Consumption- Compurutiae Staties Income and choice Suppose the consumer's income increase. Optimal choice changes. How? ra 2 The first diagram illustrates the case when both goods are normal. As income rises the demand for both goods rises The second diagram illustrates the case when good I is inferior. As income rises the demand for good 1 falls. Good I is normal if△x1/△m>0 and inferior if△r1/△my implies tr ty for all numbers t. come offer curves are also straight lines in this case. Perfect complements, perfect substitutes and Cobb-Douglas
Consumption — Comparative Statics 1 Income and Choice • Suppose the consumer’s income were to increase. Optimal choice changes. How? . ........................................................................... . ............................................................................ . ............................................................................... . .......................................................................................... ............................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................... . . 0 0 x2 x1 x2 x1 x b 2 x b 1 x b 2 x b 1 x a 2 x a 1 x a 2 x a 1 ............. ............. ............. ............. ............. ........... . . . . . . ............. ............. ............. ....... . . . . . . . . . . . . . ..... ............. ............. . . . ......... ............. ............. ............. ............. • The first diagram illustrates the case when both goods are normal. As income rises the demand for both goods rises. • The second diagram illustrates the case when good 1 is inferior. As income rises the demand for good 1 falls. • Good 1 is normal if ∆x1/∆m > 0 and inferior if ∆x1/∆m < 0. Both goods cannot be inferior. Why not? Consumption — Comparative Statics 2 Income Offer Curves and Engel Curves • When the optimal choices are connected up for each income level the resultant curve is called the income offer curve. • The Engel curve is derived from this by plotting each level of income m against the resultant optimal quantity for one of the goods — say good 1, x1. Both curves are drawn below. . ........................................................................... . .......................................................................... ....................................................................................................................... ............................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................... . . . 0 0 x2 x1 m x1 Income offer curve Engel curve Income offer curve • Engel curves distinguish between luxury goods and necessary goods. If demand rises proportionally more than income the good is a luxury — and necessary in the opposite case. • If the Engel curve is a straight line (through the origin), demand rises proportionally with income. The good is neither luxury nor necessity. Homothetic preferences guarantee this. This is when the consumer only cares about the ratio consumed of the two goods. That is, x  y implies tx  ty for all numbers t. • Income offer curves are also straight lines in this case. Perfect complements, perfect substitutes and Cobb-Douglas preferences are all homothetic
Consumption- Compurutiae Staties Price and choice Suppose the price of good I were to Optimal choice changes. How? The first diagram illustrates the case when good 1 is ordinarg. As price rises the demand for good 1 falls. The second diagram illustrates the case when good I is Giffen. As price rises the demand for good 1 rises Good I is ordinary if△r1/△p10. Both goods cannot be Giffen. Why not? Consumption- Comparative Statics Price offer Curves and demand curves When the optimal choices are connected up for each price level the resultant curve is called the price offer curve. derived from this by plotting each level of price Pi against the resultant optimal quantity of good 1. rI. Both curves are drawn below. Price offer rice offer It is also possible to derive the demand curve for good I in terms of the price of good 2 If optimal In increases with an increase in p2(Ar1/Apz>0) then the goods are(gross)substitutes, if optimal I1 eases with an increase in p2(Ar1/Apz 0)then the goods are(gross)complemen The inverse demand function is simply price in terms of quantity: P1= Pi(r1)
Consumption — Comparative Statics 3 Price and Choice • Suppose the price of good 1 were to increase. Optimal choice changes. How? . ............................................... . .......................................................................... . ............................................................................... . .................................................... ............................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................... 0 0 x2 x1 x2 x1 x b 1 x a x 1 b 1 x a 1 . . . . . . . . . . . . . . . . . . . . . . . . . . • The first diagram illustrates the case when good 1 is ordinary. As price rises the demand for good 1 falls. • The second diagram illustrates the case when good 1 is Giffen. As price rises the demand for good 1 rises. • Good 1 is ordinary if ∆x1/∆p1 0. Both goods cannot be Giffen. Why not? Consumption — Comparative Statics 4 Price Offer Curves and Demand Curves • When the optimal choices are connected up for each price level the resultant curve is called the price offer curve. • The demand curve is derived from this by plotting each level of price p1 against the resultant optimal quantity of good 1, x1. Both curves are drawn below. . ............................................... . .......................................................................... . ....................................................................................................................... .............................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................... ...................................................................................................................................................................................................... 0 0 x2 x1 p1 x1 Price offer curve Demand curve Price offer curve • It is also possible to derive the demand curve for good 1 in terms of the price of good 2. • If optimal x1 increases with an increase in p2 (∆x1/∆p2 > 0) then the goods are (gross) substitutes, if optimal x1 decreases with an increase in p2 (∆x1/∆p2 < 0) then the goods are (gross) complements. • The inverse demand function is simply price in terms of quantity: p1 = p1(x1)
Consumption- Compurutiae Staties he price effect When the price changes, demand changes. Economists decompose the overall price effect into three parts. 1. The Substitution Effect: The change in demand due to relative price changes. 2. The Income Effect: The change in demand due to changes in purchasing power with money income constant 3. The Endowment Effect: The change in demand due to changes in the value of the endowment When added together these three effects give the price effect: Price Effect= Substitution Effect +Income Effect Endowment Effect The rest of the lectur es this simple equation-the Slutsky decomposition -in some depth. Consumption- Comparative Statics A Price Chang Initially suppose the consumer has fixed money Throughout the lecture a decrease in pi will examined. An increase in Pi or a change in p2 can be analysed in a similar way. 12 a decrease in pi pivots the budget line outward resulting in a new optimal choice rb. This is illustrated in the above graph. The consumer alters consumption of good 1 from rn to rf. Notice the seco iagram also shows this but without indifference curves. Often, indifference curves can be suppressed and only imal choices drawn in. This simplifies the diagrams a great deal
Consumption — Comparative Statics 5 The Price Effect • When the price changes, demand changes. Economists decompose the overall price effect into three parts. 1. The Substitution Effect: The change in demand due to relative price changes. 2. The Income Effect: The change in demand due to changes in purchasing power with money income constant. 3. The Endowment Effect: The change in demand due to changes in the value of the endowment. • When added together these three effects give the price effect: Price Effect = Substitution Effect + Income Effect + Endowment Effect • The rest of the lecture examines this simple equation — the Slutsky decomposition — in some depth. Consumption — Comparative Statics 6 A Price Change • Initially suppose the consumer has fixed money income m. Throughout the lecture a decrease in p1 will be examined. An increase in p1 or a change in p2 can be analysed in a similar way. . ............................................... . .......................................................................... ............................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................... 0 0 x2 x1 x2 x1 x a x 1 b 1 x a 1 x b 1 • • x a x b . . . . . . . . . . . . . . . . . . . . . . • A decrease in p1 pivots the budget line outward resulting in a new optimal choice x b . • This is illustrated in the above graph. The consumer alters consumption of good 1 from x a 1 to x b 1 . Notice the second diagram also shows this but without indifference curves. Often, indifference curves can be suppressed and only optimal choices drawn in. This simplifies the diagrams a great deal
Consumption- Compurutiae Staties The Substitution Effect 1 Suppose the consumer's optimal choice changes from r to r due to a decrease in The change in demand for good I is Ar=rf-rf. This change can be decomposed into two parts-a substitution effect and pose the consumers money income m was changed so that they could sti afford to buy their initially losen bundle, r". Their initial budget line was A which pivoted to B following the decrease in pI. Now some of their income is "taken away " resulting in budget line C above. At budget line C only the relative price change has taken place. Furthermore, given budget line C the consumer light no longer choose bundle r". They could prefer a bundle further down C. The next slide illustrates this. Consumption- Comparative Statics The Substitution Effect Suppose at the new budget line C, the consumer purchases bundle r=(rf, ri)as in the graph below. The substitution effect is then the change in demand due to the relative price change alone, given Notice that r is further down budget line C than r". It could not go further up the budget line. Why not? Because of this, the substitution effect is always in the opposite direction to the price change
Consumption — Comparative Statics 7 The Substitution Effect 1 • Suppose the consumer’s optimal choice changes from x a to x b due to a decrease in p1. • The change in demand for good 1 is ∆x1 = x b 1 − x a 1 . This change can be decomposed into two parts — a substitution effect and an income effect. .............................................................................................................................................................................................................................................................................................. 0 x2 x1 A C B x a 1 x b 1 • • x a x b . . . . . . . . . . . . • Suppose the consumer’s money income m was changed so that they could still just afford to buy their initially chosen bundle, x a . Their initial budget line was A which pivoted to B following the decrease in p1. Now some of their income is “taken away” resulting in budget line C above. • At budget line C only the relative price change has taken place. Furthermore, given budget line C the consumer might no longer choose bundle x a . They could prefer a bundle further down C. The next slide illustrates this. Consumption — Comparative Statics 8 The Substitution Effect 2 • Suppose at the new budget line C, the consumer purchases bundle x c = (x c 1 , x c 2 ) as in the graph below. .............................................................................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................................................................. 0 0 x2 x1 x2 x1 A C B • • • • • • x a x b x c x a 1 x b 1 x c 1 . . . . . . . . . . . . . . • The substitution effect is then the change in demand due to the relative price change alone, given by: ∆x s 1 = x c 1 − x a 1 • Notice that x c is further down budget line C than x a . It could not go further up the budget line. Why not? • Because of this, the substitution effect is always in the opposite direction to the price change
Consumption- Compurutiae Staties The income effect Returning to the consumer the income previously taken away" results in another optimal choice -r The income effect is then the change in demand due to the change in purchasing power alone, given by If good I is normal, I' will lie to the right of r. If good 1 is inferior, r will lie to the left of r. The income effect an be in the opposite direction to the substitution effect (an inferior good) or in the same direction(a normal good ). The diagram above illustrates a normal good. Giffen goods arise when the good is inferior and the income effect is large enough to outweigh the substitution effect. In this case rb lies to the left of r"- Giffen goods are always inferio Consumption- Comparative Statics The law of demand The Slutsky decomposition can be written as△r=△ri+△r1 Although Ar could be of either sign- the good could be ordinary or Giffen, something can be said about the relationship between Ar and Ar with the current assumptions in place The substitution effect is always in the opposite direction to the price change so the following is true. The Law of Demand: If demand for a good increases when income increases then demand for that good must ecrease when its price increases
Consumption — Comparative Statics 9 The Income Effect • Returning to the consumer the income previously “taken away” results in another optimal choice — x b . .............................................................................................................................................................................................................................................................................................. .............................................................................................................................................................................................................................................................................................. 0 0 x2 x1 x2 x1 A C B • • • • • • x a x b x c x a 1 x b 1 x c 1 . . . . . . . . . . . . . . • The income effect is then the change in demand due to the change in purchasing power alone, given by: ∆x n 1 = x b 1 − x c 1 • If good 1 is normal, x b will lie to the right of x c . If good 1 is inferior, x b will lie to the left of x c . The income effect can be in the opposite direction to the substitution effect (an inferior good) or in the same direction (a normal good). The diagram above illustrates a normal good. • Giffen goods arise when the good is inferior and the income effect is large enough to outweigh the substitution effect. In this case x b lies to the left of x a — Giffen goods are always inferior. Consumption — Comparative Statics 10 The Law of Demand • The Slutsky decomposition can be written as ∆x1 = ∆x s 1 + ∆x n 1 . • Although ∆x1 could be of either sign — the good could be ordinary or Giffen, something can be said about the relationship between ∆x1 and ∆x n 1 with the current assumptions in place. • The substitution effect is always in the opposite direction to the price change so the following is true. • The Law of Demand: If demand for a good increases when income increases then demand for that good must decrease when its price increases
Consumption- Compurutiae Staties The Endowment effect 山 the endowment effect. Recall a price change will pivot the budget line through the endowment point. The first graph shows a fall in pi.w is the endowment, ra the initially chosen bundle and r the bundle chosen after the price change. The second graph shows the decomposition. Budget line A represents the initial prices. Budget line B corresponds to the substitution effect. C to the income effect and D to the endowment effect. The third graph shows the three effects. Ar=ri-ri is the substitution effect. Ar=rf-rh is the income effect. Ar=ri-ri is the endowment effect. So △n1=△r+△r+△r=-理 Consumption- Comparative Statics nd Selling Remember that the endowment effect is a change in demand due to a shift in the budget line therefore its sign is etermined by whether the good is normal or inferior. On the last graph, r lies to the right of r and to the left of r. This is because the good is normal. The income and endowment effects are related in this way. Take care -r could not lie to the left of r for example. d1 Given a fall in Pi, budget line A mowes to budget line D in both graphs. Optimal choice changes from r to r In the first In the second graph, the a net seller of good 1- after Pi falls they need not be. If they continue to be a net seller after a price fall they are worse off. If they are a net ad there is a price fall ley are better off. What about a price rise? Net sellers continue to sell and are better off. Buyers need not continue to buy, but if they do they are worse off. Why
Consumption — Comparative Statics 11 The Endowment Effect • Up until now the consumer’s income has been a fixed number m. When the consumer receives an endowment ω, there is a third effect to take into consideration — the endowment effect. • Recall a price change will pivot the budget line through the endowment point. The first graph shows a fall in p1. ω is the endowment, x a the initially chosen bundle and x d the bundle chosen after the price change. .............................................................................................................................................................................................................................................................................................. ............................................................................................................................................................................................................................................................................................... ............................................................................................................................................................................................................................................................................................... . . . . 0 0 0 x2 x1 x2 x1 x2 x1 • • • • • • • • • • • • • A D A B D C x a x a x b x c x d x d ω ω ω x a 1 x b 1 x c x 1 d 1 . . . . . . . . . . • The second graph shows the decomposition. Budget line A represents the initial prices. Budget line B corresponds to the substitution effect, C to the income effect and D to the endowment effect. • The third graph shows the three effects. ∆x s 1 = x b 1 − x a 1 is the substitution effect. ∆x n 1 = x c 1 − x b 1 is the income effect. ∆x ω 1 = x d 1 − x c 1 is the endowment effect. So: ∆x1 = ∆x s 1 + ∆x n 1 + ∆x ω 1 = x d 1 − x a 1 Consumption — Comparative Statics 12 Buying and Selling • Remember that the endowment effect is a change in demand due to a shift in the budget line, therefore its sign is determined by whether the good is normal or inferior. • On the last graph, x d lies to the right of x b and to the left of x c . This is because the good is normal. The income and endowment effects are related in this way. Take care — x d could not lie to the left of x b , for example. .............................................................................................................................................................................................................................................................................................. ..................................................................................................................................................................................................................................................................................................... ........ ........ ........ ......... ........ ........ ........ ......... ........ ........ ........ ........ ......... ........ ........ ........ ......... ........ ........ ........ ......... ........ ........ ........ ........ ......... ........ ........ ........ ......... ........ ........ ........ ...... . 0 x2 x1 0 x2 x1 • • • • • • A D A D x a x d ω x d ω x a • Given a fall in p1, budget line A moves to budget line D in both graphs. Optimal choice changes from x a to x d . • In the first graph, the consumer was a net buyer of good 1 — after p1 falls they always remain a net buyer. • In the second graph, the consumer was a net seller of good 1 — after p1 falls they need not be. • If they continue to be a net seller after a price fall they are worse off. If they are a net buyer and there is a price fall they are better off. What about a price rise? Net sellers continue to sell and are better off. Buyers need not continue to buy, but if they do they are worse off. Why?