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## UNIT I: Theory of the Consumer

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**UNIT I: Theory of the Consumer**• Introduction: What is Microeconomics? • Theory of the Consumer • Individual & Market Demand 6/30**Theory of the Consumer**From last time: • Preferences • Indifference Curves • Utility Functions • Optimization • Income & Substitution Effects How do consumers make optimal choices? How do they respond to changes in prices and income? This Time: Individual & Market Demand**Individual & Market Demand**• Income & Substitution Effects • Normal, Inferior, and Giffen Goods • Consumer Demand • Price Elasticity of Demand • Next Time: The Theory of the Firm**Individual & Market Demand**We have seen 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. Now, 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.**Optimization**From last time: The optimal consumption bundle places the consumer on the highest feasible indifference curve, given her preferences and the opportunities to trade (her income & the prices she faces). Y Y* X* X Indifference Curvesdepict consumer’s “willingness to trade” Slope = - MRS Budget Constraint depicts “opportunities to trade” Slope = - Px/Py C At point C, MRS = Px/Py, so consumer can’t improve thru trade.**Optimization**Two Conditions for Optimization under Constraint: 1. PxX + PyY = I Spend entire budget 2. MRSyx = Px/Py Tangency MRSyx = MUx/MUy = Px/Py => MUx/Px = MUy/Py The marginal utility of the last dollar spent on each good should be the same.**Optimization: An Example**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 If the price of food is $1 and the price of all other goods is $2, find Pat’s optimal consumption bundle. We know: Pat should choose the combination of food and all other goods that places her on the highest feasible indifference curve, given her income and the prices she faces. This is the point where an indifference curve is tangent to the budget constraint (unless there is a corner solution).**Optimization: An Example**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 If the price of food is $1 and the price of all other goods is $2, find Pat’s optimal consumption bundle. Since Pat’s utility function is U = X2Y, MUx = 2XY and MUy = X2. MRS = (-)MUx/MUy = (-)2XY/X2 = (-)2Y/X. Setting this equal to the (-)price ratio (Px/Py), we find ½ = 2Y/X, X = 4Y. This is Pat’s optimal ratio of the goods, given prices.**Optimization: An Example**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 If the price of food is $1 and the price of all other goods is $2, find Pat’s optimal consumption bundle. To find Pat’s optimal bundle, we substitute the optimal ratio into the budget constraint: I = PxX + PyY, 1800 = (1)X + (2)Y, 1800 = (1)4Y + (2)Y = 6Y, so Y* = 300, X* = 1200.**Optimization: An Example**Graphically: Y X Maximize: U = X2Y Subject to: I = PxX + PyY I = 1800; Px = $1; Py = $2 Y* = 300, X* = 1200. 900 Y*=300 X*=1200**Optimization: An Example**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 Now suppose the price of food rises to $2. MRS = (-)2Y/X. Setting this equal to the new (-)price ratio (Px/Py), we find 1 = 2Y/X, X = 2Y. Substituting in Pat’s new budget constraint: I = PxX + PyY, 1800 = (2)X + (2)Y, 1800 = (2)2Y + (2)Y = 6Y, so Y** = 300, X** = 600.**Optimization: An Example**Graphically: Y X U = X2Y I = 1800; Px = $1; Py = $2 Y* = 300, X* = 1200. 900 Y*=300 X*=1200**Optimization: An Example**Graphically: Y X Now: U = X2Y I = 1800; Px’ = $2; Py = $2 Y* = 300, X* = 600. 900 Y**=300 X**= 600 1200**Income & Substitution Effects**Because the relative price of food has increased, Pat will consume less food (and more of all other goods). This the substitution effect. Y X 900 Y**=300 S X**= 600 1200 S**Income & Substitution Effects**But because Pat is now relatively poorer (her purchasing power has decreased), she will consume less of both goods.This is the income effect. In this case, the 2 effects are equal and opposite for Y, additive for X. Y X 900 Y**=300 X**= 600 1200**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 S I**Income & Substitution Effects**compensating variation 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 c.v. 900 Y**=300 B A I S C X**= 600 1200 S I**Income & Substitution Effects**compensating variation • 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 S I**Income & Substitution Effects**compensating variation 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 S I**Income & Substitution Effects**compensating variation 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 Yb = 476 B A C Xb = 952**Income & Substitution Effects**compensating variation The amount of money Pat would need to be paid to remain as well off after the price increase is call the compensating variation. Y X 900 Yb = 476 B A C Xb = 952**Income & Substitution Effects**compensating variation 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 1428 c.v. = $1056 900 Yb = 476 B A C Xb = 952**Income & Substitution Effects**equivalent variation How much would Pat be willing to pay to avoid this price increase? Y X 900 Y**=300 X**= 600 1200**Income & Substitution Effects**equivalent variation To calculate this amount, start by finding the minimum income Pat needs to purchase a bundle on the new indifference curve. Y X 900 e.v. 900 1800**Income & Substitution Effects**equivalent variation 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. Y X 900 e.v. 900 1800**Income & Substitution Effects**equivalent variation 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 900 567 189 e.v. = $ 666 756**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**Normal & Inferior Goods**Normal Good Engels Curve Income-Expansion Path Y Income X = f(I) I1 I2 I3 X X**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**Normal & Inferior Goods**Inferior Good Engels Curve Income-Expansion Path Y Income X X**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**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**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**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**Normal & Inferior Goods**Do any of these cases violate the assumptions of well-behaved preferences that we look at last time? No. Well-behaved preferences can give rise to all sorts of demand curves (depending on income and prices).**Consumer Demand**How do consumers respond to changes in prices?**Consumer Demand**U = X2Y I = 1800; Py = 2 Y X Px* = $1Y* = 300, X* = 1200. 900 Y*=300 X* = 1200**Consumer Demand**U = X2Y I = 1800; Py = 2 Y X Px** = $2 Y** = 300, X** = 600. 900 Y**=300 X**= 600**Consumer Demand**U = X2Y I = 1800; Py = 2 Y X Px*** = $3 Y*** = 300, X*** = 400. 900 Y**=300 400**Consumer Demand**: U = X2Y I = 1800; Py = 2 Demand Curve Y Px Find the equation for the demand curve. X = f(Px) 400 3 600 2 1200 1 3 2 1 X X Px = 3 2 1 400 600 1200**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 Y Px X = f(Px) 400 3 600 2 1200 1 Solve for Y & substitute 3 2 1 X X Px = 3 2 1 400 600 1200**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**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**Consumer Demand**: U = X2Y I = 1800; Py = 2 Demand Curve Price-Consumption Curve Y Px DX 3 2 1 DPx X X Px = 3 2 1 400 600 1200**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**Non-Price Determinants of Demand**What determines consumer demand? • Preferences • Income • Prices of Related Goods • Substitutes • Complements**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.**UNIT II: FIRMS & MARKETS**• Theory of the Firm • Profit Maximization • Review • 7/14 MIDTERM**Theory of the Firm**Today we will build a model of the firm, based on the model of the consumer we developed in UNIT I. Where consumers attempt to maximize utility, firms attempt to maximize profit. We saw how changes in prices affect consumers’ optimal decisions and derived a demand function: X= f(Px) Now we will see how changes in prices affect firms’ profit maximizing decisions and derive a supply curve: Qs = f(Px) Later, we will put supply and demand together, and begin our analysis of markets and market structures.**Theory of the Firm**The Good News! In moving from the consumer to the firm, we replace the troublesome notion of utilitywith something nice and hard-edged: profit. Where utility is subjective and thus hard to measure, now we’ll be talking about simple, measurable quantities, physical units of inputs (tons of steel, hours of labor) and outputs, and we’ll account for everything in dollars and cents (“the bottom line”).