7- Income & Substitution effects

Normal good

Income inc => demand inc (In that income range- we r looking at small changes)

For what type of preferences are goods normal at every level

Cobb Douglas

Inferior goods

Income dec => demand dec (in that income range)

Ordinary goods

X1* goes down when P1 goes up

Giffen good

X1* goes up when P1 goes up

If giffen good normal or inferior, prove why

Inferior

If preferences are quasi linear, where x2 is linear, how does the income effect change consumption of x1, draw graph

No change to consumption of x1, as all IC’s are vertical shifts of each other

Cross price effect: when is a good a substitute

Cross price effects: when is a good a complement

What is the substitution effect, how does utility change

• when price of x1 falls, it becomes relatively cheaper

• Hence becomes relatively more attractive

• Consumers rate of sub between the two goods will increase to consume more x1 relative to x2

• Utility doesn’t change when this effect is in play

What is the income effect, how does utility change

• when price of x1 falls, even if M constant, budget set becomes bigger and effectively more PURCHASING POWER

• Utility should increase

Slutsky decomposition steps, draw pic

1) remove income effect by decreasing M such that new BL goes through initial bundle (still spends all money but doesn’t feel wealthier)

2) if this was the new BL, wld choose Y not X, hence sub effect from X to Y

Slutsky substitution equation

Slutsky income effect equation

Slutsky identity

Sign of sub effect

Always opp to price change

Sign of income effect

Depends on if good normal Or inferior

If normal - opp sign to price change

If inferior - same sign to price change

Income and sub effects on normal good

Both same way (both opp to price change)

Income and sub effects on inferior good, total effect?

Opposite directions, total effect depends on whcih dominates

I&S effects on perfect complements

I&S effects on perfect substitutes

I&S effects on quasilinear preferences

Why does hicks disagree w Slutsky

• Argues that pure substitution effect should not increase consumers welfare (ie new IC should not be able to be reached)

• But Slutsky bundle Y makes consumer better off

Hicks decomposition

• remove income effect by decreasing M such that on same IC as original choice - same U

• The new point where BL is tangent to original IC is the sub effect

Compensated demand

• what consumer chooses with HYPOTHETICAL income and new prices (hyp income is diff for Slutsky vs hicks therefore so is compensated demand)

• Original choice - compensated demand = sub effect

Difference between Slutsky and hicks

• difference in how they view compensated demand needed to isolate sub effect

• Slutsky - compensate income so consumer can j afford original choice

• Hicks - compensate consumer so they can stay on same IC