Income Elasticity (Normal Goods) Income Elasticity (Normal Goods)

e y  %  Q x %  Y [Where Y = income] Income elasticity is a measure of the change in demand [a “shift” of the demand function] that is “caused” by a change in income.. Q/ut P D At a price of P 1, the quantity demanded given the demand D is Q1 Q1. P1P1 Q1Q1 D is the demand function when the income is Y 1. For a “normal good” an increase in income to Y 2 will “shift” the demand to the right. This is an increase in demand to D 2. Due to increase in income, demand increases D2D2 The increase in income,  Y, increases demand to D 2. The increase in demand results in a larger quantity being purchased at the same Price [ P 1].. Q2Q2 %  Y > 0; %  Q> 0; therefore, e y >0 [it is positive] Income Elasticity [normal goods]

ey  ey  %  Q x %  Y Q/ut P D1D1 A decrease in income is associated with a decrease in the demand for a normal good. At income Y 1, the demand D 1 represents the relationship between P and Q. At a price [P 1 ] the quantity [Q 1 ] is demanded. P1P1 Q1Q1 For a decrease in income [-  Y], the demand decreases; i.e. shifts to the left, A decrease in income, decreases demand D2D2 at the price [P 1 ], a smaller Q 2 will be purchased. Q2Q2 %  Y 0 [ positive] For either an increase or decrease in income the e p is positive. A positive relationship [positive correlation] between  Y and  Q is evidence of a normal good.

When income elasticity is positive, the good is considered a “normal good.” An increase in income is correlated with an increase in the demand function. e y  %  Q x %  Y ey  ey  %  Q x %  Y + %  Y + %  Q x + e y A decrease in income is associated with a decrease in the demand function. - %  Y - %  Q x + e y For both increases and decreases in income, e y is positive. The greater the value of e y, the more responsive buyers are to a change in their incomes. When the value of e y is greater than 1, it is called a “superior good.”. The | %  Q x | is greater than the | %  Y |. Buyers are very responsive to changes in income. Sometimes “superior goods” are called “luxury goods.”

Income Elasticity (Normal Goods) Income Elasticity (Inferior Goods)

ey  ey  %  Q x %  Y D1D1 There is another classification of goods where changes in income shift the demand function in the “opposite” direction. An increase in income [+  Y] reduces demand. Q/ut P P1P1 Q1Q1 decreases demand D2D2 Q2Q2 +Y+Y - %Qx- %Qx -%Qx-%Qx -e y =. An increase in income reduces the amount that individuals are willing to buy at each price of the good. Income elasticity is negative: - e y The greater the absolute value of - e y, the more responsive buyers are to changes in income.

D1D1 A decrease in income [ -  Y] increases demand. Q/ut P P1P1 Q1Q1 D2D2 Q2Q2 e y  %  Q x %  Y -Y-Y +%Qx+%Qx Decreases in income increase the demand for inferior goods. +%Qx+%Qx - e y. A decrease in income [-  Y] results in an increase in demand, the income elasticity of demand is negative. For both increases and decreases in income the income elasticity is negative for inferior goods. The greater the absolute value of e y, the more responsive buyers are to changes in income

Fall '97Economics 205Principles of MicroeconomicsSlide 8 Income Elasticity Income elasticity [ e y] is a measure of the effect of an income change on demand. [ Can be calculated as point or arc.] e y > 0, [positive] is a normal or superior good an increase in income increases demand, a decrease in income decreases demand. 0 < e y < 1 is a normal good 1 < e y is a superior good e y < 0, [negative] is an inferior good

Fall '97Economics 205Principles of MicroeconomicsSlide 9 Examples of e y normal goods, [0 < e y < 1 ], (between 0 and 1) coffee, beef, Coca-Cola, food, Physicians’ services, hamburgers,... Superior goods, [ e y > 1], (greater than 1) movie tickets, foreign travel, wine, new cars,... Inferior goods, [ e y < 0], (negative) flour, lard, beans, rolled oats,...

Income Elasticity (Normal Goods) Cross-price elasticity of demand, [exy] [substitutes]

. When the price of mutton increases, it will tend to increase the demand for beef. People will substitute beef, which is relatively cheaper, for mutton, which is relatively more expensive. mutton/ut [price of mutton] PmPm DpDp When mutton is $1.50, Q m is purchased DbDb beef/ut [price of beef] PbPb QmQm When beef is $2, Q b beef is purchased. 2 QbQb price of mutton increases 2 The quantity demanded of mutton decreases. Qm’Qm’ -Qp-Qp at P b = $2 more beef will be bought to substitute for the smaller quantity of mutton. increase demand Db’Db’ Qb’Qb’ for an increase in P mutton, demand for beef increases

Cross-price elasticity In the case of beef and mutton the e bm is not the same as e mb e bm is the % change in the demand for beef with respect to a % change in the price of mutton e mb is the % change in the demand for mutton with respect to a % change in the price of beef beef may not be a good substitute for mutton mutton may not be a good substitute for beef

The cross elasticity of the demand for beef with respect to the price of mutton, e beef-mutton or e bm can be calculated: e bp = %  Q of beef %  P of mutton An increase in the price of mutton, +  P m “causes” an increase in the demand for beef. + Qb+ Qb +e bm positive cross elasticity is positive e bp = %  Q of beef %  P of mutton A decrease in the price of mutton, - Pm- Pm “causes” a decrease in the demand for beef. -  Q b +e bm positive If goods are substitutes, e xy will be positive. The greater the coefficient, the more likely they are good substitutes.

Income Elasticity (Normal Goods) Cross-price elasticity of demand, [exy] [Compliments]

colour books PcPc crayons PcPc DpDp a decrease in the price of crayons, P1P1 Q1Q1 $ PoPo Q2Q2 increases the quantity demanded of crayons as more crayons are purchased, the demand for colour books increases. DcDc Dc’Dc’ increase demand 2500 At the same price a larger quantity will be bought e bc = %  Q of b %  P of c -Pc-Pc -  P c +  Q b - e bc negative for compliments, the cross elasticity is negative for price increase or decrease.

Fall '97Economics 205Principles of MicroeconomicsSlide 16 Cross-Price Elasticity e xy > 0 [positive], suggests substitutes, the higher the coefficient the better the substitute e xy < 0 [negative], suggests the goods are compliments, the greater the absolute value the more complimentary the goods are e xy = 0, suggests the goods are not related

Income Elasticity (Normal Goods) Elasticity of Supply

Fall '97Economics 205Principles of MicroeconomicsSlide 18 Elasticity of Supply Elasticity of supply is a measure of how responsive sellers are to changes in the price of the good. Elasticity of supply [ e p ] is defined:

Q /ut P Given a supply function, supply at a price [P 1 ], Q 1 is produced and offered for sale. P1P1 Q1Q1 At a higher price [P 2 ], P2P2 a larger quantity, Q 2, will be produced and offered for sale. Q2Q2 +P+P +Q+Q The increase in price [  P ], induces a larger quantity goods [  Q]for sale. The more responsive sellers are to  P, the greater the absolute value of e s. [The supply function is “flatter”or more elastic] e s = %  Q supplied %P%P

Q /ut P The supply function is a model of sellers behavior. Sellers behavior is influenced by: 1. technology 2. prices of inputs 3. time for adjustment market period short run long run very long run 4. expectations 5. anything that influences costs of production taxes regulations,... SeSe a perfectly elastic supply [ e s is undefined.] SiSi a perfectly inelastic supply, e s = 0 as supply approaches horizontal e s approaches infinity

Income Elasticity (Normal Goods) Summary Price elasticity of demand [measures a move on a demand function caused by change in price/arc or point] elastic, inelastic or unitary elasticity income elasticity [measures a shift of a demand function associated with a change in income] superior, normal, and inferior cross elasticity measure the shift of a demand function for a good associated with the change in the price of a related good [compliment/substitute] price elasticity of supply [measures move on a supply curve]

Income Elasticity (Normal Goods) Reference: Principles of Economics, 6/e by Karl Cas, Ray Fair Slides prepared by: Fernando Quijano and Yvonn Quijano