Relative Demand-Relative Supply Analysis Suppose income-expenditure d+d*=s +s* and d tdr=s+ i C if and only if d+d* s+s + x * 16
16 Relative Demand-Relative Supply Analysis Suppose income=expenditure * + * and * * if and only if * * * * c c c c w w w w c c c c w w w w D D S S D D S S D D S S D D S S + = + = + + + = + +
Relative Demand Relative Supply Analysis To study the ricardian Model, we need to clarify what the rd and Rs are The rs is determined by the technology The rd is determined by consumers preferences The preferences to be introduced are general, applicable to other models 17
17 Relative Demand Relative Supply Analysis • To study the Ricardian Model, we need to clarify what the RD and RS are. • The RS is determined by the technology • The RD is determined by consumers’ preferences – The preferences to be introduced are general, applicable to other models
Demand Assume identical homothetic preferences I=PQ+PQ Each consumer's relative > demand depends only on relative price, and not on her income level Given the relative price, each consumer's relative demand is determined. so is that of the whole population One example is Cobb- |=P。Q+PQ Douglas utility function 18
18 Demand • Assume identical, homothetic preferences • Each consumer’s relative demand depends only on relative price, and not on her income level • Given the relative price, each consumer’s relative demand is determined, so is that of the whole population • One example is CobbDouglas utility function Qc Qw I’=PcQc+PwQw I=PcQc+PwQw I’>I
Cobb-Douglas Utility Function maxocO, u(2, 2w)=2 Q subject to /=Pe+Pg marginal utility of Cheese =aQQ marginal utility of Wine=(1-a)e 0 At Optimum MU M MO → Pr 1-a P 19
19 Cobb-Douglas Utility Function ( ) ( ) 1 , 1 1 1 1 max ( , ) subject to marginal utility of Cheese = marginal utility of Wine = 1- At Optimum or 1- 1 Qc Qw c w c w c c w w c w c w c w c c c w w w c w c c w c w w w c U Q Q Q Q I PQ P Q Q Q Q Q MU MU MU P P P MU P Q Q P Q P Q Q P Q P − − − − − − − = = + = = = = −