Intermediate Microeconomic Theory Midterm 2 "Cheat Sheet"
- 1. - Individual demand curve : the graphical 3. To find EV , . Steps to determine optimal decision under relationship btw p , EX , when optimizing i. Calculate Utility of new bundle Wnew ) uncertainty When U ( X )=XFXzLl - a ) Over budget set x. = a. ¥. ×z=u - as . ¥ ii. Solve for X. equiv and Xzequiv I. Determine the possible States of the world L= ULXITXCI - pix , - pzxz ) ( Mlk , 1MHz ) = Pxilpxz 2. Under each state , determine the - Law of demand : If p.lv , then X. T Uncw = ULX , , Xz ) t Use Old prices wealth the individual would have If ¥170 , Law of demand holds iii. Solve for compensated income 3. Setup expected utility . Engle Curve : function that shows an I equiv =p , orig X. equivtpzxzequivEU-p.ULX.lt/2zULXzlti..tpnULXn ) individual 's demand fora good at diff . iv. EV= I equiv - long 4. Take first order conditions ) of EU Levels of income 3. TO find CV , function wrtthevariablels ) the individual - Elasticity A. B : EA , , , elasticity of A Wrt i. Calc . Orig utility ( Uorig ) can choose B , B elasticity of A. the f. change in ii. Solve for Xsubsdaysubs 5. Solve for variables ) to determine the A that results from a I 't change in B t.MU//MUy)=px1py choice that would maximize EU Uorig = ULX , y ) - Risk Adverse : avoid an even bet , dislike EA ,B=fF3 . Ben = - BF iii. Solve for compensated income risk 's would pay to avoid it , ULX ) is strictly . magnitude Of Ea , B → whether effect Of lump = phew Xsubtpyysub concave , U' ' LN LO B becomes " magnified " ( IEA , 13171 ) or iv. C ✓ =/ orig - lamp . Risk Neutral : indifferent to even bet . " dampened " ( IEA , BILL ) as it Changes A CVEEV can be used to evaluate policies . indifferent to risk da wouldn't pay to . sign of EA.rs → A moves in same l t ) Or Ex : subsidy cost SIX E. est . sum of society 's avoid it . UCX ) is linear , U' ' C XI=0 opposite ( - ) direction as B CVIEV is Sly → inefficient if $4 > SIX . Risk Loving : would take an even bet , like - Demand Elasticity : Ex , , . Marginal Rate of Time Preference : risk 's would pay for a gamble , ULX ) is - Own Price Demand Elasticity :E x. p 1. The rate at which a consumer is willing to concave , U' ' LX ) > O If law of demand holds , Ex ,pL0 substitute current consumption for future . Risk Premium : the amount Less than EV If IEx.pl > I → elastic , < I → inelastic , =l→ consumption a consumer would accept in exchange unit elastic ( where rev . Maximized ) 2. MRS x. ixz When X , is con . today and for the lottery Cobb - Douglas : - I Xz is con . tomorrow 2. the ' ' fee " paid to avoid risk inherent . Cross Price Elasticity of Demand : Ex ; ,pj Usually MRSX . ,xz > I ( impatient ) to the lottery Exi , pj LO → complements ↳ U=X9 ' XYZ Where a , > Az 3. The value , r , such that ULEV - r )=EU Exi , pj > O → substitutes * Need Units of money insametimeper . where EU is the expected utility of the - Income Demand Elasticity :E x. I lntom . 's $ , budget constraint : lottery E x. I > O → normal ( Iti )IitIz= L Iti )XitX2 . To solve for risk premium : Ex , ISO → inferior ' Marginal Rate of Intertemporal Trans : I. solve for Ev MRT× , ,×z= Iti ( " luz = Iti ) 2. Solve for EU. Substitution Effect : the Change in an . L=UL× , ,×z)t×uHilI , + Iz - Lltilx , - Xz ) 3. plug into equation , ULEV - r )=EU . E individual 'S consumption Of a good due . Human capital production Function : a solve for r to the fact the relative prices have Changed math function describing how consumption U , Uz ) U , s - s - - = - good I pm, ) ¥22 Purchase more today affects future income . 1. Find optimal bundle before . z Draw new budget line p , pz becomes of good 1 price change cheaper - Intertemporal Utility Maximization with " - " - . Income Effect : change in consumption - - human capital development 's access to s - s - Of a good due to change in budget set , n n controlling for substitution effect financial markets : go , go , -1€, - Compensated budget line : shows all 1. Maximize Lifetime Income subject to , : y , . , : y ↳ bundles an individual can afford at new human cap . constraint . , . . 2. Max lifetime Utility subject to making . i . . i . . . orig . . . i . . i . . loris. . I 2 3 4 S I 2 3 4 S prices assuming they were compensated SO rig good , rig Good ' Max amount Of lifetime income s - 3. Find optimal bundle after s - 4. To calc . W . shift new they can afford Orig . level Of happiness Ex : constraint : zoo -2×12×22 , i 10%0=+1213×2113 - price change - budget line until it is Any changes in optimal bundle must be 4 - 4 - tangent to original L = ( 1. 1) X. t Xztx ( 300-2×12 - X } ) - - indifference curve due to change in prices C Sub . effect ) s - s - X. = 7.52×2=13.67 N N . Giffen Good : a good that is inferior 's o - o - f- X , "3Xz"3tX( ( 1.174.523+13.67 - I. IX , - Xz ) 802! 802-• ewtiescincmmag .EE#Es9Fwdo:tYumsan3nx.=issoxz=isi . . Lottery : Bundle of goods ( X , ,Xz , . . . , Xn ) - I - • - Bhim . I I I I l - l l toricI I , , , , I, , I , orig , , - Compensating Variation : amount Of w/ a lottery ( p , , pz , . . . , pm ) rig ' Z gig? " s n .ge#ebcti3eIIgIEIew3 4 s income someone would be willing to give s - s - Good ' I . p , t pzt . . . t pm =/ - 5. Label intersection . 4. To calc EV , shift Blorig Up ( need ) after a price reduction ( increase , z . pizo 4 - Of BLUEY - axis , 4 . until itistangenttolnew . " Xznew " G Blcompda to maintain Utility before change y-axis as " xzcomp " - 3. pi is the prob . of receiving bundle Xi , - 6. CV=p{ Xznew - Xzcomp ) 3 - new price , Old utility Level . Degenerate lottery : all prob . on I outcome o - 512-1.25=3.75 - - . equivalent variation : amount of income . expected value :p ,×,+pz×z+ . . . + pn× , I÷÷u¥•§↳;§o, .§ ,a consumer would need ( be willing to give . Mixing : Given 2 lotteries Lp , , Pz , . . . . pm ) E = i - a - • I Blcoymp - IBLequiv I new Up ) before a price reduction ( increase ) to ( t , ,tz , . . .tn ) and OLXLI , a MIX Of . . . . . . Kris. . , , . Kori. , iorig. ?rig I Zxcompxnew } 4 S I 2 = 3 4 S give the same level of utility as after the these 2 lotteries is the new lottery : good , rig yoga, S - 5. Label intersection of > rice change ( AP .tl/-X)ti,XPztll-X)t2 , . . . , April ' - d) th ) n - Blom .gg y-axis " xzorig " 's Sub . Effect :X sub - Xorig/ Old prices , new utility . Independence : If lottery PI lottery q E I " - Bleauivday - axis as Income Effect :X new - Xsubs or - " Xz equiv ' ' CV=pz( Xznew - Xzcomp ) both are Mixed with lottery tither lottery xzeausi-6.eu-pzlxzeauiu-xzon.gl s I 2178 p is still preferred to lottery q - Scs -23 . - s EV = Pz ( Xzequiv - Xzorig ) xzorig - Find CVEEV mathematically . Expected Utility Theorem : VNM Can be 2 , ; ¥ , Yg , 1. Use Lagrangian to find optimal bundle interpreted as the cardinal Utility received . Iaea " s > i i , Phon, , Iorio, , ( giffen before price change → X orig from good I such that ( p , , Pz , . . . , Pm ) I rig , z Inns4 s I ICO 2. Use Lagrangian to find optimal bundle ( q , ,qz , . . . , qn ) Iff p . U , tpzuzt . . . tpnun Good ' III > 151 after price change → Knew Iq , U , tqzuzt . . . tqnvn