CHAPTER 2 UTILITY AND CHOICE

Objective Build a model to understand how a consumer makes decisions under scarcity. To understand his choice we need to know: 1. Preferences 2. Constraints

Consumer makes a choice that results in the maximum satisfaction or UTILITY. Two goods available: X1 and X2. Utility = U(X1, X2; other things) Utility depends on the amount of X1 and X2 consumed and other things. Assume other things are held constant. Utility

Three Assumptions About Preferences We make the following assumptions about preference so we can represent preferences by a utility function Completeness Given two options, A and B, a person can state which option they prefer or whether they find both options equally attractive. Transitivity Preferences are internally consistent. If I prefer A to B, and prefer B to C, then I must prefer A to C. More is Better Economic “goods” What’s an economic “bad”?

Quantity of Y per week Y* Quantity of X per week ? ? X* More is Better Graphically Combinations of X and Y in the green area are preferred to (X*, Y*) (X*, Y*) is preferred to combinations of X an Y in the red area. Can’t say about the other points.

Indifference Curves We want to find a way to compare points in the two ? regions from the last picture. Two goods: soft drinks and hamburgers. Indifference curve A curve that shows all the combinations of two goods that give the same level of utility If you get the same utility you must be indifferent.

Hamburgers per week 6 A B C D U1U Soft drinks per week Indifference Curve Let’s say you are indifferent between A, B, C and D. Draw a curve through those points. Every point gives the same level of utility.

Hamburgers per week 6 A B C D U1U Soft drinks per week Indifference Curve E What can we say about combination E? What about F? F

Hamburgers per week 6 A B C D U1U Soft drinks per week Indifference Curve E F Why does the indifference curve have a negative slope? Because, if you give up hamburgers, you need to get more soft drinks to still get the same level of utility.

Hamburgers per week Soft drinks per week Indifference Curve Maps U1U1 U2U2 U3U3 An indifference curve map shows the utility a person gets from all possible combinations of two goods. As you move to the northwest, utility increases: U 3 > U 2 > U 1

Marginal Rate of Substitution (MRS) The absolute value of the slope of the indifference curve The MRS measures the rate at which you are willing to reduce the consumption of one good to get one more unit of another good and still remain indifferent.

Hamburgers per week 6 A B C D U1U Soft drinks per week MRS E F From A to B: the person is willing to give up 2 burgers to get 1 more soda. From B to C: the person is willing to give up 1 burger to get 1 more soda. From C to D: the person is willing to give up ½ burger to get 1 more soda.

Diminishing MRS As you consume more and more soda, the number of burgers you are willing to give up to get one more soda gets smaller and smaller. This is known as diminishing marginal rate of substitution. People prefer balanced consumption to extremes. From convexity Move along the indifference curve Same utility level MRS decreases

Calculating MRS MRS=-MU1/MU2 Calculate Mui, where i =1 or 2, from utility function

Hamburgers per week 6 A G D U1U1 4 2 Soft drinks per week Convexity of Preferences You would prefer 4 burgers and 4 sodas to 6 of one good and 2 of the other good. Suppose we create a basket that is ½ of A and ½ of D: point G.

Representing Preferences Graphically 16 Upward sloping indifference curves A good and a bad Flat indifference curves Goods that yield no utility Useless goods Straight-line indifference curves Goods that are perfect substitutes MRS - constant along an indifference curve In a two-good world Indifference curve - straight line

17 Good 1 ( x 1 ) 0 Good 2 ( x 2 ) (a) Flat indifference curves. The good measured on the horizontal axis is yielding no utility for the consumer. (b) Straight-line indifference curves: perfect substitutes. The same amount of good 2 is always needed to compensate the consumer for the loss of one unit of good 1. (a) (b) a Good 1 ( x 1 ) Good 2 ( x 2 ) ∆x 2 -∆x 1 +∆x 2 -∆x 1

Representing Preferences Graphically 18 Right-angle indifference curves Goods that are perfect complements Must be consumed in a fixed ratio to produce utility Bowed-out indifference curves Nonconvex preferences

I1I1 19 Good 1 ( x 1 ) 0 Good 2 ( x 2 ) (c) Right-angle indifference curves: perfect complements. Adding any amount of only one good to bundle a yields no additional utility. (d) Bowed-out indifference curves: non- convex preferences and the MRS. As the consumer gets more of good 2, he values it more. (c) (d) Good 2 ( x 2 ) ∆x 1 Good 1 ( x 1 ) 0 56 b c a -∆x 1 b a +∆x 2

Perfect substitutes 20 Coke 0 Pepsi Mary’s marginal rate of substitution is constant at any bundle of Pepsi and Coke.

Budget line 21 Points on the budget line indicate all the bundles of goods that the consumer can afford. Good Good

Budget Line and Government Policy What is the effect of the following on the budget line? Quantity tax Value tax Lump sum tax Voucher rationing

Optimal Consumption Bundle 23 Optimal consumption bundle Maximize consumer’s utility Within the economically feasible set Best bundle According to consumer’s preferences Characteristics of optimal bundles Indifference curve tangent to budget line Slope of indifference curve = MRS = -∆x 2 /∆x 1 Slope of budget line = price ratio = p 1 /p 2 MRS = p 1 /p 2

The optimal consumption bundle 24 At the optimal point e, the indifference curve is tangent to the budget line Good 1 ( x 1 ) 0 Good 2 ( x 2 ) x e z B B’ F m n k