Substitution Effect, Income Effect, Giffen GoodsFrom Individual Demand to Market DemandConsumer SurplusCite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 1 Substitution Effect, Income Effect, Giffen Goods 14.01 Principles of Microeconomics, Fall 2007 Chia-Hui Chen September 19, 2007 Lecture 7 Substitution and Income Effect, In dividual and Market Demand, Consumer Surplus Outline 1. Chap 4: Substitution Effect, Income Effect, Giffen Goods 2. Chap 4: From Individual Demand to Market Demand 3. Chap 4: Consumer Surplus 1 Substitution Effect, Income Effect, Giffen Goods Substitution and Income Effects The impact of price change on quantity demanded are divided into two effects: Substitution effect. Substitution effect is the change in an item’s consump-tion associated with a change in the item’s price with the utility level held constant. Income effect. Income effect is a change in an item’s consumption associated with a change in purchasing power with the price held constant. Figure 1 shows the two effects: L is the old budget line. Px decreases, and hence the new budget line is L′. A is the optimal consumption before price change, and C is the optimal consumption after price change. L′′ is a line that has the same slo pe as L′ and is tangent with the green indifference curve that passes through A, and B is the tangent point. • The change from A to B is because of the substitution effect; • The change from B to C is beca use of the income effect. So the total effect is point A moving to C. Inferior Good and Giffen Good Now consider different p ositions of C (Figure 1): • The income effect is B changing to C. In this case, an incre ase in income causes an incre ase in the demand of x. x is a normal g ood.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2 1 Substitution Effect, Income Effect, Giffen Goods Figure 1: Substitution Effect and Income Effect.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 3 1 Substitution Effect, Income Effect, Giffen Goods • The income effect is B changing to C′ or C′′. In these cases, an increase in income causes a decrease in the demand of x. x is an inferior good; • If the total e ffect is A changing to C′′, such that a decrease in price causes a decrease in the demand, we call x is a Giffen good. Price increases substitution effect quantity increases Normal good income effect quantity increases substitution effect quantity increases Inferior good income effect quantity decre ases Table 1: Normal Good and Inferior Good In Table 1, if x is a normal g ood, b oth substitution and income effects increase its quantity; if x is an inferior good, discuss as follows: 1. substitution effect > income effect quantity increases → 2. substitution effect < income effect quantity decreases. This unusual good is called a Giffen good. A Giffen → good must be a n inferior good, but an inferior good is no t necessarily a Giffen good. Giffen good. Good with an upward demand curve. (Figure 2) Example (Giffen Good Example: Irish Potato Famine). People consumed lots of potato but little meat (and other food) since meat was more expensive. Price o f potato rose. People had less money to consume meat, so they ate more potatoes instead of meat. An Example of Substitution Effects and Income Effects Utility function Figure 3: U(x, y) = x + 2√y. Parameters: Px = 1, Py = 1, I = 5. The optimal solution is: x = 4, y = 1.4 1 Substitution Effect, Income Effect, Giffen Goods P 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0 0.5 1 1.5 2 2.5 3 3.5 4 QD Figure 2: Demand Curve of Giffen Good. i.e. the solution is at point A: (4, 1). If price of x changes to 2, Px ′ = 2, then the new optimal solution is: 1 x = ,2y = 4. 12i.e. the solution is at point C: ( ,4). Try to find out the substitution effect, i.e. the change from A to B. At B, the slope of the indifference curve equals the slope of the new budget constraint. Thus, 1 P ′ 2xMRS = = = . P ′ 11 √y y = y = 4.⇒ On the other hand, U(x, y) = x + 2 ×√4 = 4 + 2 ×√1. = x = 2.⇒ Thus, point B is at (2,4 ). Decomposition of the two effects: Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. � 5 2 From Individual Demand to Marke t Demand y 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 x 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 C (1/2,4) B (2,4) A(4,1) Figure 3: Showing the Substitution effect and Income Effect. Substitution effect (A to B)• (4,1) = (2,4). ⇒ Income effect (B to C)• (2,4) = (1 ,4). ⇒ 2 2 From Individual Demand to Market Demand Assume in a market there are two individuals A and B. And their demand functions are: QA = 1 − P, 1 QB = P. 1 −2 When P < 1, both individuals consume, and the market demand is the sum of the individual demands: 2 Q = QA + QB = 2 − P. 3 However, if P is larg e r than 1, only B consumes, so the market demand equals the demand of B. Thus, the market demand function is P if P � 1 Q =2 −123 . 1 −2 P if P > 1Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month