The Consumer’s Optimization Problem Individual consumption decisions are made with the goal of maximizing total satisfaction from consuming various goods and services

Consumer Theory Assumes buyers are completely informed about: Range of products available Prices of all products Capacity of products to satisfy Their income

Indifference Curves Locus of points representing different bundles of goods, each of which yields the same level of total utility Negatively sloped & convex

Properties of Consumer Preferences Completeness For every pair of consumption bundles, A and B, the consumer can say one of the following: A is preferred to B B is preferred to A The consumer is indifferent between A and B

Properties of Consumer Preferences Transitivity If X is preferred to Y, and Y is preferred to Z, then X must be preferred to Z

Properties of Consumer Preferences Nonsatiation More of a good is always preferred to less

Utility The benefits consumers obtain from the goods and services they consume is called utility. A utility function shows an individual’s perception of the utility level attained from consuming each conceivable bundle of goods

Marginal Utility Addition to total utility attributable to the addition of one unit of a good to the current rate of consumption, holding constant the amounts of all other goods consumed MU= Changes in Total Utility / Change in No of Units Consumed

Constrained Utility Maximization (Figure 5.8) 50 A • I • E III • D IV 45 Quantity of pizzas C • B II R T 40 30 20 15 10 10 20 30 40 50 60 70 80 90 100 Quantity of burgers

Marginal Rate of Substitution MRS shows the rate at which one good can be substituted for another while keeping utility constant Negative of the slope of the indifference curve Diminishes along the indifference curve as X increases & Y decreases Ratio of the marginal utilities of the goods

How to get MRS Formula U = ƒ(XY) (Here, U= Utility; X,Y= 2 goods) by differentiation, dU= ƒ1dX + ƒ2dY Here, ƒ1= ΔU/ ΔX = MUx ƒ2= ΔU/ ΔY = MUy as per indifference curve, U remains constant. So, U = 0 → ƒ1dX + ƒ2dY = 0 → ƒ1dX = - ƒ2dY → ƒ1 / ƒ2 = - dX/dY as indifference curve is neutral, so…. IdX/dYI = I ƒ1 / ƒ2 I = MUx/ MUy So, MRSxy = MUx/ MUy

Slope of an Indifference Curve & the MRS (Figure 5.3) 600 800 A B T T’ Quantity of good Y C (360,320) 320 360 Quantity of good X

MRS = slope of indifference curve = slope of tangent line

The slope is 35/35 = 1

MRS = − ΔY /ΔX = 5 /10 = 1 2 5 10

10:5 or 2:1 Before, − ΔY /ΔX = 5/10 or 1/ 2, After, − ΔX/ ΔY = 10/5 or 2 10:5 or 2:1 5 10

Consumer’s Budget Line Shows all possible commodity bundles that can be purchased at given prices with a fixed money income or

Consumer’s Budget Constraint (Figure 5.5)

Typical Budget Line (Figure 5.6) • A B Quantity of Y Quantity of X

Shifting Budget Lines (Figure 5.7) 120 240 A Panel B – Changes in price of X 200 100 A B 100 250 D 125 C F Z 80 160 Quantity of Y Quantity of Y B 200 Quantity of X Quantity of X Panel A – Changes in money income

The following figure shows a portion of a consumer’s indifference map The following figure shows a portion of a consumer’s indifference map. The consumer faces the budget line ZL, and the price of Y is $20. 600 The consumer's income = $__________. The price of X is $_____________. 20

The following figure shows a portion of a consumer’s indifference map The following figure shows a portion of a consumer’s indifference map. The consumer faces the budget line ZL, and the price of Y is $20. The equation for the budget line ZL is Y = ______________________. 30 - 1x 30/ 30

The following figure shows a portion of a consumer’s indifference map The following figure shows a portion of a consumer’s indifference map. The consumer faces the budget line ZL, and the price of Y is $20. What combination of X and Y would the consumer choose? Why? 15X and 15Y

consumer faces the budget line ZL, and the price of Y is $20. The following figure shows a portion of a consumer’s indifference map. The consumer faces the budget line ZL, and the price of Y is $20. The marginal rate of substitution at the combination in part c is __________. MRS=Px / PY = 20 / 20 = 1

The following figure shows a portion of a consumer’s indifference map The following figure shows a portion of a consumer’s indifference map. The consumer faces the budget line ZL, and the price of Y is $20. If the budget line pivots to ZM, the consumer chooses _______ units of good X and _________ units of good Y. 10 15

The following figure shows a portion of a consumer’s indifference map The following figure shows a portion of a consumer’s indifference map. The consumer faces the budget line ZL, and the price of Y is $20. Along budget line ZM, the price of X is $_________ and the price of Y is $________. 20 30

The following figure shows a portion of a consumer’s indifference map The following figure shows a portion of a consumer’s indifference map. The consumer faces the budget line ZL, and the price of Y is $20. MRS= 30/ 20 =1 The new MRS is equal to __________.

The figure below shows a portion of a consumer’s indifference map, and a budget line. The consumer’s income is $1,200 and the price of Y is $6. Using the given budget line, what is one point on the consumer’s demand for X? (Both Price & Quantity) Px = $1,200/200 = $6 and X = 100

The figure below shows a portion of a consumer’s indifference map, and a budget line. The consumer’s income is $1,200 and the price of Y is $6. Pivot the budget line and derive two other points on the consumer’s demand for X. At A, Px = $1,200/100 = $12 and X = 50 At B, Px = $1,200/200 = $6 and X = 100 At C, Px = $1,200/300 = $4 and X = 150

Market Demand Market demand is a list of prices and the quantities consumers are willing and able to purchase at each price in the list, other things being held constant. Marketdemand is derived by horizontally summing the demand curves for all the individuals in the market.

Derivation of Market Demand Quantity demanded Price Consumer 1 Consumer 2 Consumer 3 Market demand $6 3 12 13 5 8 10 7 10 1 3 5 6 8 1 4 3 5 6 4 12 3 19 2 25 1 31

Derivation of Market Demand Figure (5.10)