Review Answers From Economics 11December 18, 1996 © David K. Levine1. Consumer and Demand Theoryincome $1,000,000utility is log logxx122+marginal rate of substitution uxuxxxpp//1221122== or px px22 112=budget constraint px px I11 22+=substitute and get xIpp11131000 0003==,,elasticity of demand for champagne pxxppxIp11111112311=- =-()so a 10% price increase in champagne results in a 10% fall in demand for champagnecross elasticity of demand for champagne pxxppx21122100==so a 10% price increase in diamonds does not change the demand for champagne2. General Equilibrium TheoryRockstardemand xIpR113= ; excess demand zpppR11211000 10031000=+-Turkeyfeathersdemand xIpT1123= ; excess demand zpppT1121200 403100=+-aggregate excess demand zzppppppppRT11121121211000 10031000200 4031001403700 0+=+-++-=-=solve for equilibrium price ratio pp2115=2plug prices into demand to find equilibrium consumptionxR11000310031525003=+ =xT12003403158003=+ =3. Lagrange MultipliersLagrangean is xxxpxpxpxI12311223223++- ++-l()lLxix pii112120=-=-27/solving we get xipii=2224l27plugging into the budget constraint we get14449421 22 23ll lpppI++=orl =++144494123Ip Ip Ipsubstituting back in we get the answerxIp Ip Ipp11231214144494=++27as a check observe that this function is homogeneous of degree zero in prices and income:if prices and income both double, demand (a real quantity) does not