When the food stamp program was established in the early 1960s, the designers had to determine to what extent the food stamps would provide people with more food and not just simply subsidize the food they would have bought anyway.
Indifference curves represent all combinations of market baskets that provide the same level of satisfaction to a person.
Consumer Preferences Food (units per week) 10 20 30 40 10 20 30 40 Clothing (units per week) 50 The consumer prefers A to all combinations in the blue box, while all those in the pink box are preferred to A. G A E H B D
Consumer Preferences Food (units per week) 10 20 30 40 10 20 30 40 Clothing (units per week) 50 U 1
This would violate the assumption that more is preferred to less.
Consumer Preferences Food (units per week) Clothing (units per week) U 2 U 3 U 1 A B D Market basket A is preferred to B. Market basket B is preferred to D.
Consumer Preferences Food (units per week) Clothing (units per week) Indifference Curves Cannot Cross U 1 U 2 A D B The consumer should be indifferent between A , B and D . However, B contains more of both goods than D .
Consumer Preferences Food (units per week) Clothing (units per week) 2 3 4 5 1 2 4 6 8 10 12 14 16 Question : Does this relation hold for giving up food to get clothing? A B D E G -1 -6 1 1 -4 -2 1 1 Observation: The amount of clothing given up for a unit of food decreases from 6 to 1
Assume: The utility function for food (F) and clothing (C) U(F,C) = F + 2C
Market Baskets: F units C units U(F,C) = F + 2C A 8 3 8 + 2(3) = 14 B 6 4 6 + 2(4) = 14 C 4 4 4 + 2(4) = 12 The consumer is indifferent to A & B The consumer prefers A & B to C
Consumer Preferences Food (units per week) 10 15 5 5 10 15 0 Clothing (units per week ) Utility Functions & Indifference Curves U 1 = 25 U 2 = 50 (Preferred to U 1 ) U 3 = 100 (Preferred to U 2 ) A B C Assume: U = FC Market Basket U = FC C 25 = 2.5(10) A 25 = 5(5) B 25 = 10(2.5)
A decrease in income causes the budget line to shift inward, parallel to the original line (holding prices constant).
Budget Constraints Food (units per week) Clothing (units per week) 80 120 160 40 20 40 60 80 0 A increase in income shifts the budget line outward ( I = $160) L 2 ( I = $80) L 1 L 3 ( I = $40) A decrease in income shifts the budget line inward
If the price of one good decreases, the budget line shifts outward, pivoting from the other good’s intercept.
Budget Constraints Food (units per week) Clothing (units per week) 80 120 160 40 40 ( P F = 1) L 1 An increase in the price of food to $2.00 changes the slope of the budget line and rotates it inward. L 3 ( P F = 2) ( P F = 1/2) L 2 A decrease in the price of food to $.50 changes the slope of the budget line and rotates it outward.
It can be said that satisfaction is maximized when marginal rate of substitution (of F and C) is equal to the ratio of the prices (of F and C).
Consumer Choice Food (units per week) Clothing (units per week) 40 80 20 20 30 40 0 U 1 B Budget Line Pc = $2 P f = $1 I = $80 Point B does not maximize satisfaction because the MRS (-(-10/10) = 1 is greater than the price ratio (1/2). -10 C +10 F
Consumer Choice Pc = $2 P f = $1 I = $80 Food (units per week) Clothing (units per week) 40 80 20 20 30 40 0 Budget Line U 3 D Market basket D cannot be attained given the current budget constraint.
Consumer Choice Pc = $2 P f = $1 I = $80 Food (units per week) Clothing (units per week) 40 80 20 20 30 40 0 U 2 Budget Line A At market basket A the budget line and the indifference curve are tangent and no higher level of satisfaction can be attained. At A: MRS =P f /P c = .5
If part of the money could be used for the purchase of other goods, her consumption preferences change.
A College Trust Fund
Consumer Choice Education ($) Other Consumption ($) A College Trust Fund The trust fund shifts the budget line P Q U 2 A U 1 A: Consumption before the trust fund B B: Requirement that the trust fund must be spent on education C U 3 C: If the trust could be spent on other goods
If we know the choices a consumer has made, we can determine what her preferences are if we have information about a sufficient number of choices that are made when prices and incomes vary.
Revealed Preferences-- Two Budget Lines D l 1 A I 1 : Chose A over B A is revealed preferred to B l 2 : Choose B over D B is revealed preferred to D Food (units per month) Clothing (units per month) l 2 B
Revealed Preferences-- Two Budget Lines Food (units per month) Clothing (units per month) B is preferred to all market baskets in the green area l 2 B l 1 D A All market baskets in the pink shaded area are preferred to A.
Revealed Preferences-- Four Budget Lines Food (units per month) Clothing (units per month) All market baskets in the pink area preferred to A l 1 l 2 l 3 l 4 A: preferred to all market baskets in the green area E B A G I 3 : E revealed preferred to A I 4 : G revealed preferred to A
Revealed Preferences for Recreation Amount of Exercise (hours) Other Recreational Activities ($) 0 25 50 75 20 40 60 80 100
Roberta’s recreation budget = $100/wk
Price of exercise = $4/hr/week
Exercises 10 hrs/wk at A given U 1 & I 1
Would the Club’s profits increase? l 1 C l 2 U 2 B
If consumption moves along an indifference curve, the additional utility derived from an increase in the consumption one good, food (F), must balance the loss of utility from the decrease in the consumption in the other good, clothing (C).
The horizontal axis shows her annual consumption of gasoline at $1/gallon.
The vertical axis shows her remaining income after purchasing gasoline.
Marginal Utility and Consumer Choice
Marginal Utility and Consumer Choice Gasoline (gallons per year) Spending on other goods ($) 20,000 B 20,000 A 5,000 U 1 C 15,000 2,000 D With a limit of 2,000 gallons, the consumer moves to a lower indifference curve (lower level of utility). 18,000 U 2
The ideal cost-of-living adjustment for Rachel is $760.
The ideal cost-of-living index is $1,260/$500 = 2.52 or 252.
This implies a 152% increase in the cost of living.
Cost-of-Living Indexes Food (lb./quarter) Books (per quarter) 450 25 20 15 10 5 0 600 50 100 200 250 300 350 400 550 500 For Rachel to achieve the same level of utility as Sarah, with the higher prices, her budget must be sufficient to allow her to consume the bundle shown by point B. l 2 B l 1 U 1 A
The amount of money at current year prices that an individual requires to purchase the bundle of goods and services that was chosen in the base year divided by the cost of purchasing the same bundle at base year prices.
Her cost of living adjustment would now be $1,220.
The Laspeyres index is: $1,720/$500 = 344.
This overstates the true cost-of-living increase.
Cost-of-Living Indexes l 2 Food (lb./quarter) Books (per quarter) 450 25 20 15 10 5 0 600 50 100 200 250 300 350 400 550 500 Using the Laspeyres index results in the budget line shifting up from I 2 to I 3 . l 3 B l 1 U 1 A
By increasing purchases of those items that have become relatively cheaper, and decreasing purchases of the relatively more expensive items consumers can achieve the same level of utility without having to consume the same bundle of goods.