Topic 4b Competitive consumer

Transcription

1 Competitive consumer About your economic situation, do you see the light at the end of the tunnel? I think the light at the end of the tunnel has been turned off due to my budget constraints. 1 of 25

2 The Budget Constraint (I): What the consumer can afford Now Hurley has an income. So he divides his income between two goods: fish and mangos. A budget constraint represents the combinations of goods and services that a consumer can purchase given current prices with his/her income. Thus, it requires that the cost of a consumer s consumption bundle be no more than the consumer s total income. A consumer s consumption possibilities is the set of all consumption bundles that can be consumed given the consumer s income and market prices, and a consumer s budget line is the consumption bundles available to a consumer who spends all of his/her income. 2 of 25

3 The Budget Constraint (II):! Example 1 (I) Hurley s income is $1,200 Market prices are P F = $4 per fish and P M = $1 per mango. A. If Hurley spends all his income on fish, how many fish does he buy? B. If Hurley spends all his income on mangos, how many mangos does he buy? C. If Hurley buys 100 fish, how many mangos can he buy? D. Plot each of the bundles from parts A C on a graph that measures fish on the x-axis and mangos on the y-axis, connect the dots. 3 of 25

4 The Budget Constraint (III):! Example 1 (II) A. $1200/$4 = 300 fish B. $1200/$1 = 1200 mangos Mangos B! C. 100 fish cost $400, $800 left buys 800 mangos C! D. Hurley s budget line shows the bundles he can afford. A Quantity of Fish 4 of 25

5 The Slope of the Budget Line! Example 1 (III): Slope and Prices Hurley must give up 4 mangos to get one fish: Slope = 4 and is constant along the budget line. The slope of the budget line equals: 1) the rate at which Hurley can trade mangos for fish. 2) the opportunity cost of fish in terms of mangos 3) the relative price of fish: price of fish $ 4 = = price of mangos $ 1 4 mangos per fish Mangos C! D Quantity of Fish 5 of 25

6 Budget Constraint and Budget Line Algebraic expressions The budget constraint: (Q X P X ) + (Q Y P Y ) N The budget line: (Q X P X ) + (Q Y P Y ) = N Or, basically: Q Y = N / P Y (P X / P Y ) Q X 6 of 25

7 Budget Constraint and Budget Line Example 1 (IV)! mangos Hurley s income: $1200 Prices: P F = $4 per fish, P M = $1 per mango 1200 A B Unaffordable consumption bundles Hurley s budget line: Q M = N/P M (P F /P M ) x Q F Q M = Q F C Consumption possibilities set D E Budget line F fish 7 of 25

8 Shifts of the Budget Line Example 2 (I) Show what happens to Hurley s budget line if: A. His income falls to $800, or B. The price of mangos rises to P M = $2 per mango. 8 of 25

9 Shifts of the Budget Line Example 2 (II) A. Now, Hurley can buy $800/$4 = 200 fish, or Mangos $800/$1 = 800 mangos, or any combination in between. A fall in income shifts the budget line downwards and decreases the consumption possibilities set Fish 9 of 25

10 Shifts of the Budget Line Example 2 (III) B. Hurley can still buy 300 fish. But now he can only buy $1200/$2 = 600 mangos. The slope is smaller, relative price of fish is now only 2 mangos. Mangos An increase in the price of one good pivots the budget line downward, decreasing its slope (in absolute value) Fish 10 of 25

11 What the consumer chooses (I) Optimization (I) A is the optimum: the point on the budget constraint tangent to the highest possible indifference curve. Mangos 1200 Hurley prefers B to A, but he cannot afford B. Hurley can afford C and D, but A is on a higher indifference curve. The optimum is the bundle Hurley most prefers out of all the bundles he can afford. 600 A! B! C! D! Fish 11 of 25

12 What the consumer chooses (II) Optimization (II) At the optimum, the slope of the indifference curve equals the slope of the budget constraint: Mangos 1200 MRS F M = P F /P M marginal value of fish (in terms of mangos) price of fish (in terms of mangos) 600 A! B! C! D! Fish of 25

13 What the consumer chooses (III) The Relative Price Rule The tangency condition between the indifference curve and the budget line defines the optimal consumption bundle (when indifference curves are convex) the slope of the budget line is the relative price of good X in terms of good Y, P X /P Y, the rate at which X trades for Y in the market. At the optimal consumption bundle, the marginal rate of substitution between two goods is equal to their relative price. This is known as the Relative Price Rule. Y B 30 I C I 1 BL X A Optimal consumption bundle I 3 13 of 25

14 What the consumer chooses (IV) Understanding the Relative Price Rule restaurant meals 80 At the optimal consumption bundle: MRS R M = P R /P M! B A At the optimal consumption bundle, MRS R M is equal to the relative price. 30 I 2 20 C 10 I 1 BL rooms 14 of 25

15 Preferences and Choices (I) Differences in Preferences When we say that two consumers have different preferences, we mean that they have indifference curve maps with different shapes. And those different maps will translate into different consumption choices, even among consumers with the same income who face the same prices. restaurant meals restaurant meals (a) Ingrid s Preference and Her Optimal Cons. Bundle Ingrid s optimal consumption bundle I 3 I 2 I 1 BL rooms (b) Lars s Preference and His Optimal Cons. Bundle Lars s optimal consumption bundle I 3 40 I I 1 10 BL rooms 15 of 25

16 Preferences and Choices (II) Consumer Choice between Perfect Substitutes (a) Mike Buys Only Peanut Butter Cookies (b) Mike Buys Only Chocolate Chip Cookies peanut butter cookies A 2 BL I 1 I chocolate chip cookies peanut butter cookies I 2 I 1 BL 2 B chocolate chip cookies 16 of 25

17 Preferences and Choices (III) Consumer Choice between Perfect Complements milk (glasses) 5 4 A B C I 4 3 I I 2 I 1 BL cookies 17 of 25

18 Prices, Income and Demand (I) Effects of a Price Increase in the Budget Line BL 1 : Income = 2400$, maximum number of rooms she can afford: 2400/150 = 16, maximum number of meals: 2400/30 = 80. restaurant meals New BL 2 : price of rooms = $600 An increase in the relative price of rooms rotates the budget line inward. Original BL 1 : price of rooms = $150 BL 2 : Income = 2400$, maximum number of rooms she can afford: 2400/600 = 4, maximum number of meals: 2400/30 = BL 2 BL rooms 18 of 25

19 Prices, Income and Demand (II) Responding to a Price Increase restaurant meals 3. and increases restaurant meal consumption C 10 BL 2 I 1 BL reduces housing consumption New optimal consumption bundle A Original optimal consumption bundle I 2 rooms 1. An increase in the relative price of rooms rotates the budget line 19 of 25

20 Prices, Income and Demand (III) The Demand Curve: Movements along the curve Price of rooms Demand curve for rooms 600 C 150 A D R (I,P m,pref) rooms 20 of 25

21 Prices, Income and Demand (IV) Effects of a Change in income on the Budget Line! restaurant meals A fall in income results in a parallel inward shift of the budget line. 40 A rise in income results in a parallel outward shift of the budget line. BL 2 BL 1 BL rooms 21 of 25

22 Prices, Income and Demand (V) Income and Consumption: Normal goods! restaurant meals Optimal consumption bundle income at of $1, and a fall in consumption of restaurant meals B Optimal consumption bundle at income of $2,400 A 10 I BL 1 2 BL rooms I 2 2. resulting in a fall in consumption of rooms 1. A fall in income shifts the budget line inward, 22 of 25

23 Prices, Income and Demand (VI) Income and Consumption: An inferior good! restaurant meals Optimal consumption bundle at income of $2, and a fall in consumption of restaurant meals D I 2 Optimal consumption bundle at income of $1,200 E 2. resulting in a rise in consumption of second-hand furniture BL 2 I 1 BL 1 second-hand furniture 1. A fall in income shifts the budget line inward, 23 of 25

24 Prices, Income and Demand (VII) The Demand Curve: Shifts in the curve Price of rooms Demand curve for rooms B A D R (I,P m,pref) rooms 24 of 25

25 K E Y T E R M S Income Budget constraint Consumption bundle Budget line Consumption Possibilities Optimal Consumption Bundle Tangent Condition Marginal Rate of Substitution (MRS) Relative Price Relative Price Rule Choice between Perfect substitutes Choice between Perfect complements Shifts in the Budget Line Normal goods Inferior goods Demand Curve Shifts in the Demand Curve Movements along the Demand Curve 25 of 25