write x y Transitivity (Rationality) If a consumer weakly prefers bundle z to bundle y (zy) and weakly prefers bundle y to bundle x (y x) then he/she will weakly prefer bundle z to bundle x (z x) More is better- more of a commodity is better then less of that commodity

3. Preferences maps Consider a choice between 2 goods. (Lisa chooses between pizza and burritos) Graph: Suppose we ask Lisa to identify all the bundles that gave her the same amount of pleasure as consuming bundle e.We can construct indifference curve I1. Indifference map

4. Indifference curve- properties All indifference curves must have 4 important properties: -Bundles on indifference curves further from the origin are preferred to those on indifference curves closer to the origin -There is an indifference curve through each possible bundle -Indifference curves slope downwards -Indifference curves cannot cross Indifference curves cannot be thick Suppose the indifference curve is thick enough to contain both a and b. The consumer is -indifferent between a and b because both are on I. The consumer also prefers b to a because -more-is-better assumption(b lies above and to the right of a) Because of this contradiction, indifference curves cannot be thick.

5. Willingness to substitute between goods A consumer’s willingness to trade one good for another is measured by the marginal rate of substitution MRS(Marginal rate of substitution) is the maximum amount of one good a consumer is willing to sacrifice to obtain one more of another good e.g. In our example, the marginal rate of substitution for Lisa refers to the trade-off of burritos for a small chance(incremental) in the number of pizzas. The marginal rate of substitution is the slope of the indifference curve In our example where Z is the amount of pizza Lisa will give up to get B burritos Problem Linda loves to buy shoes and to go out to dance. She gets utility from the shoes she is buying and from the number of times she is going out dancing. The equation of one of her indifference curves is 1=2ST • Draw this indifference curve • Find MRS at a point of your choice

6. Curvature of indifference curves An indifference curve does not have to be convex but casual observation suggest that most people’s indifference curves are convex. For our example: Convex ~ as you move along theindifference curve(down and right), Lisa iswilling to give up fewer burritos for an additional pizza. Diminishing rate of marginal substitution – the marginal rate of substitution approaches 0 as we move down and to the right along the indifference curve

7. Some ‘extreme’ cases Perfect substitutes: goods that consumer is completely indifferent as to which to consume Example 1: a consumer is indifferent between 1 can of Coke and 1 can of Pepsi Example 2: a consumer is indifferent between 1gal. Clorox bleach and 2 gal. Generic brand bleach

8. Some ‘extreme’ cases-cont’d Perfect complements: goods that a consumers is interested in consuming in fixed proportions Example: John likes to eat a slice of pizza and to drink 1 can of coke ? Show on the graph her consumption bundles

9. UtilityOrdinal preferences Utility function: a relationship between utility measures and every possible bundle of goods Example: Assume bundle X =( B=9, Z=16) and bundle Y=(B=13, Z=13) ?Which bundle makes this consumer happier? Answer: She will prefer bundle Y Ordinal preferences If we only know consumers’ relative rankings of bundles, our measure of pleasure is ordinal rather than cardinal. Example: ordinal measure – letter grades cardinal measure – point grades

10. Utility and marginal utility In our example, as Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases and her marginal utility of pizza, MUZ decreases( though remains positive)

11. Utility and marginal rates of substitution In our example, MUZ=20/1=20 Important:

12. Budget constraint We usually assume that a consumer has a fixed amount of money to spend - the budget. Example In our example, Lisa’s budget constraint will be pBB+pZZ = Y, where pB is the price of burritos and pZ is the price of pizza. How many burritos will she buy? Answer: Budget line equation Y=Z*PZ+B*PB If Y=$50, PZ=$1, PB=$2, draw the budget line Opportunity set – the set of all bundles a consumer can buy The slope of the budget line is called marginal rate of transformation: the amount of one good theconsumer must give up to obtain more of the other good In our example Y=BPB+ZPZ MRT=B/Z=-PZ/PB

13. Effect of a change in price and income on consumption Change in price Assume the budget line equation Y=ZPZ+BPB. Assume also that the price of one good changes from P Z=1 to PZ=$2.Y=50, PB=2. Draw the new budget line. Change in income Assume the budget line equation Y=ZPZ+BPB. Assume also that Lisa’s income doubles.The new income is Y=$100. If PZ=$1, PB=$2. Draw the new budget line.

15. The math behind the graphs At point e on our previous graph, the indifference curve is tangent to the budget line. • the indifference curve has the same slope as the budget line the slope of the indifference curve = MRS the slope of the budget line = marginal rate of transformation • MRS=MRT

16. Consumer’ s optimal bundle Every consumer chooses to consume a bundle of goods so that it maximizes his happiness (utility).If an individual chooses to consume both goods, good 1 and good 2 (interior solution), the individual’s utility is maximized when the following 4 conditions hold: 1. The indifference curve between the 2 goods is tangent to the budget constraint 2. The consumer buys the bundle of goods that is on the highest attainable indifference curve 3. The consumer’s marginal rate of substitution (the slope of the indifference curve) equals the marginal rate of technical substitution(the slope of budget line) 4. The last dollar spent on good 1 gives the consumer as much extra utility as the last dollar spent on good 2