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UNIT I: Theory of the Consumer

UNIT I: Theory of the Consumer. Introduction: What is Microeconomics? Theory of the Consumer Individual & Market Demand. 9/ 14. Individual & Market Demand. Income & Substitution Effects Normal, Inferior, and Giffen Goods Consumer Demand The Determinants of Demand Elasticity

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UNIT I: Theory of the Consumer

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  1. UNIT I: Theory of the Consumer • Introduction: What is Microeconomics? • Theory of the Consumer • Individual & Market Demand 9/14

  2. Individual & Market Demand • Income & Substitution Effects • Normal, Inferior, and Giffen Goods • Consumer Demand • The Determinants of Demand Elasticity • Next Time: Theory of the Firm

  3. Individual & Market Demand Last time, we looked at how consumers make optimal choices. A rational consumer will attempt to maximize utility subject to market conditions (relative prices) and income. That is, given I, Px, Py, she chooses X and Y to maximize U. Today, we want to ask, how do changes in prices effect these consumption decisions? X = f(Px). We will see that changes in prices affect quantities through two causal channels: Income and substitution effects.

  4. Optimization Arlene has $100 income to spend on food (F) and Clothing (C). Food costs $2, and Clothing costs $10. She is currently consuming 30 units of F and 4 units of C. At this point, she is willing to trade 1 unit of C for 2 units of F. Is she choosing optimally? C Utility = No. of Apples + 2(No. of Oranges) F What is the maximum number of clothing units that can be bought?

  5. Optimization Arlene has $100 income to spend on food (F) and Clothing (C). Food costs $2, and Clothing costs $10. She is currently consuming 30 units of F and 4 units of C. At this point, she is willing to trade 1 unit of C for 2 units of F. Is she choosing optimally? C Utility = No. of Apples + 2(No. of Oranges) I/Pc=10 U 4 30 I/Pf =50 F PfF + PcC = I 2F + 10C = I 2(30) + 10(4) = 100 Recall: Conditions for Optimization Spend entire budget Tangency

  6. Optimization Arlene has $100 income to spend on food (F) and Clothing (C). Food costs $2, and Clothing costs $10. She is currently consuming 30 units of F and 4 units of C. At this point, she is willing to trade 1 unit of C for 2 units of F. Is she choosing optimally? C Utility = No. of Apples + 2(No. of Oranges) I/Pc=10 U 4 30 I/Pf =50 F MRScf= 1/2 Pf/Pc = 1/5 Recall: Conditions for Optimization Spend entire budget Tangency MRS = Px/Py

  7. Optimization Arlene has $100 income to spend on food (F) and Clothing (C). Food costs $2, and Clothing costs $10. She is currently consuming 30 units of F and 4 units of C. At this point, she is willing to trade 1 unit of C for 2 units of F. Is she choosing optimally? C Utility = No. of Apples + 2(No. of Oranges) I/Pc=10 U 4 30 I/Pf =50 F No. Arlene is willingto trade 1 C for 2 F, but she is able to trade 1 C for 5 F. So she should trade and move away from her current bundle. Recall: Conditions for Optimization Spend entire budget Tangency MRS = Px/Py

  8. Income & Substitution Effects Bullwinkle Moose faces a choice between leisure (X) and income (Y). He can work up to 100 hours a week at a wage of $8/hr. Initially, he chooses to work 50 hrs/wk. Now his wage rises to$12/hr for the first 40 hrs/wk; it remains $8/hr above 40 hrs/wk. Will he work more than, less than, or equal to 50 hrs/wk?

  9. Income & Substitution Effects Bullwinkle Moose faces a choice between leisure (X) and income (Y). He can work up to 100 hours a week at a wage of $8/hr. Initially, he chooses to work 50 hrs/wk. Y X Now his wage rises to$12/hr for the first 40 hrs/wk; it remains $8/hr above 40 hrs/wk. Will he work more than, less than, or equal to 50 hrs/wk? What is the income effect? His purchasing power is greater, so he will consume more leisure, work less. 1200 960 800 50 60 100 1200

  10. Income & Substitution Effects Bullwinkle Moose faces a choice between leisure (X) and income (Y). He can work up to 100 hours a week at a wage of $8/hr. Initially, he chooses to work 50 hrs/wk. Y X Now his wage rises to$12/hr for the first 40 hrs/wk; it remains $8/hr above 40 hrs/wk. Will he work more than, less than, or equal to 50 hrs/wk? What is the substitution effect? At 50 hrs/wk., the new wage rate is the same as the old ($8/hr). => no substitution effect! 1200 960 800 Px/Py = 8 50 60 100 1200

  11. Income & Substitution Effects Pat divides a monthly income of $1800 between consumption of food (X) and consumption of all other goods (Y). Pat’s preferences can be described by the following utility function: U = X2Y Originally, the price of food is $1 and the price of all other goods is $2. Then the price of food rises to $2. Because the relative price of food has increased, Pat will consume less food (and more of all other goods). This the substitution effect. But because Pat is now relatively poorer (her purchasing power has decreased), she will consume less of both goods.This is the income effect.

  12. Income & Substitution Effects The move from A to B is the substitution effect; B to C is the income effect. B is a point on the original indifference curve, tangent to the new budget constraint, indicating the bundle the consumer would choose at the new prices. Y X 900 Y**=300 B A I S C X**= 600 1200 1200 S I

  13. Income & Substitution Effects U = X2Y We are looking for a point on the indifference curve that includes Y = 300, X = 1200, for which MRS = 1 (the new price ratio): At point B, MRS = 2Y/X = 1 => X = 2Y. Also, Ua = Ub = 432,000,000 U = X2Y 4Y3 = 432,000,000 Y3 = 108,000,000 Yb = 476; Xb = 952 Y X 900 Y**=300 B A I S C X**= 600 1200 1200 S I

  14. Income & Substitution Effects U = X2Y 4Y3 = 432,000,000 Y3 = 108,000,000 Yb = 476; Xb = 952 So the substitution effect is a decrease in X of 248 and an increase in Y of 176. The income effect is a decrease in X of 352 and a decrease in Y of 176. Y X 900 Y**=300 B A I S C X**= 600 1200 1200 S I

  15. Income & Substitution Effects The amount of money Pat would need to be paid to remain as well off after the price increase is call the compensating variation. Yb = 476; Xb = 952 Px =$2; Py = $2 So to purchase B, she would need $2856 or an extra $1056. Y X 900 Yb = 476 B A C Xb = 952 1200

  16. Income & Substitution Effects How much would Pat be willing to pay to avoid this price increase? Y X To calculate this amount, start by finding the minimum income Pat needs to purchase a bundle on the new indifference curve. The difference between the market price of this bundle and her income ( = 1800) is the amount she’d be willing to pay to avoid the price increase. We call this the equivalent variation measure of utility loss. 900 Y**=300 X**= 600 1200 1200

  17. Income & Substitution Effects We are looking for a point on the indifference curve that includes Y = 300, X = 600, for which MRS = 1/2 (the old price ratio): MRS = 2Y/X = 1/2=> X = 4Y. Also,U = X2Y = 108,000,000 So, 16Y3 = 108,000,000 Y3 = 6,750,000 Yb = 189; Xb = 756 The market price of this bundle is $1134, so Pat is willing to pay $666 to avoid the price increase. (values are rounded) Y X 900 Y**=300 X**= 600 1200 1200

  18. Normal & Inferior Goods Normal Good Income-Expansion Path For most goods, the quantity consumed will increase as income increases. We call these normal goods. Y Y = f(X) optimal ratio X

  19. Normal & Inferior Goods Normal Good Engels Curve Income-Expansion Path Y Income X = f(I) X X

  20. Normal & Inferior Goods Inferior Good Income-Expansion Path For some goods, consumption will decrease at higher levels of income (e.g., hamburger). We call these inferior goods. Y X

  21. Normal & Inferior Goods Inferior Good Engels Curve Income-Expansion Path Y Income X X

  22. Normal & Inferior Goods Normal Good Y Y Px increases from $1 to $2. The movement from A to B is the substitution effect. B B A A Px = 1 Px = 2 X X S S

  23. Normal & Inferior Goods For both normal and inferior goods, the substitution effect is negative: consumption will increase as price decreases. Inferior Good Normal Good Y Y B Px increases from $1 to $2. B A A Px = 1 Px = 2 X X S S

  24. Normal & Inferior Goods For normal goods the income effect is positive, and for inferior goods it is negative. Inferior Good Normal Good Y Y B B A A C C X X I I

  25. Normal & Inferior Goods For some inferior goods, the income effect is so large it outweighs the substitution effect (eg., ?). Giffen Good Px 2 1 … giving rise to a upward sloping demand curve. Y C B A A Px = 1 C Px = 2 X X S I

  26. Normal & Inferior Goods Do any of these cases violate the assumptions of well-behaved preferences that we look at last time?

  27. Consumer Demand U = X2Y I = 1800; Py = 2 Y X PxY X $1 300 1200 2 300 600 3 300 400 900 Y***=300 X***=400 1200

  28. Consumer Demand : U = X2Y I = 1800; Py = 2 Demand Curve X = f(Px) 1200 1 600 2 400 3 Y Px Find the equation for the demand curve. 3 2 1 X X Px = 3 2 1 400 600 1200

  29. Consumer Demand U = X2Y I = 1800; Py = 2 MUx = 2XY; MUy = X2 MRS = 2Y/X = Px/Py = Px/2 => Y = (1/4)PxX I = PxX + PyY 1800 = PxX + (2)(1/4)PxX = (3/2)PxX X = 1200/Px Demand Curve X = f(Px) 1200 1 600 2 400 3 Y Px Solve for Y & substitute 3 2 1 X X Px = 3 2 1 400 600 1200

  30. Consumer Demand : U = X2Y I = 1800; Py = 2 Demand Curve Price-Consumption Curve Y Px In this case, consumption of Y is unaffected by changes in Px. Cross-price elasticity is zero. 3 2 1 X X Px = 3 2 1 400 600 1200

  31. Consumer Demand Demand Curve Price-Consumption Curve Y Px … with a smaller response in demand. Or, cross-price elasticity can be positive ... DX 3 2 1 DPx X X

  32. Consumer Demand Demand Curve Price-Consumption Curve Y Px … with a smaller response in demand. Or, cross-price elasticity can be positive ... DX 3 2 1 DPx X X

  33. Non-Price Determinants of Demand What determines consumer demand? • Preferences • Income • Prices of Related Goods • Substitutes • Complements

  34. Price Elasticity of Demand Price Elasticity of Demand (Ep) Measures how sensitive quantity demanded is to changes in price. Demand Equation: Qd = a – bP Ep = (%DQ)/(%DP) = (DQ/Q)/(DP/P) = DQ/DP(P/Q) = -b(P/Q) Ep < 1 Inelastic: Total expenditure increases as price increases. Ep > 1 Elastic: Total expenditure decreases as price increases. Ep = 1 Unit Elastic: Total expenditure doesn’t change

  35. Determinants of Price Elasticity What determines price elasticity of demand? • Substitutes (+) • Budget share • Normal (+) • Inferior ( -) • Short v long run (+) ex. Oil • Network Effects • Bandwagon and Snob Effects normal goods have higher elasticities, because income effect reinforces substitution effect.

  36. Next Time 9/21Theory of the Firm Pindyck & Rubenfeld, Chapter 6. Besanko, Chapters 6-7.

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