Price Elasticity of SupplyConsumer PreferencesCite 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 Price Elasticity of Supply 14.01 Principles of Microeconomics, Fall 2007 Chia-Hui Chen September 12, 2007 Lecture 4 Price Elasticity of Supply; Consumer Preferences Outline 1. Chap 2: Elasticity - Price Elasticity of Supply 2. Chap 3: Consumer Behavior - Consumer Preferences 1 Price Elasticity of Supply Price elasticity of supply. The percentage change in quantity supplied re-sulting from one percentage change in price. dQS EPS = QS = P dQS .dP QS dP P In the short run, if price increases, firms will want to produce more but canno t hire workers and buy machines immediately, thus the supply is less elastic. In contrast, supply is more elastic in the long run. Example (Example in Elasticities of Demand). Assume the quantity demanded is QD = 14 − 3P + I + 2PS − PC . • P - Price • I - Income • PS - Price of substitute • PC - Price o f complement Calculate EPD , EI , EQPS and EQPC when P = 1, I = 1 0, PS = 2 a nd PC = 1. Solution: Given the values of variables, the quantity demanded is: QD = 14 − 3 × 1 + 10 + 2 × 2 − 1 = 24.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 2 Consumer Preferences The elasticities are EPD = P dQD =1 × (− 3) = − 1 , QD dP 24 8 I dQ 10 5 EI = = × 1 = , Q dI 24 12PS dQ 2 1 EQPS = = × 2 = , Q dPS 24 6PC dQ 1 1 EQPC = = × (− 1) = − . Q dPC 24 24 2 Consumer Preferences Consumer preferences Consumer behavior =⇒ Budget constraints • What amount and types of goods will be purchased. • Origin of demand, how to decide demand. Topics 1. Preference 2. Indifference Curve, Marginal Rate of Substitution (MRS) 3. Utility Functions Preference Notation • A ≻ B: A is pre ferred to B. • A∼ B: A is indifferent to B. Basic assumptions for preferences • Completeness - can rank any basket of goods. (always possible to decide preference or indifference) • Tra ns tivity - A≻B and B≻C implies A≻ C. This assumption seems obvious, but can have contradiction (see example below).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 2 Consumer Preferences Property I Property II Property III Good A 3 1 2 Good B 2 3 1 Good C 1 2 3 Table 1: Example of contradiction of transitivity. Example (A contradiction of transtivity). Chart below lists 3 goods and 3 pr operties, ass ume that people will prefer one to another if 2 pr operties are better. Table 1. Actually A ≻ B, B ≻ C and C ≻ A - this loop contradicts the assumption. • Non-satiation - more is better. (Monotonicity) Assume we discuss goo ds, since in general, more is not always better. • Convexity - given two indifferent bundles, always prefer the average to each of them. In Figure 1, the average point C is more preferr ed to A or B. Figure 1: Convexity of indifference curve. Indifference Curve, Marginal Rate of Substitution (MRS) Properties of indifference curves • Downward sloping: if no t, non-satia tion violated. Refer to Figure 1.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]. 4 2 Consumer Preferences Figure 2: Compare the Shapes of Indifference Curve. • Cannot cross: if not, non-satiation and transitivity ca nnot be satisfied simultaneously. In Figure 1, assume there is another indifference curve through A and D. A ∼ B, A ∼ D =⇒ B ∼ D. However, B ≻ D in this figure. Contradiction exists. • Shape: describes how willing one is to substitute one good for a nother. See Figure 2. Marginal rate of substitution (M RS) Marginal rate of substitution (M RS). How many units of Y one is willing to give up in order to get one more unit o f X. −Δy −dy = Δx dx People prefer a balanced basket of goods. • MRS decreasing. • Preferred set is convex. • The left o ne in Figure 2 makes mor e sense in the re al world. Perfect substitution. MRS is constant. Perfect complements. Indifference curves are shaped as right angles. Example (Perfect complements). Buying shoes. People need both the left one and the right one.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 Consumer Preferences Figure 3: Perfect Substitution and Perfect Complements. Figure 4: Indifference Curve with Utility Function u(x, y) = xy. Utility Functions Utility function. Assig ns a level of utility to each basket of consumption. Example (A sample utility function). u(x, y) = xy. For example, (5,5) is indifferent to (25,1) and (1,25). Ordinal utility function. Ranks the preferences, but does not indicate how much one is preferre d to another. Cardinal utility function. Describes the extent to which one of the bundles is preferred to another . Only the o rdinal utility function is re quired in this cours e