Microeconomic Analysis

Transcription

1 Microeconomic Analsis Consumer Choice Marco Pelliccia Room 474 Reading: Perloff, Chater 4

2 Outline Preferences Utilit Budget Constraint Constrained Consumer Choice

3 Preferences Individual references determine the amount of leasure eole derive from the goods and services the consume. Consumers face constraints or limits on their choices. Consumers maimize their well-being or leasure from consumtion, subject to the constraints the face.

4 Proerties of Consumer Preferences Comleteness - when facing a choice between an two bundles of goods, a consumer can rank them so that one and onl one of the following relationshis is true: 1.The consumer refers the first bundle to the second 2.The consumer refers the second to the first 3.The consumer is indifferent between them

5 Proerties of Consumer Preferences Transitivit - a consumer s references over bundles is consistent in the sense that, if the consumer weakl refers Bundle z to Bundle (likes z at least as much as ) and weakl refers Bundle to Bundle, the consumer also weakl refers Bundle z to Bundle.

6 Proerties of Consumer Preferences Nonsatiation - all else being the same, more of a commodit is better than less of it Good - a commodit for which more is referred to less, at least at some levels of consumtion Bad - something for which less is referred to more, such as ollution

7 Indifference Curves Indifference curve - the set of all bundles of goods that a consumer views as being equall desirable. Indifference ma - a comlete set of indifference curves that summarize a consumer s tastes or references

8 B, Bur r itos er semester (a) B, Bur r itos er semester Which of these two bundles would be referred b c Lisa? d B e b f a A Lisa refers an bundle in area A over e (b) c Lisa refers bundle e f over 15 bundle d, e, since e f has more 10 of both goods: Pizza and Burritos e a b I 1 Lisa If Lisa refers is indifferent bundle between e bundles to an e, a, bundle and c.. in area B Z, Pizzas er semester Z, Pizzas er semester we can draw an indifferent curve over those three oints

9 B, Bur r itos er semester (a) (c) B, Bur r itos er semester c d e b f a A c d e f a I 2 I 1 5 B I Z, Pizzas er semester Z, Pizzas er semester we can draw an indifferent curve over those three oints

10 Imossible Indifference Curves B, Bur r itos er semester e a b I 1 I 0 Lisa is indifferent between e and a, and also between e and b so b transitivit she should also be indifferent between a and b but this is imossible, since b must be referred to a given it has more of both goods. Z, Pizzas er semester

11 B, Bur r itos er semester Imossible Indifference Curves Lisa is indifferent between b and a since both oints are in the same indifference curve But this contradicts the more is better assumtion. Can ou tell wh? Yes, b has more of both and hence it should be referred over a. I a b Z, Pizzas er semester

12 Imossible Indifference Curves B, Bur r itos er semester b a I Z, Pizzas er semester Consumer is indifferent between b and a since both oints are in the same indifference curve But this contradicts the more is better assumtion since b has more of both and hence it should be referred over a.

13 Imossible Indifference Curves

14 Marginal Rate of Substitution marginal rate of substitution (MRS) - the maimum amount of one good a consumer will sacrifice to obtain one more unit of another good. MRS B Z The sloe of the indifference curve!

15 MRS along an Indifference curve B, Bur r itos er semester Indifference Curve Conve to the Origin a 1-2 b 1-1 c The MRS from bundle a to bundle b is -3. From bundle a to bundle This b, Lisa the same as the is willing to give u 3 Burritos sloe in of the indifference echange for 1 more Pizza curve between those two oints. d From bundle b c to bundle d, c, Lisa is willing to give From u 21 b to c, Burritos in echange for MRS 1 = -2. more Pizza This is the same as the sloe of the indifference I curve between those two oints. Z, Pizzas er semester

16 B, Bur r itos er semester Marginal Rate of Substitution (b) Indif f erence Cu r v e Conc a v e to the O r igin a 1 3 b 1 c I Z, Pizzas er semester From bundle a to bundle b, Lisa is willing to give u 2 Pizzas for 1 Burrito. Nevertheless, from b to c she is willing to give u 3 Pizzas for 1 burrito. This is ver unlikel Could ou think wh?

17 Curvature of Indifference Curves Casual observation suggests that most eole s indifference curves are conve. Ecetions: Perfect substitutes - goods that a consumer is comletel indifferent as to which to consume. Perfect comlements - goods that a consumer is interested in consuming onl in fied roortions

18 Perfect Substitutes Co k e, Cans er w eek I 1 I 2 I 3 I Bill views Coke and Pesi as erfect substitutes: can ou tell how his indifference curves would look like? Straight, arallel lines with an MRS (sloe) of 1. Bill is willing to echange one can of Coke for one can of Pesi. P esi, Cans er w eek

19 Perfect Comlements Ice cream, Scoos er w eek e d a b c I 3 I 2 I 1 If she has onl one iece of ie, she gets as much leasure from it and one scoo of ice cream, a, as from it and two scoos, d, Pi e, Slices er w eek or as from it and three scoos, e.

20 B, Bur r itos er semester Imerfect Substitutes f The standard-shaed, conve indifference curve in anel lies between these two etreme eamles. Conve indifference curves show that a consumer views two goods as imerfect substitutes. I Z, Pizzas er semester

21 Indifference Curves Between Food and Clothing

22 Utilit Utilit - assigns numerical value to allow ranking of bundles utilit function - relationshi between utilit values and ever ossible bundle of goods U(B, Z) Ordinal utilit refers to the relative ranking of two bundles Cardinal utilit refers to the eact numerical values

23 Marginal utilit marginal utilit - the etra utilit that a consumer gets from consuming the last unit of a good. the sloe of the utilit function as we hold the quantit of the other good constant. Marginal Utilit of good Z is: MU Z U Z

24 MU Z, Marginal utilit of izza U, Utils Utilit and Marginal Utilit (a) Utilit 350 Utilit function, U (10, Z ) As Lisa consumes more izza, holding her consumtion of burritos constant at 10, her total utilit, U, increases and her marginal utilit of izza, MU Z, decreases (though it remains ositive). Marginal utilit is the sloe of the utilit function as we hold the quantit of the other good constant (b) Marginal Utilit U = 20 U Z = 1 MU Z Z Z, Pizzas er semester 20 MU Z Z, Pizzas er semester

25 Utilit and Marginal Rates of Substitution The MRS is the negative of the ratio of the marginal utilit of another izza to the marginal utilit of another burrito. Formall, MRS B MU Z Z MU B

26 Marginal Rate of Substitution MU MU MRS U U d d d U d U d U d U d U d U du U U 0,

27 Budget Constraint budget line (or budget constraint) - the bundles of goods that can be bought if the entire budget is sent on those goods at given rices. oortunit set - all the bundles a consumer can bu, including all the bundles inside the budget constraint and on the budget constraint

28 Effect of Budget Constraint Budget constraint limits choice due to income restrictions Mathematicall: Can determine the amount of good consumed: Effect on consumtion due to increase in income Effect on consumtion due to increase in Effect on consumtion due to increase in rice of m m m 1 0 m m

29 Budget Constraint If Lisa sends all her budget, Y, on izza and burritos, then B B + Z Z = Y This equation is her budget constraint. It shows that her eenditures on burritos and izza use u her entire budget.

30 Budget Constraint (cont). How man burritos can Lisa bu? To answer solve budget constraint for B (quantit of burritos): P B B P Z Z Y P B B Y P Z Z B Y P Z Z P B

31 Budget Constraint (cont). From revious slide we have: B Y P P B Z Z If Z = $1, B = $2, and Y = $50, then: $50 ($1 Z) B Z $2

32 Budget Constraint B, Bur r itos er semester 25 = Y / B a Amount of Burritos consumed if all income is allocated for Burritos. b L 1 Oortunit set From revious slide we have that if: c Z = $1, B = $2, and Y = $50, then the budget constraint, L 1, is: $50 ($1 Z) B Z $2 Amount of Pizza consumed if all income is allocated for Pizza d 50 = Y / Z Z, Pizzas er semester

33 The Sloe of the Budget Constraint We have seen that the budget constraint for Lisa is given b the following equation: B Y P Z Z P B P B Sloe = B/Z = MRT The sloe of the budget line is also called the marginal rate of transformation (MRT) rate at which Lisa can trade burritos for izza in the marketlace

34 Changes in the Budget Constraint: An increase in the Price of Pizzas. B, Bur r itos er semester 25 0 Sloe = -$1/$2 = -0.5 L 2 ( Z = $2) Sloe = -$2/$2 = -1 L 1 ( Z = $1) Loss 25 B = 50 Z, Pizzas er semester Y P B - P Z = $1 $2 P B If the rice of Pizza doubles, (increases from $1 to $2) the sloe of the budget line increases This area reresents the bundles she can no longer afford!!! Z

35 B, Burritos er semester Changes in the Budget Constraint: Increase in Income (Y) B = $100 $50 - P B P Z P B Z L 1 ( Y = $50) L 3 ( Y = $100) Gain Z, Pizzas er semester If Lisa s income increases b $50 the budget line shifts to the right (with the same sloe!) This area reresents the new consumtion bundles she can now afford!!!

36 Effect of Rationing

37 Consumer Maimization B, Bur r itos er semester A c B d f e Would Lisa be able to consume an otimum. bundle an along bundle I 1? along I 3 (i.e. bundle f)? Would Bundle Lisa e is be called able a to consumer s Yes; she could afford bundles d, c, If Lisa is consuming this and a. bundle, she has no incentive No! Nevertheless, Lisa does there not are have other enough affordable to change income bundles her behavior to that afford should b be referred substituting and affordable. one good an bundle along I 3 for another. For instance bundle e a I 3 I 2 I Z, Pizzas er semester

38 Consumer Maimization: Interior Solution B, Bur r itos er semester 25 The budget constraint and the indifference curve have the same sloe at the oint e where the touch. Therefore, at oint e: e MRS MU MU Z B Sloe of I 2 P P Z B MRT Sloe of BL I Z, Pizzas er semester

39 Mathematicall U U m L iii U L ii U L i foc m U L m s t U : (ii) b Divide (i) 0 0 ) ( 0 0 ) ( 0 0 ) ( :,,,.., ma,

40 Other Tes of Otimal Solutions

41 Otimal Bundles on Conve Sections of Indifference Curves