Consumption -Applications Hicks deco There is another way to decompose the price effect. For simplicity consider a consumer with fixed income m. The Hicks decomposition involves pivoting the budget line around the initial indifference curve rather than the initial bundle. The diagram below illustrates for a price decrease in good 1 The consumer now chooses(as before)ri on the outermost budget line. The Hicks substitution effect is the change in demand due to the relative price change given a constant level of utility rather than income r parallel budget line, the consume no longer afford r-unlike before. The Hicks substitution effect is then given by Arisrf-rf The hicks effect is Arn=s-rf. These can be different in size from the Slutsky effects. The price effect is the This means a Slutsky inferior good is not always a Hicks inferior good and The substitution effect is still always in the opposite direction to the price change. Why Consumption-Applicatiorsa Returning to Slutsky decompositions, consider the cases of perfect complements and perfect substitutes. In both cases there is a decrease in pi-The changes from rf to zh The first graph shows the perfect complement case- it is all income effect. The substitution effect is The second graph shows the perfect substitute case- it is all substitution effect. The income effect is zer Note the Slutsky and Hicks decompositions are identicnl for both cases. Why?Consumption — Applications 1 Hicks Decomposition • There is another way to decompose the price effect. For simplicity consider a consumer with fixed income m. • The Hicks decomposition involves pivoting the budget line around the initial indifference curve rather than the initial bundle. The diagram below illustrates for a price decrease in good 1. . ................................................................................ . .................................................................................................... ............................................................................................................................................................................................................................................................................................. . . 0 x2 x1 x a 1 x b 1 x c 1 . . . . . . . . . . . . . . . . • The consumer now chooses (as before) x b 1 on the outermost budget line. The Hicks substitution effect is the change in demand due to the relative price change given a constant level of utility rather than income. • Notice the consumer is indifferent between bundles x a and x c . On this new parallel budget line, the consumer can no longer afford x a — unlike before. The Hicks substitution effect is then given by ∆x s 1 = x c 1 − x a 1 . • The Hicks income effect is ∆x n 1 = x b 1 − x c 1 . These can be different in size from the Slutsky effects. The price effect is the same of course. This means a Slutsky inferior good is not always a Hicks inferior good and vice-versa. • The substitution effect is still always in the opposite direction to the price change. Why? Consumption — Applications 2 Some Examples • Returning to Slutsky decompositions, consider the cases of perfect complements and perfect substitutes. ............................................................................................................................................................................................................................................................................................. . . ............................................................................................................................................................................................................................................................................................. . . ............................................................................................................. ............................................................................................................. ................................................................................................................................................................................................................................................................................................................ . . ........................................................................................................................................................ ...... ...... ... ...... ...... ...... ... 0 0 x2 x1 x2 x1 x a 1 x b 1 x a 1 x b 1 • • • . • . . . . . . . . • In both cases there is a decrease in p1. The consumer changes from x a 1 to x b 1 . • The first graph shows the perfect complement case — it is all income effect. The substitution effect is zero. • The second graph shows the perfect substitute case — it is all substitution effect. The income effect is zero. • Note the Slutsky and Hicks decompositions are identical for both cases. Why?