HE2001 -Decomposition of Price change Effect

• Substitution effect is the change in demand due to the change in the rate of exchange between the two goods
• Income effect is the change in demand due to having more purchasing power
• Change in demand = Pure substitution effect + Income effect
• Budget line that has the same slope implies that the budget line has same relative price as the final budget line
• At (x1, x2), the consumption bundle is just affordable and the purchasing power of the consumer has remained constant

  
• At (x1, x2), the consumption bundle is affordable but it is not the optimal purchase at the pivoted budget line

  
• m' is the amount of money income that will make the original consumption bundle just affordable

  
• According to the equation, ∆m = m' - m represents the change in income necessary to make the old bundle just affordable

  
• According to the equation, ∆p1 = p'1 - p1 is the change in price of good 1
• According to the equation, ∆m = x1(∆p1) shows the change in income and the change in price will always move in the same direction
• When the price of good 1 goes down, the adjustment in income will be negative

  
• When prices goes down, the consumer's purchasing power goes up, so we will have to decrease the consumer's income in order to keep purchasing power fixed

  
• Movement from X to Y is know as the substitution effect, it indicates how the consumer "substitutes" one good for another when price changes but purchasing power remains constant

  
• The substitution effect is the change in the demand for good 1 when the price of good 1 changes to p1', and at the same time, money income changes to m'

  
• Substitution effect is sometimes called the change in compensated demand, this would mean that if price goes down, consumer is "compensated" by having money taken away from him
• Income effect is changing the income while keeping the prices fixed at the new price

  
• If the good is a normal good, an increase in income will lead to an increase in demand
• If the good is an inferior good, an increase in income will lead to a decrease in demand
• A substitution effect is negative means if the price increases, the demand for the good due to the substitution effect decreases
• The total change in demand ∆x1 = x1 (p1', m) - x1 (p1, m). It is the change in demand due to the change in price, holding income constant
• When the price of a normal good increases, the ∆x1^s decreases + ∆x1^n decrease, therefore the change in demand ∆x1 decreases
• When the price of a not too inferior good increases, the substitution effect is greater than the income effect, therefore the total change in demand decreases
• When the price of Giffen good increases, the substitution effect is lesser than the income effect, therefore the total change in demand increases
• The law of demand states that choices made by rational consumers must satisfy strong axiom of revealed preference
• The law of demand is defined as if the demand for a good increases when income increases, then the demand for that good must decrease when its price increases
• Slustky decomposition assures the negativity of substitution effect such that if the demand increases when income increase, we have normal good
• The change in demand on perfect complements goods is due entirely to the income effect

  
• The change in demand on perfect substitutes are entirely to the substitution effect

  
• When preferences are quasilinear, the entire change in demand for good 1 is due to substitution effect as income effect is zero because shift in income does not change the demand

  
• Slutsky substitution effect pivots the budget line around the original consumption bundle but Hicks roll the budget line around the indifference curve through the original bundle
• Slustky substitution effect makes the original bundle just affordable but Hicks substitution effect makes the original bundle no longer available, but sufficient purchasing power to be indifferent
• Slutsky substitution effect gives the consumer just enough money to get back to his old level of consumption, but Hicks substitution effect gives the consumer just enough money to get back to his old indifference curve
• Slutsky substitution effect and Hicks substitution effect have the same relative prices as the final budget line
• Slutsky and Hicks substitution effect have negative substitution effect which means it is in a direction opposite that of the price change
• In Hicks substitution effect, utility is kept constant rather than keeping purchasing power constant

  
• For a small change in price, the two substitution effects are virtually identical
• Using the definition of revealed preference for Hicks substitution effect, this means that the 2 inequalities are not true: 1. p1x1 + p2x2 > p1y1 + p2y2 2. q1y1 + q2y2 > q1x1 + q2x2

  
• The general statement about how demand changes when price changes if income is adjusted so as to keep the consumer on the same indifference curve is (q1 - p1)(y1 - x1) ≤ 0
• (q1 - p1)(y1 - x1) ≤ 0 states that the change in the quantity demanded must have the opposite sign from that of the price change
• When price change, we are able to hold different factors fixed such as for standard case, we hold nominal income constant. For Slutsky substitution effect, we hold purchasing power constant. For Hicks substitution effect, we hold utility constant.