ch 8 slutsky equation

given good

optimal demand decreases when price falls

slutsky substitution effect

the change in demand due to the relative price change, assuming their purchasing power (real income) has not changed, such that they can only just buy the original bundle at new prices

income effect

the change in demand due to having more purchasing power (as if the income rose)

pivot is due to

substitution effect; goes around the original choice

shift is due to

income effect, budget line shifts outward to the new demanded bundle

slutsky substitution effect dx₁^s =

x₁(p₁’, m’) - x₁(p₁, m), where p1’ is the new price, m’ is the income to make OG bundle just affordable, and m is the OG income

slutsky income effect, dx₁ⁿ =

x₁(p1’, m) - x₁(p₁’, m’)

substitution effect always acts

opposite to price movement

total change in demand =

x₁(p₁’, m) - x₁(p₁, m) = dx1s + dx1n

income effect acts in

opposite direction as price movement for normal goods, same direction for inferior/giffen good

perverse case/giffen good when

income effect outweighs substitution effect in opposite direction

law of demand

if demand for a good increases with income, then demand must decrease when price increases

what effect do perfect complements have

just income effect

what effect do perfect subsitutes and quasilinear preferences have

just substitution

hicks substitution effect

keeps utility constant rather than purchasing power, rolling line around indifference curve

compensated demand curve

Hicks; adjusting income as price changes to keep utility constant