The Rational Consumer The Objective of Consumers 2 Chapter 8 and the appendix Announcements We have studied demand curves. We now need to develop a model of consumer behavior to understand where demand comes from. Utility and indifference curves Budget constraints Optimal consumption decisions Effects of price and income changes Income and substitution effects. We assume consumers wish to maximize utility. Utility is like happiness or pleasure. For some of our discussion we will assign numbers to utility. But all that is required for the theory is that we can rank potential choices. We generally assume utility increases with consumption. And we generally assume that marginal utility, the incremental utility from an additional unit of consumption, declines at some point. Utility increases less when going from 1 to 1 chocolate covered peanuts than it does going from 0 to! The Budget Set for Consumers Wants are insatiable. But as the Rolling Stones remind us, we can t always get what we want. Why? There is a budget constraint. Our incomes are limited. In most of our examples we are going to simplify things by considering only two goods (though the theory is easy to generalize). The budget constraint can be written as: Income = P * + P * The slope of the budget constraint: P Slope = P 3 4 Maximizing Utility Maximizing utility means that households choose a feasible consumption bundle that yields the greatest happiness. This will be on, and not inside the budget constraint. This is a result of the more is better assumption. To give you a simple example, consider clams and potatoes. Potatoes cost $2/pound; Clams cost $4/pound, and Sammy has $ for meals. Utilities from consuming various combinations of clams and potatoes are given in the following chart. 1
Sammy s Budget & Utility: Clams $4, Potatoes $2,=$ Q of Clams Utils of Clams Q of Potatoes Utils of Potatoes Total Utility 0 0 56.7 56.7 1 15 8 53.2 68.2 2 25 6 47.0 72.0 3 31 4 36.8 67.8 4 34 2 21.4 55.4 5 36 0 0 36.0 Thinking Like an Economist We will develop these further in the coming lectures: but for now #1: The optimal consumption rule: the marginal utility per dollar spent must be the same for all goods and services that are consumed when consumers maximize utility. Optimal consumption rule: = P P The intuition of this should be clear you want the happiness (utility) to be equal for each dollar you spend. 6 Back to Utility Maximization: A Utility 7 Function 8 Indifference Curves are Like a Topographical Map for Utility An indifference curve is a line that shows all the consumption bundles that yield the same amount of total utility for an individual. An indifference curve map shows indifference curves for several different levels of utility. U3 U2 U1 A contour line that maps consumption bundles yielding the same amount of total utility is known as an indifference curve. Rooms 2
Properties of Indifference Curves Why Indifference Curves Are Convex 9 #1: More is better Utility is higher as you move outward in the indifference curve map. #2: Indifference curves never cross Otherwise, will violate assumption #1. #3: Indifference curves are downward sloping and convex They are bowed in toward the origin as a result of diminishing marginal utility. The household is willing to give up more meals to get rooms when moving from V to W (when they have a lot of meals) than the will when moving from to Z (when they have few rooms). 11 The Marginal Rate of Substitution: Tradeoffs Along an Indifference Curve The marginal rate of substitution (MRS) is The rate at which consumers will tradeoff goods (holding utility constant); and The slope of the indifference curve; and How much of the good on the axis is the household willing to give up for the good on the axis. 12 More on the Curvature of Indifference Curves Indifference curves for perfect substitutes Big Macs Increasing utility Indifference curves for perfect complements Jelly Increasing utility MRS ΔQ = Δ Q along the indifference curve Constant MRS Whoppers Peanut butter Consume in fixed ratios 3
13 Optimal Consumption: Slope of the I.C. = Slope of the B.C. 14 What is the Effect of a Price Increase (in rooms)? Optimal Q of At optimal consumption, P MRS = Slope of BC = P = Optimal Q of Rooms Rooms Different preferences will clearly result in different choices U3 U2 U1 U4 Q of M1 M2 R2 R1 As the price of rooms increases, you optimally consume fewer rooms. The two ordered pairs the price and quantity of rooms at the old and the new equilibriums - identify two points on the individual s demand curve. Q of Rooms Responding to a Price Increase, But with Different Preferences, Meal Consumption Goes Up 16 Summing Individual Demands to Get Market Demands Kate: Q=-P Libby: Q=-.5P At P>=, P=-2Q, at P<=, add Kate and Libby s Q s. Q K +Q L =-1.5P Solve for P and find P=40/3-(2/3)*Q when P<. P 5 Market Demand Q 4
17 Price Changes and Perfect Substitutes (MRS~=-1!) Big Macs P BM =$2, P W =$1, =$ 25 Big Macs Increasing utility P BM =$0.80, P W =$1, =$ Optimal C 18 Income and Consumption: Normal Goods Restaurant 80 =$2400/mo 40 An increase in income lead to an increase in both the size of housing and the number of restaurant meals. We call both these goods normal goods since consumption goes up (down) when income goes up (down). Optimal C Whoppers 25 Whoppers =$/mo 8 16 Rooms in your house 19 Income and Consumption: An Inferior Good Price Changes and Income and Substitution Effects Restaurant 80 =$2400/mo 40 =$/mo An increase in income lead to a decrease in 2 nd hand furniture consumption. This is an example of an inferior good since consumption moves inversely with income. Quantity of Second-Hand Furniture The substitution effect refers to the substitution of the good that is now relatively cheaper for the good that is now relatively more expensive, holding utility constant. The income effect is the change in consumption that results from a change in income, ceteris parabus. For normal consumption goods, the SE and IE works in the same direction. For inferior goods, the SE and IE work in opposite directions. Since SE is generally stronger than the IE, demand curves still slope downwards (except for Giffen goods). 5
21 Income and Substitution Effects (price of rooms rises) 22 IE and SEs: (price of 2 nd hand furniture rises) SE: Find a hypothetical budget line with the new price ratio just tangent to the original IC. Income effect Substitution effect Rooms IE SE 2 nd hand Furniture 6