7. Slutsky Equation

balancing income and prices

(x1,x2) is affordable at both (p1,p2,m) and (p'1,p2, m') m' = p1'x1+p2x2 m = p1x1+p2x2 subtracting from the second equation from the first gives m'-m = (p1'-p1)x1 change in income equals change in price of commodity 1

the law of downward sloping demand

Since both the substitution and income effects increase demand when own price falls, a normal good's ordinary demand curve slopes down. If the demand for a good increases when income increases, then the demand for that good must decrease when its price increases

x2 (p1, p2', m') - x2 (p1,p2,m)

Substitution effect equation, in which we plug back in to the demand function to find the numbers

△m=x2⋅△p2

finding the new income for the substitution effect

perfect substitutes

when the budget line tilts, the demand bundle jumps from the vertical axis to the horizontal axis. There is no shifting left to do. This entire change in demand is due to the substitution effect.

perfect complements

when we pivot the budget line around the chosen point, the optimal choice at the new budget line is the same as at the old one. This means the substitution effect is zero. This change in demand is due entirely to the income effect.

the total change in demand

while the substitution effect must always be negative, the income effect can go either way. thus the total effect may be postive or negative. Total effect = SE + IE ? - ?

compensated demand curve

A demand curve that shows how quantity demanded varies with price, holding utility constant. the consumer is "compensated" for the price changes ( or adjusts income as price changes) to keep his utility the same at every point.

giffen goods

in rare cases of extreme income-inferiority, the income effect may be larger in size than the substitution effect causing quantity demanded to fall as own prices rises. slutsky's decomposition of the effect of a price change into a pure subsitiution effect and income effect thus explains why the law of downward-sloping demand is violated for extremely income inferior goods

x2 (p1, p2', m) - x2 (p1,p2',m')

income effect equation

Hicks substitution effect

it is the change in demand when prices change but a consumer's utility is held constant, so that the new bundle is indifferent to his original bundle. It is negative

substitution effect (graph)

lower p1 makes good 1 relative cheaper and causes a substitution from good 2 to good 1. This increase in x1 is the substitution effect.

normal goods

most goods are normal (demand increases with income) the substitution and income effects reinforce each other when a normal good's own price changes a decrease in price means that demand will go up due to the substitution effect. if the price goes down, it is like a increase in come, for a normal good, means a increase in demand

substitution effect expanded

slutsky isolated the change in demand due only to the change in relative prices by asking what is the change in demand when the consumer's income is adjusted so that, at the new prices, she can only just buy the original bundle? the commodity is relatively cheaper, so consumers substitute it for now relatively more expensive other commodities. when a price goes down, a consumer's purchasing power goes up, so we will ahve to decrease the consumer's income in order to keep purchasing power fixed. purchasing power remains constant

inferior goods

some goods are income inferior (demand is reduced by high income) the substitution and income effects oppose each other when an income-inferior good's own price changes

income effect (1)

the change in demand due to having more purchasing power. A parallel shift of the budget line is the movement that occurs when income changes while relative prices remain constant

sum of a substitution effect and income effect

the changes to demand from a price change are always the

quasilinear preferences

the shift in income causes no change in demand for good 1 when preferences are quasilinear. This means that the entire change in demand for good 1 is due to the substitution effect, and that the income effect is zero.

sign of the substitution effect

the substitution effect always moves opposite to the price movement. it is negative if the price increases, the demand for the good due to the substitution effect decreases

substitution effect and income effect

what happens when a commodity's price decreases? the commodity is relatively cheaper, so consumers substitute it for now relative more-expensive other commodities the consumer's budget of income can purchase more than before, as if the consumer's income rose, with consequent income effects on quantities demanded