Chapter5 - 2009-10-12 people try to maximize their utility...

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Unformatted text preview: 2009-10-12 people try to maximize their utility and still stay within budget 1. over one good 2. over two goods -- consume until the point marginal utility drops below 0 -most desirable consumption bundle -Budget constraint is not binding : market demand consumption bundle still affordable -BC binding : rational spending rule: mu1/P1 = mu2/p2 optimal consumption bundle :AU the budget in spent good x |slope|=O.C. of good 1 Chapter 5 Demand good1 good 2 every consumption bundle can be put on a indifference curve IC1 indifference curves never cross each other IC2 good1 IC1>IC2 MRS=|Δgood2/Δgood1| = |slope of IC| MRS + MU1/MU2 Key Key Determinants of Consumer Behavior Behavior What factors influence how much of a good or service people buy? availability of substitutes 1. prices 2. preferences 3. income 1 2009-10-12 Preferences and Utility • Preferences: describe how much an individual values different goods and services. A,B,C A>C>B 10 8 6 • Utility: the happiness/satisfaction an individual gets from consumption. • The unit of measurement is a util. • Measured indirectly, by observing consumers’ behavior. • Cannot be compared between people Utility Pizza Slices Total Utility 0 0 1 20 2 36 3 50 4 60 5 68 6 65 Marginal Utility 20 16 14 10 8 -3 • Marginal utility : the additional utility you get from consuming an additional unit of a good. • Law of Diminishing Marginal Utility: marginal utility will start decreasing as consumption increases beyond some point. • Marginal Utility & Total Utility As long as marginal utility increases , total utility increases vice versa as MU decreases, TU decreases 2 2009-10-12 The Budget Constraint • A budget constraint shows the limits of a household’s consumption. • Example: suppose you have $10 to spend on party food. – – – – Price of pizza=$2/slice; Price of coke=$1/can. Is 1 slice of pizza and 1 can of coke affordable? Yes Are 4 slices of pizza and 4 cans of coke affordable? no What are all the possible combinations of pizza and coke that you can buy? Pizza Coke 1 8 2 6 3 4 yadada Determine Determine Demand • Goal: Maximize utility within budget constraint. • Consider two cases: – Consumer decision over one good – Consumer decision over two goods • Rational Spending Rule 3 2009-10-12 Consumer Decision over One Good Total Utility and Marginal Utility from Eating Pizza NUMBER OF SLICES OF PIZZA 0 1 2 3 4 5 6 7 TOTAL UTILITY FROM EATING PIZZA 0 20 36 50 60 68 65 60 MARGINAL UTILITY FROM THE LAST SLICE -20 16 14 10 8 3 -5 If there is no budget constraint, how many slices should you order? What if you only have $8 and the price of pizza is $2 a slice? 5 slices of pizza 4 slices of pizza What if you have $15 and the price of pizza is $2 a slice? 5 slices of pizza non-binding budget constraint Consumer Decision over Two Goods Total Utility and Marginal Utility from Eating Pizza and Drinking Coke NUMBER OF SLICES OF PIZZA 0 1 2 3 4 5 6 TOTAL UTILITY FROM EATING PIZZA 0 20 36 50 60 68 65 TOTAL MARGINAL NUMBER UTILITY MARGINAL UTILITY OF CANS FROM UTILITY FROM THE OF DRINKING FROM THE LAST SLICE COKE COKE LAST CAN 0 0 --1 20 8 8 2 16 15 7 3 14 21 6 4 10 26 5 5 8 29 3 6 28 3 1 If there is no budget constraint, how many slices of pizza and how many cans of coke should you order (Ppizza = $2, Pcoke = $1)? 4 2009-10-12 Consumer Decision over Two Goods Total Utility and Marginal Utility from Eating Pizza and Drinking Coke NUMBER OF SLICES OF PIZZA 0 1 2 3 4 5 6 TOTAL UTILITY FROM EATING PIZZA 0 20 36 50 60 68 65 TOTAL MARGINAL NUMBER UTILITY MARGINAL UTILITY OF CANS FROM UTILITY FROM THE OF DRINKING FROM THE LAST SLICE COKE COKE LAST CAN 0 0 --1 20 8 8 2 16 15 7 3 14 21 6 4 10 26 5 5 8 29 3 6 28 3 1 If you only have $12, how many slices of pizza and how many cans of coke should you order (Ppizza = $2, Pcoke = $1)? 1 slice of pizza + 2 cans of coke? cost=$4 TU = 20+15=35 TU=78 3 slices of pizza + 6 cans of coke? cost=$12 5 slices of pizza + 2 cans of coke? cost =$12 TU=83 Rational Rational Spending Rule • Rational Spending Rule: when budget constraint is binding, spending should be allocated across goods so that the marginal utility per dollar is the same for each good. 5 2009-10-12 Consumer Decision over Two Goods Converting Marginal Utility to Marginal Utility per Dollar (3) Marginal Utility per Dollar (6) Marginal Utility per Dollar (1) Slices of Pizza 1 2 3 4 5 6 (2) Marginal Utility (MUPIZZA) 20 16 14 10 8 (5) Marginal Utility (MUCOKE) 8 7 6 5 3 (4) Cans of Coke 1 2 3 4 5 6 10 8 7 5 4 -- 8 7 6 5 3 -- 3 1 If you only have $12, how many slices of pizza and how many cans of coke should you order (Ppizza = $2, Pcoke = $1)? 2 pizza & 1 coke : MU/P = 8 3 pizza & 2 coke : MU/P = 7 4 pizza & 4 coke = 5 Consumer Decision over Two Goods Combinations of Pizza and Coke with Equal Marginal Utilities per Dollar 2 Slices of Pizza and 1 Can of Coke 3 Slices of Pizza and 2 Cans of Coke 4 Slices of Pizza and 4 Cans of Coke Marginal Utility per Total Spending Total Utility Dollar (Marginal Utility/Price) 8 7 5 $1 + $2 = $3 36 + 8 = 44 $6+$2=$8 50+15=65 $8 +$4 = $12 60+26 = 86 6 2009-10-12 Consumer Decision over Two Goods We can summarize the two conditions for maximizing utility: 1 MU Pizza MU Coke PPizza PCoke Spending on pizza + Spending on Coke = Budget 2 These two conditions need to be satisfied most of the time. MU/P pizza 8 > MU/P coke 6 increase spending on pizza decrease spending on coke move dollars from pizza MU/P pizza < MU/P coke Consumer Consumer Decision over Two Goods (1) Slices of Pizza 1 2 3 4 5 6 (2) Marginal Utility (MUPIZZA) 20 16 14 10 8 (3) Marginal Utility per Dollar (4) Cups of Coke 1 2 3 4 5 6 (5) Marginal Utility (MUCOKE) 8 7 6 5 3 (6) Marginal Utility per Dollar 10 8 7 5 4 -- 8 7 6 5 3 -- 3 1 If you have $20, how many slices of pizza and cups of coke would you purchase? 5 slices of pizza and 5 cans of coke 7 2009-10-12 When Price Changes • What if the price of coke increases to $2 per can? – substitution Effect: When the price of a good goes up, people __________ buy more of its substitutes. – __________ Effect: An increase in price decreases the buyers' income purchasing power. (3) Marginal Utility per Dollar (5) Marginal Utility (MUCOKE) 8 7 6 5 3 (6) Marginal Utility per Dollar (1) (2) Slices Marginal Utility of Pizza (MUPIZZA) 1 2 3 4 5 6 20 16 14 10 8 (4) Cans of Coke 1 2 3 4 5 6 10 8 7 5 4 -- 4 3.5 3 2.5 1.5 -- 3 1 Budget = $12 -> 5 slices of pizza & 1 can of coke MU/P = 4 Qd (coke) = 4 --> Qd(coke) = 1 Derive Individual Demand Curve • Use the utility maximization rule to decide the quantity demanded at different prices. • Draw the demand curve. 8 2009-10-12 Deriving Market Demand Your Demand P P Jackie’s Demand P Market -your demand Demand Q Q Q Horizontal Summation: fix a price Graphical Graphical Representation of Consumer Choice Choice • Budget Constraint – e.g., Ppizza=$2, Pcoke=$1, budget $10 • Budget constraint: Just Affordable Consumption Bundles 2x1+1*x2=10 coke slope =o.c of pizza consumption bundle A B C D E F slices of pizza 0 1 2 3 4 5 cans of coke 10 8 6 4 2 0 B.C. pizza 9 2009-10-12 More formally . . . • • • • • M=income x1=quantity of good 1 x2=quantity of good 2 p1=price of good 1 p2=price of good 2 • Budget Constraint: P1*x1 + P2*x2 = M Graphing Graphing the Budget Constraint Constraint P1*x1+P2*x2=M => x2= (M-P1*x1)/P2 = M/P2 - (P1/P2)x1 Good 2 M/P2 slope = - P1/P2 |slope| = P1/P2 = oc. of good 1 M/P1 Good 1 10 10 2009-10-12 A Change in Income Good 2 M'/P2 B.C.' Suppose income increases from M to M’. How will the budget constraint change? |slope| = P1/P2 , slope stays the same so OC stays the same M/P2 B.C. M/P1 M'/P1 Good 1 A Price Decrease (Good 1) Good 2 P1-> P1' (decrease) A decrease in the opportunity cost of good 1. M/P2 |slope| = P1'/P2 < P1/ P2 M/P1 M/P1' Good 1 11 11 2009-10-12 A Price Decrease (Good 2) Good 2 M/P2' |slope| = P1/P2' > P1/P2 M/P2 P2->P2' An increase in the O.C. of good 1 M/P1 Good 1 Consumer Preferences Consumer Preferences • Indifference curve A curve that shows the combinations of consumption bundles among which consumers are indifferent. coke C indifference curve 4 . 2 . . . B A D E 1 2 5 Pizza 12 12 2009-10-12 Consumer Preferences Consumer Preferences Utility : IC1 > IC2> IC3 coke ICs never cross each other! 11 A 5 4 2 B D IC1 C IC2 IC3 1 2 3 5 Pizza Tracing Constant Elevation 13 13 2009-10-12 Marginal Rate of Substitution • Marginal rate of substitution (MRS): the amount of the good on the y-axis the consumer is willing to give up to compensate for the gain of 1 unit of the good on the xaxis. • Diminishing MRS: There is a tendency for the MRS to fall as the individual consumes more of the good on the xaxis. coke (11-4)/1=7=MRS 11 A 4 2 1 B Indifference Curve (4-2)/(5-2) = 2/3 C 2 5 Pizza MRS & Slope of ICs • MRS at a point: the absolute value of the slope of the indifference curve at that point. Good 2 MRS = |slope|= | Δcoke/Δpizza| Δcoke . A Δpizza Good 1 14 14 2009-10-12 MRS & Marginal Utility • MRS=MU1/MU2 – – – – MU1 = units of utility per unit of good 1 1/MU1 =units of good 1 per util MU2 = units of utility per unit of good 2 1/MU2 = units of good 2 per util Good 2 increase quantity of good 1 by 1 unit, you can get MU1 util to keep utility the same, you need to give up of MU1*1/MU2 of good 2. MRS = MU1/MU2=|slope of IC| Good 1 Perfect Substitutes Two goods are called perfect substitutes for a consumer if the consumer would always be willing to give up one unit of one good for a fixed number of units of the other good, and keep his utility fixed. 1 cup of sugar = 2 * 1/2 cup of sugar Cups of Duracell AA Sugar 10 9 8 IC3 IC2 IC1 12 MRS=1 10 6 Eveready AA MRS = 1/2 12 ½ Cups Of Sugar 15 15 2009-10-12 Perfect Complements Two goods are perfect complements for a consumer if the consumer consumes the goods in fixed proportions. Left Shoes IC Bike Frame b 2 1 a 1 c IC IC' 2 1 2 (4,2) (2,1) A 4 IC' IC Right Shoes Bike Tires How much do you consume? consume? What you can afford What you want Good 2 Good 2 M/P2 -P1/P2 |slope|= P1/P2 U2 U1 M/P1 Good 1 Good 1 Slope of a BC tells you how much of good 2 you MUST give up to get one more unit of good 1. Slope of an IC (MRS) tells you how much of good 2 you are WILLING to give up to get one more unit of good 1. 16 16 2009-10-12 Many points to choose from Good 2 M/P2 C not attainable B A attainable Good 1 M/P1 Optimal Consumption Bundle Good 2 P1/P2=|slope| at A : MRS > P1/P2 willing must 10 5 increase the quantity of good 1 and decrease quantity of good 2 • A C MRS=P1/P2 E optimal at B : MRS < P1/P2 increase Q of good 2 and decrease Q of good 1 IC2 • B IC2 MRS= 2 P1/P2=5 give up 1 unit of good 1 => can get 5 units of good 2 => 2 units of good 2 enough to keep utility level the same => utility level icnreases Good 1 17 17 2009-10-12 Utility Maximization Two Conditions must hold: • p1x1+p2x2 = M -> optimal bundle on the B.C. • MRS = p1/p2 -> point where B.C. is tangent to the I.C. MU1/P1= Mu2/P2 Rational Spending Rule MRS = MU1/MU2 = P1/P2 => MU1/P1= MU2/P2 normal goods Change in Income M'>M Good 2 M'/P2 M/P2 Q2 E' IC3 E IC2 IC1 M/P1 M'/P1 Q1 Good 1 18 18 2009-10-12 Change in Price Good 2 P1' < P1 a decrease in price of good 1 Q2'<Q2 Q1'>Q1 substitution effect Q2 Q2' A• IC2 IC1 Q1 Q1'' Q1' SE IE M/P1' Q1->Q1'' income effect Good 1 Q1"->Q' 19 19 ...
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This note was uploaded on 12/07/2009 for the course ECON ECON 1 taught by Professor Foster during the Fall '08 term at UCSD.

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