Part IIA, Paper 1 Consumer and Producer Theory. Lecture 4 Revealed Preferences and Consumer Welfare Flavio Toxvaerd. Today’s Outline. Leftovers from Lecture 2 Revealed preferences WARP, SARP, GARP Indices . Primal Approach. Dual Approach. Duality. Integrability problem. Solve. Solve.
Revealed Preferences and Consumer Welfare
x1(p,m) and x2(p,m)
Substitute into cost equation
Substitute into u(x,y)
Following a price change,
If, at prices p1 , p2 and income m, a consumer purchases a consumption bundle a, then this bundle is said to have been Directly Revealed Preferred to all other affordable bundles
No two different bundles, a and b, can be directly revealed preferred to each other
That is, if at prices (p1,p2) bundle (a1,a2) is chosen, and at prices (q1,q2) bundle (b1,b2) is chosen, then it cannot be the case that
, b affordable when a chosen
, a affordable when b chosen
Graphically, we cannot have
If a bundle a is directly revealed preferred to a different bundle b, and bundle b is directly revealed preferred to an alternative bundle c, then we can say that bundle a is Indirectly Revealed Preferredto bundle c.
The Consumer Price Index (CPI) measures the proportional change in the cost of purchasing a ‘given’ bundle of commodities. Specifically,
The CPI is commonly compared with the growth in nominal incomes to assess ‘real’ income changes
Is this comparison justifiable?
If CPI < M (ratio of incomes) then consumers are better off.
But if CPI > M cannot conclude that consumers are worse off.
Increasing incomes by CPI will generally improve welfare