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Econ326 Intermediate Microeconomics

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1 Econ326 Intermediate Microeconomics
Fall 2011 Instructor: Ginger Z. Jin TA: Aaron Szott

2 Lecture 1 Course introduction Syllabus Teaching style and expectations
Textbook Chapter 1,

3 Goal of the class Teach you to think like a micro-economist
Labor market issues Industrial organization Public policies International trade Derive the major concepts and intuitions from introductory microeconomics We will emphasize analytic logic and mathematical rigor.

4 Class will cover: Consumer demand Firm production
Describe consumer preference Derive consumer demand Market vs. individual demand Consumer welfare Firm production Production technology Firm choice of input and output Cost and profit How demand meets supply? Exchange economy Market structure Market failures: monopoly, asymmetric info, externality Policy interventions

5 Example: rental market in College Park
Product definition: one bedroom apt off-campus rental in College park Players: tenants, landlords, city government? University? Actions and incentives Tenants: reservation price/willingness to pay Landlords: cost, earn money if possible Market outcomes: price, vacancy rate, tax revenue?

6 Monthly rent supply equilibrium demand Units available Why is the demand downward sloping?

7 When will we observe a fixed supply?
Monthly rent supply equilibrium demand We observe fixed supply if it is too costly to enter the market right away (time lag of construction, need to apply for rental permit, etc.) and an empty apartment has no alternative use other than rental. Units available When will we observe a fixed supply?

8 Market scenario 1: convert some apartments to condos
supply Monthly rent demand Units available Both demand and supply get reduced, the effect on market equilibrium price is unclear

9 Market scenario 2: impose $50/month tax on landlord
supply Monthly rent demand Units available No change in demand and supply thus no change in price ONLY TRUE with fixed supply What happens if the supply is not fixed?

10 Market scenario 3: non-discriminating monopoly
supply Monthly rent demand Units available The monopolist may want to restrict the supply so that he can charge higher price  not efficient from the society point of view What if the monopolist can charge different price on different tenants?

11 Market scenario 4: rent control
supply Monthly rent demand Units available Keep the price down, but create excessive demand How to allocate the limited supply to excessive demand? lottery, ration, allow secondary market trade?

12 At the end of this class, You know how to derive a simple demand curve given individual preference You know how to derive the supply decision of each firm You know how to compute market equilibrium under different market structures You can compute who gains and who loses by how much under a simple policy intervention

13 Syllabus on my personal website
click on Econ326 Also available on

14 Prerequisites – very strict rules by Economics Department
(1) have completed Econ300 with a grade of "C" (2.0) or better,  OR (2) have completed or are concurrently taking Math 240 or Math 241.  If you satisfy either (1) or (2), you should have already completed ECON200, ECON201, and Calculus I. But completion in these four courses are not sufficient for enrollment in Econ326. For those who do not meet the prerequisites but believe that an exception could be made, please talk to Shanna Edinger in Tydings 3127B. Conversely, having completed ECON200, ECON201, and Calculus I does NOT imply that you are eligible to register this class for credit unless you satisfy either (1) or (2) as mentioned above

15 Syllabus Textbook: Evaluation
Pindyck and Rubenfeld, Microeconomics, Edition 7 Evaluation Three problem sets, 10 points each Two midterms, 20 points each One cumulative final, 30 points Five random in-class quizzes, 2 bonus points each Total 110 points Conversely, having completed ECON200, ECON201, Calculus I and Calculus II does NOT imply that you are eligible to register this class for credit unless you satisfy either (1) or (2) as mentioned above

16 Fixed grade definition (No curve, no rounding)
F: <40 D: [40,45) D+ [45,50) C-: [50,55) C: [55,60) C+: [60,65) B-: [65,70) B: [70,75) B+: [75,80) A-: [80,90) A: [90,100) A+: [100,110]. No curves

17 Important dates Sept. 8: Handout problem set 1 Sept. 22 Problem set 1 due Oct. 4 Midterm 1 Oct. 11 Handout problem set 2 Oct. 28 Problem set 2 due Nov. 8 Midterm 2 Nov. 15 Handout problem set 3 Dec. 8 Problem set 3 due ???? Final exam No curves There will be 5 in-class quizzes at unannounced dates.

18 Exam policies If you miss exams for reasons in line with university policy, you can take makeup exams or roll over your missed points to final For other reasons to miss the exam, you are allowed to skip at most one midterm (with points rolled over to final) upon one-month written notice to the Professor

19 Problem sets Hard copy distributed in class, soft copy available on elms You can turn in problem sets in class or in your TA’s mailbox (in 3105 Tydings) by 4pm of due date. Graded problem sets will be returned in TA sessions Collaborative discussion on problem sets is ok but outright copying is cheating. Everyone should turn in individual problem sets.

20 Teaching Assistant: Aaron Szott
Office: 0124F Cole Field House Office Hours Monday 2:15-3:15pm, Friday 2-3pm Office Phone Change of office hours for Sumedha

21 Teaching Style Power point lecture notes are posted on elms (subject to update) More details and examples may be covered during the class Handouts, problem sets, answer keys will be posted on elms. I will also distribute handouts and problem sets in class Graded work will be returned in TA sessions

22 Expectation on You Attend the class Read related textbook chapters
Mute your cell phone at least If you have to use your computer, make sure it is muted and you do not bother others Read related textbook chapters date-specific chapter numbers are available in syllabus Attend TA sessions (will be very useful) Sharpen your calculus Ask for help EARLY if you encounter difficulty Feel free to give us feedback any time so we can improve during the class

23 Lecture 2 Utility Theory Consumer preferences
Constructing Indifference curves Properties of Indifference curves Textbook chapter

24 Intuition of consumer theory
How does a consumer choose the best things that she can afford? What is the best Afford  budget constraint How to choose  constrained optimization Examples: Individual choice of work time Apple rolls out iphone4 Tax cut at the end of 2010

25 Axioms of preferences Completeness Transitivity Non-satiation:
A > B, B > A, A ~ B for all bundles A, B Transitivity A > B and B > C => A > C Otherwise we won’t be able to tell which bundle is the best Non-satiation: more is preferred to less. Goods are always “good” Counter examples: bad (dislike), neutral goods (indifferent) Balance: averages preferred to extremes Also called convex preference

26 Utility Definition of Utility In what unit?
Numerical score representing the satisfaction that a consumer gets from a given basket of goods. In what unit? ordinal versus cardinal

27 Marginal Utility the increase in utility you get when you consume one more unit of good X Units of Apples Total utility (TU) Marginal Utility (MU) 1 5 5-0=5 2 9 9-5=4 3 12 12-9=3 4 14 14-12=2 15 15-14=1 One common property: Diminishing marginal utility

28 Show MU in graph Total Utility U Units of apples (X)

29 Exercise: compute MU, diminishing MU?
U=5(X+1) U=5ln(X+1) U=X0.3 U=100-X2 U=X0.4Y0.6

30 Ordinal vs Cardinal Ordinal Utility Utility Function
the measurement of satisfaction that only requires a RANKING of goods in terms of consumer preference. This is the concept of utility that is embodied in the so-called "utility function" that forms the basis of CONSUMER THEORY… Utility Function Utility function that generates a ranking of market baskets in order of most to least preferred. This function is defined up to an order-preserving, monotonic transformation

31 Exercise: monotonic transformation of U function?
U=5X vs U=5(X+1) U=5(X+1) vs U=5ln(X+1) U=5X+5Y vs. U=5lnX+5lnY U=X0.5Y0.5 vs U=XY U=XY vs U=lnX+lnY U=X+Y2 vs U=X+Y Note: monotonic transformation does not change the order of preference, it may change the property of MU It does NOT change the relative tradeoff between two goods (MUx vs MUy) Answer: Yes, yes, no, yes, yes, no

32 How to graph utility of two goods
U(X,Y) U(X,Y) Y Y X X

33 Indifference curves Definition of Indifference Curve:
the set of consumption bundles among which the individual is indifferent. That is, the bundles all provide the same level of utility. each indifference curve corresponds to a specific utility level Indifference curves never cross each other

34 Axioms of preferences Completeness Transitivity Non-satiation:
A > B, B > A, A ~ B for all bundles A, B Transitivity A > B and B > C => A > C Otherwise we won’t be able to tell which bundle is the best Non-satiation: more is preferred to less. Goods are always “good” Counter examples: bad (dislike), neutral goods (indifferent) Balance: averages preferred to extremes Also called convex preference

35 Examples of indifference curves
U(X, Y)=X * Y Y point X Y U 1 2 4 3 9 16 5 6 7 8 I1=4, I2=9, I3=16 X Typical convex preference Satisfy all four axioms of preference

36 Examples of indifference curves
U(X, Y)=X + Y Y point X Y U 1 2 4 3 6 8 5 7 5 3 4 7 I1=2, I2=4, I3=5 8 2 1 6 X Perfect substitutes Violate “balance” because avg is not better than extremes MUx is a constant (not diminishing), so is MUY

37 Examples of indifference curves
U(X, Y)=min(X, Y) Y point X Y U 1 2 3 4 5 6 7 8 I1=2, I2=4, I3=5 X Perfect complements Violate “non-satiation” sometimes U is not always differentiable, MU is not well defined at the kinks

38 Lecture 3 Marginal rate of substitution
Properties of indifference curves Shape of indifference curves Special examples Textbook Chapter 3.1 & 3.2 Assign problem set #1

39 Marginal rate of substitution (MRS)
Definition: Marginal Rate of Substitution (of X for Y) = -dy/dx | same satisfaction (i.e. same U) How many units of Y would you like to give up to get one more unit of X? Can be interpreted as marginal willingness to pay for X if Y is numeraire (money left for other goods)

40 Marginal rate of substitution (MRS)
Y A Slope = - MRS at point A X

41 Diminishing MRS (MRS of X for Y diminishes with X)
Consistent with diminishing marginal utility

42 Mathematical derivation of MRS
U=U(X,Y) Total differentiation: dU = MUx * dX + MUy * dY =0 -dY/dX = MUx / MUy = MRS (of X for Y)

43 MRS and ordinal utility
Calculate MRS: U=XY U=lnX + lnY U=X+Y U=X+Y2 U=(X+1)(Y+2) U=X2 Y2 Which and which are monotonic transformations of each other? first ,second and seventh are monotonic transformation to each other. Others are not.

44 Properties of indifference curves for typical preferences
Indifferent curves are downward sloping Violate non-satiation if upward sloping Indifference curves never cross Violate transitivity if they cross Indifference curves are convex Violate balance if they are concave or linear Draw pictures to show what happened if these properties are violated

45 Like apples and bananas Like apples up to a satiation level
How would the indifference curves (on apples and bananas) look like if: Like apples and bananas Like apples up to a satiation level Like apples, but dislike bananas Like apples, but indifferent to bananas Must eat one apple with one banana Dislike apples, dislike bananas Like both apples and bananas up to a satiation level

46 Like apples and bananas
U apples

47 Like apples up to a satiation level
bananas U apples What happens if one likes both apple and banana up to a satiation level?

48 Like apples but dislike bananas
What if one dislikes both apples and bananas?

49 Like apples but indifferent to bananas

50 Must eat one apple with one banana (perfect complements)
bananas U Locus line What determines the locus line? What if one must each two apples with one banana? apples

51 Always willing to exchange one apple for one banana (perfect substitutes)
bananas U What determines the slope of the indifference curve? What if one is always willing to exchange two apples for one banana? apples

52 Cobb-Douglas Utility Typical functional form: U=Xc Yd Transformations: U=c*lnX + d*lnY or U= Xa Y1-a where a=c/(c+d) Calculate MRS at point (X,Y)

53 Lecture 4: Budget constraints Textbook Chapter 3.1 & 3.2 definition
Shocks to consumer budget Kinked consumer budget Textbook Chapter 3.1 & 3.2

54 Budget constraints Definition: Equation: Px * X + Py * Y = I
The budget constraint presents the combinations of goods that the consumer can afford given her income and the price of goods. Equation: Px * X + Py * Y = I Rearrange: Y = I/ Py + (- Px / Py ) * X intercept slope

55 Graph budget constraint
Y I/Py Slope = - Px / Py I/Px X Px/Py = the rate at which Y is traded for X in the marketplace Unlike MRS, the price ratio does not depend on consumer psyche

56 Exercise My 11-year-old son has 20 dollar allowance each month.
He likes bakugan balls and pokemon cards Bakugan ball is $5 each Pokemon card is $2 each Draw his budget line

57 What happens with income tax cut?
Tax cut  more income I/Px I/Py X Y Slope = - Px / Py Does the intercept on Y change? Does the intercept on X change? Does the slope of the budget line change?

58 What happens if gasoline price goes up? (assume gasoline is X)
Px increases I/Px I/Py X Y Slope = - Px / Py Does the intercept on Y change? Does the intercept on X change? Does the slope of the budget line change?

59 Examples of kinked budget constraints (if price depends on how many units to buy)
Assume income = $2000 Two goods: X=food, Y=health care Prices: Px= $2, Py = $1 if Y<=500 (deductible $500) Py = $0.2 if Y> $500 (coinsurance 20%)

60 Y (health care) 8000 Slope = -Px /Py = -2/0.2=-10 Slope = -Px /Py = -2
Step 1: if only buy food, you can buy $2000/2=1000 Step 2: if Y=500, $1500 left for food  1500/2=750 Step 3: if Y<500, price ratio is 2/1 Step 4: if Y>500, price ratio is 2/0.2=10 Step 5: if all income is used for health care, we can buy 500+( )/0.2=8000 Slope = -Px /Py = -2 500 750 1000 X (food)

61 Example 2: 1979 food stamp program
Income I=2000 Two goods: food (X), other (Y) Px =1, Py = 1 A household is granted $200 food stamp But the food stamp can only be used for food

62 What happens if there is a black market to trade food stamps?
other 2000 2000 2200 food What happens if there is a black market to trade food stamps?

63 Example 3: role of financial market

64 #1: no financial market Y (tomorrow) 2*I I I 2*I X (today)

65 #2: a financial market allows saving and borrowing at interest rate r
Y (tomorrow) The opportunity cost of not saving today makes one feel as if today’s price is increased to (1+r). X (today)

66 Now we have a kink due to the asymmetric terms of borrowing and saving
Y (tomorrow) Now we have a kink due to the asymmetric terms of borrowing and saving X (today)

67 Recap so far Indifference curves describe consumer preference
Budget constraints describe what consumers can afford Put the two together to determine the best bundle one can afford

68 Graphical presentation
Y MRS > Px/Py I/Py A Slope = - Px / Py C B MRS < Px/Py I/Px X Px/Py = the rate at which Y is traded for X in the marketplace MRS = the rate at which the consumer is willing to trade Y for X

69 At the best choice: Must spend every penny (assume no savings, goods are divisible) Equal Marginal Principle MRS = the rate at which the consumer is willing to trade Y for one extra unit of X Px / Py = the rate at which Y is traded for X in the market place MRS = Px / Py  MUx /Px = MUy /Py

70 Mathematical derivation
Max U(X, Y) by choosing X and Y Subject to I = Px * X + Py * Y Define Lagrangian function L = U(X,Y) + λ (I – Px * X – Py * Y) λ is an additional variable, now need to choose X, Y, λ

71 Mathematical derivation

72 We get the equal marginal principle back!
λ is the shadow price of the budget constraint Tell us how much the objective function will increase if the budget constraint is relaxed by one dollar ((dL/dI = dU/dI when I is binding) Therefore, λ is also called the marginal utility of income when utility is maximized

73 Exercise: find the best choice when
U (Food, Clothes) = ln (F) + ln (C) Price of food = $2 Price of clothes =$1 Income=100 Answer: F=25, C=50

74 Lecture 5 Consumer’s optimal choice Cobb-Douglas utility
Inner solution, corner solution Cobb-Douglas utility Price and consumer choice Income and consumer choice Normal, inferior and giffen goods Textbook Chapter 4 appendix,

75 Typically: Inner solution
At the optimal choice: MRS = Px/Py I=Px * X + Py * Y I/Py I/Px X

76 I/Px I/Py X Y What if the equal marginal principle cannot be satisfied?  corner solution Spend every penny: I=Px * X + Py * Y Check which corner gives higher utility U

77 Example 1 of corner solution: perfect substitutes
U=X+2Y Px=10 Py=10 Income=1000 Y U 100 100 X

78 Example 2 of corner solution: perfect complements
100 X Y U=min(X,2Y) Px=10 Py=10 Income=1000

79 Demand Optimal choice Properties: X=f(Px, Py, Income)
Homogenous degree of zero Typically depends on income, own price, price of other goods

80 Special example: Cobb-Douglas Utility
Two equations Solve for two unknowns (X and Y) Solve on the blackboard

81 Demand only depends on own price, not price of other goods
Demand only depends on own price, not price of other goods Homothetic preferences: MRS only depends on the ratio of X and Y Fixed share of income for each good

82 Graph consumer choice in response to:
Price changes Income changes

83 Two goods: food, clothing Price of food drops

84 Two goods: food, clothing Income increases Note that income-consumption curve is not necessarily linear

85 Normal goods Inferior goods Examples?
Consumers want to buy more quantity of normal goods as their incomes increase. Inferior goods Consumers want to buy fewer quantity of inferior goods as their incomes increase. Examples?

86 Hamburger is a normal good from A to B,
but an inferior good from B to C

87 Engel curve Normal goods has an upward sloping Engel curve. Within normal goods, necessities will have an Engel curve bending towards Y-axis, and luxury goods will have an Engel curve bending towards x-axis.

88 Giffen goods Normal and inferior goods are defined by how consumer choice changes in response to income change Giffen goods depend on price change Typical goods have downward sloping demand curve Giffen goods have upward sloping demand curve: as price increases, consumers buy more; as price decreases, consumers buy less. Luxury goods is not a giffen good, because in the definition of giffen good price does not enter the utility itself.

89 Lecture 6 Decompose income and substitution effects in response to price change Slusky Equation Textbook chapter: Handout #1: an example

90 Food price falls Initial choice A  new choice B Imaginary D: same utility as A, but face new price

91 Slusky Equation Total effects Substitution effects Income effects

92 What if X is an inferior good
What if X is an inferior good?  income effect works against the substitution effect

93 What if X is a Giffen good
What if X is a Giffen good?  income effect works against and more than cancels off the substitution effect

94 Example 1:

95 Example 2: Introduction of health insurance
X=food, Y=health care, Px=$2, Py=$1 if no insurance, Income=2000 Benchmark: no insurance Scenario #1: insurers pay 80% of the cost of any medical service Scenario #2: insurers pay 80% after $500 deductible

96 10000 Y (health care) A: choice with no insurance C: choice with insurance A to B: substitution effect B to C: income effect Slope = -Px /Py = -2/0.2=-10 C B A Slope = -Px /Py = -2 1000 X (food) Scenario #1: insurers pay 80% of the cost of any medical service

97 insurers pay 80% after $500 deductible
Scenario #2: insurers pay 80% after $500 deductible Y (health care) 8000 Slope = -Px /Py = -2/0.2=-10 Slope = -Px /Py = -2 500 750 1000 X (food) How would the insurance coverage affect those who are healthier and do not need more than $500 health care before the insurance coverage?

98 Lectures 7-8 Application to labor supply Individual and market demand
Demand elasticity and cross elasticity Textbook chapter:

99 Individual demand A consumer’s optimal choice of a good depends on
The price of this good The price of other goods Income

100 Example

101 Two goods Income

102 C (24w+y)/Pc C* Solution: L=12, C=10*12=120. L* 24 24+y/w L

103 L=24Pc^2/(2w+Pc^2)"Type equation here."

104 w 1 0.5 4.8 8 24 L

105 Pc 1 0.5 19.2 42.7 C

106 More generally: Market demand Q(P)= sum of individual demand Qi(P)

107 Textbook example of market demand

108 How to summarize market demand?

109 Meaning of demand elasticity

110 Classify demand by demand elasticity

111 Market demand Q(P) Example: Q=100-2P
If you are the producer, why do you want to know demand elasticity? Q(P) Example: Q=100-2P What is demand elasticity at p=10,20,30? At what price is the demand isoelastic? P 50 Demand elasticity changes along the demand curve. What kind of demand curve has constant demand elasticity? Q 100

112 Special cases P Q Completely inelastic demand
Infinitely elastic demand Q

113 Other elasticities

114 Example

115 More on cross elasticity
X and Y are substitutes If an increase in Px leads to an increase in the quantity demanded of Y. X and Y are complements If an increase in Px leads to a decrease in the quantity demanded of Y. X and Y are Independent If Px does not affect the quantity demanded of Y Cobb-Douglas utility  independent goods

116 Consumer surplus Individual consumer surplus = difference between what a consumer is willing to pay for a good and the amount actually paid Total consumer surplus = sum of individual consumer surplus For six consumers, CS = $6+$5+$4+$3+$2+$1=$21

117 Total Consumer Surplus
= ½ *(20-14)*6500=19,500

118 Textbook example of market demand
Calculate the demand elasticity of total demand and total consumer surplus at p=18.

119 To summarize Consumer preference (utility function) Budget Constraint
 optimal choice X=X(Px, Py, I) Income-consumption curve, price- consumption curve, engel curve, demand curve Income and substitution effects Sum of Individual demand=market demand Demand elasticity, income elasticity, cross elasticity Consumer surplus

120 Lecture 11 Risk and Consumer behavior
Describe risk Preferences towards risk Demand for risky assets

121 Risk, Uncertainty, and Profit, by Frank Knight (1921)
Risk: random events that can be quantified in probability Uncertainty: random events that cannot be quantified in probability Today we focus on “risk” only

122 Describe risk Outcome: a random event is associated with multiple outcomes, for instance: head/tail when we flip a coin gain/loss when we invest in a risky asset Healthy or sick in the future Probability: likelihood that a given outcome will occur Payoff: value associated with a possible outcome

123 Describe risk Expected value: probability-weighted average of the payoffs associated with all possible outcomes E(X)=Prob1*X1+ Prob2*X2 +…+ Probn*Xn Variance: Extent to which possible outcomes of a risky event differ Var(X)= Prob1*(X1-E(X))2 + Prob2*(X2 -E(X))2 +…+ Probn*(Xn -E(X))2 Standard deviation: square root of variance, same unit as X

124 Example Job1: 50% probability with income $2000 50% probability with income $1000 Job2 99% probability with income $1510 1% probability with income $1500 Calculate expected values, variance, standard deviation

125 Job1 is riskier

126 Preferences toward risk
For outcome Xi, utility = U(Xi) Expected utility EU=Prob1*U(X1)+ Prob2*U(X2) +….+Probn*U(Xn) Risk averse: prefers a certain given outcome to a risky event with the same expected value: EU(X)<U(E(X)) Risk neutral: indifferent between a certain given outcome and a risky event with the same expected value: EU(X)=U(E(X)) Risk loving: prefer a risky event to a certain outcome with the same expected value: EU(X)>U(E(X))

127 Example Eric now has a job with annual income $15000
He is considering a new job: 50% prob with income $30,000 50% prob with income $10,000

128 Risk averse (EU(X)?, U(E(X))?)

129 Risk neutral (EU(X)?, U(E(X))?)

130 Risk loving (EU(X)?, U(E(X))?)

131 Risk premium: maximum amount of money that a risk averse person will pay to avoid taking the risk

132 Indifference curves for a risk averse person
Like higher expected value, But dislike risk (measured in standard deviation) U How would the indifference curves look like if the person is risk neutral? What if he is risk loving?

133 How to reduce risk? Diversification Insurance
Practice of reducing risk by allocating resources to a variety of activities whose outcomes are not closely related Most effective if the activities are negatively correlated (examples?) Insurance Pay insurance premium to avoid risky outcomes Actuarially fair: the insurance premium is equal to the expected payout

134 Choosing between risk and return
Risk free asset: Rf Asset with market risk: Rm, m ( Rm – Rf ) Portfolio p: Rp= Rf * p m

135 Choice of a risk averse person

136 Exercise: Chapter 5, Question 7
Suppose two investments have the same three payoffs, but the probability of each payoff differs: Find the expected return and standard deviation of each investment. Jill has the utility function U=5*X where X denotes the payoff. Which investment will she choose? Ken’s utility function is U=5*X0.5, which investment will he choose? For Ken, what’s the risk premium of investment A? What’s the risk premium of investment B? payoff Prob (investment A) Prob (investment B) $300 0.10 0.30 $250 0.80 0.40 $200 For investment A, EX=0.1* * *200=250, stdev=sqrt(0.1*50^2+0.8*0^2+0.1*50^2)=22.36 For investment B, EX=0.3* * *200=250, stdev=sqrt(0.3*50^2+0.4*0^2+0.3*50^2)=38.73 Jill is indifferent between the two investments because she is risk neutral and the two investments yield the same expected value. Ken is risk averse and prefers less risk if the expected value is the same. So he will choose investment A. To calculate risk premium, we need to find a safe asset (zero risk) that yields the same expected utility as investment A for Ken. The expected utility for A is EU=0.1*5*sqrt(300)+0.8*5*sqrt(250)+0.1*sqrt(200)= Suppose the safe asset yields payoff X. U(X)=5*sqrt(X)= , so X=249.49, which implies risk premium= =0.51. Same logic applies to investment B. Ken’s expected utility for B is EU=0.3*5*sqrt(300)+0.4*5*sqrt(250)+0.3*5*sqrt(200)= For U(X)=5*sqrt(X)= , we have X= , so the risk premium is =

137 Lectures 12, 13 Technology of production Production with two inputs
Production function Average product, marginal product Law of diminishing marginal return Malthus and the food crisis Production with two inputs Isoquant curve Marginal rate of technical substitution Returns to scale

138 Technology of Production
Production function: shows the highest output that a firm can produce for each specified combination of inputs Single input (labor): q=F(L) Two inputs (capital, labor): q=F(K,L) Short-run: time in which quantities of one or more inputs cannot be changed Long-run: time needed to make all production inputs variable.

139 Single-input production q=F(L)
Average product: q /L Marginal product: dq /dL L q Avg product q/L Marginal product dq/dL 1 10 2 30 3 60 4 80 5 95

140 Graphically:

141 Marginal Product (MP) and Average Product (AP)
Total product q = q (L) Marginal Product = dq / dL Average Product = q / L Question: How does AP change with L? 𝑑(𝐴𝑃) 𝑑𝐿 = 𝑑 𝑞 𝐿 𝑑𝐿 =− 𝑑𝑞 𝑑𝐿 ∙𝐿−𝑞 𝑑𝐿 𝑑𝐿 𝐿 2 = 𝑀𝑃−𝐴𝑃 𝐿 If MP>AP, AP increases with L If MP<AP, AP decreases with L AP=MP at the maximum of AP

142 Law of diminishing marginal returns
As the use of an input increases with other inputs fixed, the resulting additions to output (i.e. marginal product) will eventually decrease. This is different from technological improvement Example: Malthus and the food crisis

143 How to describe production with more than one inputs?
Isoquant curve: shows all possible combinations of inputs that yield the same output Similar to “indifference curve” for consumer utility

144 Marginal rate of technical substitution (MRTS)
Amount by which the quantity of one input can be reduced when one extra unit of another input is used so that output remains constant. MRTS of L for K = - dK/dL | same q = MPL / MPk MRTS = - slope of isoquant curve Diminishing MRTS Similar to MRS in consumer utility

145 Example Plot isoquant curve for K=2, L=1, calculate marginal product of labor, marginal product of capital and MRTS at this point q=3KL q=3K+L q=min(3K, L)

146 Diminishing MRTS

147 Special case #1: K and L are perfect substitutes if production function is linear, MRTS is always a constant

148 Special case #2: K and L are perfect complements if production function is min(f(K), g(L), MRTS is not well defined at the kink (i.e when f(K)=g(L))

149 𝐴: technological factor
Cardinal vs Ordinal Consumer utility is ordinal because we only care about the relative preference on bundles and it is hard to compare utility across individuals Production function is cardinal because the absolute scale matters Cobb-Douglas production: 𝑞=𝐴∙ 𝐾 𝛼 ∙ 𝐿 𝛽 𝐴: technological factor 𝛼+𝛽: return to scale

150 Returns to scale Rate at which output increases as ALL inputs are increased proportionally Note it is different from marginal product It is a property of a given production function, also different from technological improvement Simple rule of thumb: will the output double when all the inputs double? q more than double  Increasing returns to scale q exactly double  Constant returns to scale q less than double  Decreasing returns to scale

151 Constant return to scale Increasing return to scale
Example of constant returns to scale: lawn mowing increasing returns to scale: specialization decreasing returns to scale: mgmt can’t keep track, communication breaks down, difficulty monitoring workers. Then firms realize they got too big … Can you think of any real-world examples that have constant, increasing or decreasing returns to scale?

152 Cobb-Douglas production Why does 𝛼+𝛽 represent returns to scale?
𝑞=𝐴∙ 𝐾 𝛼 ∙ 𝐿 𝛽 Suppose K increases to xK, L increases to xL Let q’ denote the new production by xK and xL 𝑞 ′ =𝐴∙ 𝑥𝐾 𝛼 ∙ 𝑥𝐿 𝛽 = 𝑥 𝛼+𝛽 ∙𝐴∙ 𝐾 𝛼 𝐿 𝛽 = 𝑥 𝛼+𝛽 ∙𝑞 If 𝛼+𝛽<1, decreasing returns to scale If 𝛼+𝛽=1, constant returns to scale If 𝛼+𝛽>1, increasing returns to scale

153 Example: are these production functions decreasing, increasing or constant returns to scale?
q=3KL q= K0.5L0.3 q=0.5lnK + 0.8lnL q=3K+L q=min(3K, L) q= 3KL + 3KL2 Answer: (1) increasing (2) decreasing (3) undetermined (4) constant (5) constant (6) increasing

154 Lecture 14, 15 and 16 Cost functions
Firm decision Given production technology Given input prices of input  firm decides on optimal choice of inputs  cost function Short run Long run

155 Cost w = wage rate r = capital rental cost
Both could be opportunity cost Cost function C (q) = w*L(q) + r*K(q) Firm’s decision does not include “sunk cost” after the cost is sunk Example?

156 Fixed vs. Variable Cost w = wage rate r = capital rental cost
In the long run when every input is variable 𝐶 𝑞 =𝑤∗𝐿 𝑞 +𝑟∗𝐾(𝑞) In the short run, if K is fixed at 𝐾 , 𝐶 𝑞 =𝑤∗𝐿 𝑞 +𝑟∗ 𝐾 Variable cost fixed cost

157 How to determine cost with only one variable input?
𝑞=𝐹 𝐾 , 𝐿  𝐿= 𝐹 −1 ( 𝐾 , 𝑞) 𝐶 𝑞 =𝑤∗𝐿+𝑟∗ 𝐾 =𝑤∗ 𝐹 −1 𝐾 , 𝑞 +𝑟∗ 𝐾 Example: 𝑞= 𝐾 ∙ 𝐿 0.5 𝐶=𝑤∗𝐿+𝑟∗ 𝐾 =𝑤∗ 𝑞 𝐾 𝑟∗ 𝐾 The production function is concave with diminishing marginal product, this implies that every extra labor is less productive than before, so the cost function is convex in q, every extra unit of output needs higher cost to produce

158 More generally Total production function Total cost function

159 Marginal cost (MC) and avg cost (AC)
Total cost function Marginal cost MC = dC/dq Average Variale cost = VC/q Average total cost = TC/q = (VC + FC)/q When MC=AC, it is the minimum of AC

160 How to determine cost with two variable inputs?
Choose L and K in order to minimize 𝐶 𝑞 =𝑤∗𝐿+𝑟∗𝐾 Subject to 𝑞=𝐹 𝐾, 𝐿 The production function is concave with diminishing marginal product, this implies that every extra labor is less productive than before, so the cost function is convex in q, every extra unit of output needs higher cost to produce

161 Define Lagrangian function 𝐺=𝑤𝐿+𝑟𝐾−𝜆 𝑞−𝐹 𝐾,𝐿 First order conditions
𝜕𝐺 𝜕𝐿 =𝑤+𝜆 𝜕𝐹 𝜕𝐿 =0 𝜕𝐺 𝜕𝐾 =𝑟+𝜆 𝜕𝐹 𝜕𝐾 =0 𝜕𝐺 𝜕𝜆 =𝑞−𝐹(𝐾,𝐿)=0 𝑤 𝑟 = −𝜆 𝜕𝐹 𝜕𝐿 −𝜆 𝜕𝐹 𝜕𝐾 = 𝑀𝑃 𝐿 𝑀𝑃 𝐾 =𝑀𝑅𝑇𝑆 The production function is concave with diminishing marginal product, this implies that every extra labor is less productive than before, so the cost function is convex in q, every extra unit of output needs higher cost to produce

162 Graphically: Isoquant curve at q Isocost curves

163 Special case 1: when K and L are perfect substitutes, we may get corner solutions
If 𝑤 𝑟 >𝑀𝑅𝑇𝑆, capital is cheaper, hire all capital and zero labor If 𝑤 𝑟 <𝑀𝑅𝑇𝑆, labor is cheaper, hire all labor and zero capital

164 Special case 2: when K and L are perfect complements, we always use the “perfect” proportion of K and L Optimal inputs are at the kink of the isoquant curve

165 Follow the previous example
𝑞= 𝐾 ∙ 𝐿 0.5 In the short run when K= 𝐾 , we find 𝐶=𝑤∗𝐿+𝑟∗ 𝐾 =𝑤∗ 𝑞 𝐾 𝑟∗ 𝐾 In the long run when both L and K are variable: 𝐶=𝑤∗ 𝑟𝑞 𝑤 𝑟∗2 𝑤 𝑞 2 𝑟

166 Long run AC and MC

167 Inflexibility of short run

168 Short run and long run costs

169 Exercise Production function q=10KL
Wage w=10, rental cost of capital r=20 Total, average and marginal cost of producing q units in the short run when K is fixed at 5? Total, average and marginal cost of producing q units in the long run? What happens if wage rate increases to 20?

170 Lectures 16 & 17 Profit Maximization of competitive firms
So far we know how to choose inputs and derive cost function for a specific level of production under a specific technology, but how does a firm determine how much to produce? This class: Competitive market Profit maximization of competitive firms Total revenue, marginal revenue Choice of output given market prices

171 Perfectly competitive market
Homogenous goods must charge same price Free entry and exit of producers Price-taking: numerous firms in the market so no firm's individual supply decision affects price. All firms face perfectly elastic demand Any example that violates the above assumption(s)?

172 Demand curve faced by a competitive firm (perfectly elastic)
Individual firms vs. the industry Demand curve faced by a competitive firm (perfectly elastic) Demand curve faced by the industry

173 Profit-maximizing firms
We assume a for-profit firm aims to maximize profit Total profit = total revenue – total cost 𝜋 𝑞 =𝑇𝑅 𝑞 −𝑇𝐶 𝑞 The firm chooses q to maximize total profit

174 Graphic illustration of profit maximization

175 Algebraically: Choose q in order to maximize First order condition:
𝑑𝜋 𝑑𝑞 = 𝑑𝑇𝑅(𝑞) 𝑑𝑞 − 𝑑𝑇𝐶 𝑞 𝑑𝑞 =𝑀𝑅−𝑀𝐶=0 At the optimal choice of q, MR=MC 𝜋 𝑞 =𝑇𝑅 𝑞 −𝑇𝐶 (𝑞)

176 For a competitive firm, price-taking implies:
𝑇𝑅 𝑞 =𝑝∙𝑞 𝑀𝑅 𝑞 =𝑝 At the optimal choice of q 𝑀𝑅=𝑀𝐶=⇒ 𝑝=𝑀𝐶

177 About fixed cost 𝜋 𝑞 =𝑇𝑅(𝑞)−𝑇𝐶 𝑞
In the short run, fixed cost does not vary by q, so it does not affect the optimal choice of q, what matters is marginal cost (MC). In the long run, fixed cost occurs if and only if the firm enters the market. So it may affect the entry decision.

178 Graphic example

179 Exercise Output price p=10 Total cost = 100 + q + 0.5 * q2
Write down FC, VC, AC and MC. How much should the firm choose to produce in the short run (after it incurs FC)? Should the firm shut down in the long run? At what price will the firm enter the market? FC=100 MC=1+q In the short run, q=9 The total profits = p*q-100-q-0.5q^2 At the optimal choice of output, MC=MR=p=1+q  q=p-1 Plug q=p-1 into total profit function, total profit =0.5*(p-1)^2-100>=0  p>=15.14

180 Short run supply curve of a competitive firm
How will the supply curve change in the long run?

181 Industry supply curve in the short run

182 Producer surplus Sum over all units produced by a firm of differences between the market price of a good and the marginal cost of production 𝑃𝑆 𝑞 = 𝑥=0 𝑞 𝑝−𝑀𝐶 𝑥 𝑑𝑥 =𝑝𝑞−𝑇𝑉𝐶 𝑞 = 𝑝−𝐴𝑉𝐶 𝑞

183 Producer surplus for a firm

184 Producer surplus for the industry in the short run

185 Long run profit maximization for an individual firm
More flexible in input choices  production can be more cost-efficient in the long run Can shut down and exit the market if the expected profit is lower than the fixed cost Short run production: q1 Long run production: q3 Long run production with free entry: q2

186 Long run competitive equilibrium for the industry – three conditions
All firms are maximizing profit. No firm has an incentive to entry or exit because all firms earn zero economic profit Zero economic profit represents a competitive return for the firm’s investment of financial capital The price of the product is such that the quantity supplied by the industry is equal to the quantity demanded by consumers.

187 Continue the previous example for the whole industry start with p=40

188 The industry’s long run supply curve
Constant cost industry All firms face same cost Every firm is small as compared to the market Long run supply curve is horizontal

189 The industry’s long run supply curve
increasing cost industry The prices of some or all inputs increase as the industry expands Long run supply curve is upward sloping

190 Is it possible for the industry’s long run supply curve to be downward sloping?
Yes, for decreasing cost industry The prices of some or all inputs may fall as the industry expands and takes advantage of the industry size to obtain cheaper inputs

191 Price elasticity of supply
𝑒 𝑠𝑢𝑝𝑝𝑙𝑦 = 𝑑𝑄/𝑄 𝑑𝑃/𝑃 In a constant cost industry, 𝑒 𝑠𝑢𝑝𝑝𝑙𝑦 is infinitely large. In an increasing cost industry, 𝑒 𝑠𝑢𝑝𝑝𝑙𝑦 is positive and finite, with magnitude depending on the extent to which input costs increase as the market expands.

192 Exercise Suppose that a competitive firm has a total cost function 𝐶 𝑞 =450+15𝑞+2 𝑞 2 . If the market price is P=$115 per unit, find the level of output produced by the firm, the level of profit and the level of producer surplus. Suppose all firms are identical. At P=115, is the industry in long-run equilibrium? If not, find the price and every firm’s production associated with long-run equilibrium . MC=15+4q=115  q=25 At q=25, total cost is 2075, total revenue is 2875, so total profit is 800. Producer surplus = Total revenue – Total variable cost = =1250. No, it is not in the long run equilibrium because positive profit will attract entry. In the long run equilibrium, p=minimum of AC = 60, at this price, every firm produces 15 units.

193 Lecture 18 Competitive market equilibrium
Demand equal to supply Consumer surplus Producer surplus Dead weight loss Consequence of price regulations

194 Competitive market equilibrium
Every consumer is a price-taker and a utility-maximizer Every firm is a price-taker and a profit- maximizer Free entry and exit Demand equal to supply

195 Consumer surplus and producer surplus
Consumer surplus = sum of (consumer willingness to pay – price paid) over all units sold = 0 𝑄 𝑊𝑇𝑃−𝑃 𝑑𝑥 Producer surplus = sum of (market price – marginal cost) over all units sold = 0 𝑄 𝑃−𝑀𝐶 𝑑𝑥

196 Price control #1: impose a maximum price that is below the market clearing price

197 Price control #2: impose a minimum price that is above the market clearing price
Regulating price away from free-market price (in either direction) will introduce some deadweight loss.

198 Exercise: Demand: P=100-Q Supply: P=1+2Q
Calculate market price, quantity sold, consumer surplus, producer surplus and total welfare Suppose the government imposes a price ceiling of $50. How would market price, quantity sold, consumer surplus, producer surplus and total welfare change? How much is the dead weight loss? Free market: Q=33, P=67, CS=544.5, PS=1089, Total welfare=CS+PS=1633.5 With price control: P=50, Q=24.5 (determined by supply), CS= , PS=600.25, total welfare= , DWL=

199 More about price regulation
Price regulation will distort the market and generate dead weight loss in total welfare Price regulation will also generate a redistribution between consumers and producers What if you care more about consumer surplus than about producer surplus? Lower price may lead consumers to suffer a net loss if the demand is sufficiently inelastic With price ceiling, new CS=old CS-B+A

200 Example: the market of kidney and the National Organ Transplantation Act
Market clearing price is 20,000. The law makes the price zero. At market price, total welfare=(D+B+…)+(A+C) At regulated price, total welfare=(D+.A+..)+0

201 Other regulations: supply restriction
Limited taxi licenses Trade barriers At world price, buy Qs from domestic, and import Qd-Qs If import is not allowed, price rises to P0 How much is the deadweight loss? How much is the loss of consumer surplus?

202 What if there is an import quota?
At world price, buy Qs from domestic, and import Qd-Qs If import is only allowed up to the quota, price rises to P* How much is the deadweight loss? How much is the loss of consumer surplus? What about domestic and foreign producers?

203 What about we impose a lump sum tax on gasoline?
Changes in CS? Changes in PS? Gov revenue?

204 Impact of tax depend on demand and supply elasticity

205 Lecture 19 Exchange economy
Edgeworth box Determination of trade price and trade amount Contract curve Textbook: Chapter 16

206 Edgeworth box 2 individuals No production, exchange only
Every one is price taker

207 Contract curve

208 Pareto optimal (pareto efficient)
There is no way to make one better off and the others not worse off Every point on the contract curve is pareto optimal.

209 Competitive equilibrium

210 Example: Handout Two individuals: A and B Two goods: X and Y
Endowment: each one has 5 unites of X and 5 units of Y Utility: UA=XA*YA, UB=XB2*YB. Question: is there a trade? How much to trade? Market price?

211 Lecture 20 First welfare theorem Reasons for market failure
Monopoly: Marginal revenue = MC Monoposony: Marginal expenditure = MC

212 First theorem of welfare economics:
Competitive equilibrium is the best! More formally, textbook Page 597: If everyone trades in the competitive marketplace, all mutually beneficial trades will be completed and the resulting equilibrium allocation of resources will be economically efficient.

213 Three reasons for market failure
Market power: some party is not price taker Monopoly: one seller, non price taker Monoposony: one buyer, non price taker Asymmetric information Externality

214 Monopoly Keep market demand as given
A single seller (or a group of colluding sellers) Maximize profit by choosing output 𝜋=𝑝 𝑞 ∙𝑞−𝑇𝐶(𝑞) Total revenue Total cost First order condition: 𝑀𝑅=𝑝+ 𝑝 ′ 𝑞 ∙𝑞=𝑀𝐶

215 Marginal revenue < price  restrict supply
Monopoly choice competitive choice MC

216 The Principle of Monopoly pricing
𝑀𝑅=𝑝+ 𝑑𝑝 𝑑𝑞 ∙𝑞=𝑝 1+ 𝑑𝑝 𝑑𝑞 ∙ 𝑞 𝑝 = 𝑝 1+ 𝑑𝑝 𝑝 𝑑𝑞 𝑞 =𝑝 1+ 1 𝜀 =𝑀𝐶 Rewrite it, we get 𝑝−𝑀𝐶 𝑝 =− 1 𝜀 Mark up Inverse of demand elasticity

217 This implies: The more elastic the demand is, the lower the monopoly mark up. Demand elasticity limits the monopolist’s market power Monopolist will always choose to operate at an elastic part of the demand curve.

218 Example Demand: P=100-Q Total cost: TC = 20+4Q Competitive P and Q?
Monopoly P and Q? Demand elasticity at this point? Confirm the Lerner rule. Loss of CS due to monopoly? Change of PS due to monopoly? Total welfare changes? MC=4 Competitive: P=MC=100-Q=4  Q=96, P=4 Monopoly: MR=100-2Q MR=MC  100-2Q=4  Q=48, P=100-Q=52 Change of CS: CS of competitive = 0.5*(100-4)*96=4608 CS of monopoly =0.5*(100-52)*48=1152 CS is reduced by 3456 Change of PS: PS of competitive: 0 PS of monopoly: (52-4)*48=2304 Total welfare change = =1152 Note: because of fixed cost (20), competitive equilibrium does not support long run variable profit to cover the fixed cost. So in the long run, no competitive firm can survive. In this sense, it is better to have monopoly than not having a market at all!

219 Exercise: Drug innovation needs FC=5 billion
Demand per month P= Q Marginal cost =$2 If we grant X years of monopoly power for the inventor, what should X be? MR= Q=2  Q=490000, P=51 Variable profit = *(51-2)=24.01 million per month X=5000/(24.01*12)=17.35 years

220 Lecture 21 Price discrimination
Price discrimination – the practice of selling a particular good at different prices to groups with different valuations. When does price discrimination occur? The seller has some market power (i.e. facing downward demand) Sellers can distinguish different types of consumers No arbitrage

221 Types of Price discrimination
1st degree charge each consumer their maximum willingness to pay 2nd degree don’t know who is willing to pay more, offer a menu of deals to sort out consumers 3rd degree: offer different prices according to consumers’ observable attributes (age, gender, …) Can you think of examples for each?

222 Third degree of price discrimination
Two types of demand: 𝑝 1 = 𝑓 1 𝑞 1 𝑝 2 = 𝑓 2 𝑞 2 Monopolist’s profit: 𝜋= 𝑝 1 𝑞 1 + 𝑝 2 𝑞 2 −𝑇𝐶 𝑞 1 + 𝑞 2 Profit maximization leads to: 𝑀𝑅 1 = 𝑀𝑅 2 =𝑀𝐶

223 Third degree of price discrimination
Profit maximization leads to: 𝑀𝑅 1 = 𝑀𝑅 2 =𝑀𝐶 Which type of consumers get charged more? Who benefits from price discrimination? Who loses? Less elastic consumers get charged more, they lose from price discrimination More elastic consumers get charged less, they benefit from price discrimination

224 Example: Chapter 11, Exercise 8
Sal’s satellite company broadcasts TV to subscribers in Los Angeles and New York. The demand functions for each group are: 𝑄 𝑁𝑌 =60−0.25 𝑃 𝑁𝑌 𝑄 𝐿𝐴 =100−0.50 𝑃 𝐿𝐴 Cost of production: 𝐶=100+40𝑄 𝑤ℎ𝑒𝑟𝑒 𝑄= 𝑄 𝐿𝐴 + 𝑄 𝑁𝑌 Price and quantity with price discrimination? What if the firm must charge the same price for NY and LA? With price discrimination, MR of NY=240-8QNY=MC=40  QNY=25, PNY=140 MR of LA=200-4QLA=MC=40  QLA=40, PLA=120 If P must be the same, Q= P, which can be written as P=(160-Q)/0.75 MR= Q=MC=40  Q=64.91, of which QNY=28.302, QLA=36.604, P=

225 Recap on competitive equilibrium and monopoly
Both sellers and buyers are price-takers Demand = supply P=MC Monopoly Buyers are price takers, but the seller is not MR=MC>P Seller has market power, will push price up to consumer willingness to pay (i.e. the demand curve)

226 Lecture 22 Monoposony Monopoly one seller vs. competitive buyers
The seller realizes his power to set market price This power is only useful when demand is downward sloping (rather than horizontal) Monopsony: one buyer vs. competitive sellers The buyer realizes his power to set market price This power is only useful when supply is upward sloping (rather than horizontal)

227 >𝑀𝐶 if MC is upward sloping
Mathematically Monopsony tries to maximize 𝑁𝑒𝑡 𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠 𝑓𝑟𝑜𝑚 𝑏𝑢𝑦𝑖𝑛𝑔 𝑞 =𝑇𝑜𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑞 −𝑇𝑜𝑡𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑞 =sum of WTP for each unit −p∙𝑞 First order condition: 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑞 =𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑞  inverse demand p(q)=𝑀𝐶+ 𝑑𝑀𝐶(𝑞) 𝑑𝑞 ∙𝑞 Willingness to pay for the marginal unit of q = inverse demand p(q) 𝑑[𝑝∙𝑞] 𝑑𝑞 = 𝑑[𝑀𝐶(𝑞)∙𝑞] 𝑑𝑞 =𝑀𝐶+ 𝑑𝑀𝐶(𝑞) 𝑑𝑞 ∙𝑞 >𝑀𝐶 if MC is upward sloping

228 Graphically -> marginal expenditure >MC -> supply curve MC
-> demand curve

229 Compare monopsony with monopoly
Monopoly pushes price to demand curve Monopoly is more powerful if demand is inelastic Monopsony pushes price to supply curve Monopsony is more powerful if supply is inelastic

230 Monopsony leads to dead weight loss

231 Exercise: Walmart is a monopsony of apparel in China. There are many sellers of apparel in China. Based on US demand for apparel, Walmart is willing to pay P= Q for Q units of apparel. The supply of apparel is P=80+0.2Q Calculate P and Q in competitive equilibrium Calculate P and Q in monopsony equilibrium Welfare consequence of monopsony Competitive equilibrium: demand = supply  Q=80+0.2Q  420=0.3Q  Q=1400, P=360, CS=98000, PS=196,000, total welfare=294,000 Monopsony: willingness to pay = marginal expenditure  Q=80+0.2Q+0.2Q  420=0.5Q  Q=840, P=248, CS=176400, PS=70560, total welfare=246960, Dead weight loss=47040

232 Lectures 23 and 24 Imperfect competition
Recall conditions for perfect competition Homogenous goods Every one is price taker Free entry and exit We talked about two extremes: perfect competition and monopoly (monopsony) Between the two extremes: Monopolistic competition Oligopoly

233 Monopolistic competition
large number of small firms freedom of entry and exit perfect info Differentiated products What does this imply? Every firm faces downward sloping demand  have some power is setting price above MC Every firm earns zero economic profit

234 Monopolistic competition in short-run and long-run

235 Inefficiency in monopolistic competition
Downward sloping demand  market power to set price above MC  dead weight loss P>MC and Zero profit in the long run  operate at AC>MC  extra capacity, economy of scale not fully exploited

236 Oligopoly a market structure in which Simplest case Examples?
a small number of firms serve market demand. The industry is characterized by limited entry. Homogenous goods Simplest case duopoly (i.e. only two sellers) Each aware of the existence of the other firm Compete instead of collude  each firm has market power less than monopolist Examples?

237 Nash Equilibrium Each firm is doing the best it can given what its competitors are doing. No one has incentive to deviate at the equilibrium

238 Cournot model of Duopoly
Two profit maximizing firms produce the same goods (e.g. gasoline) Both firms try to set its own output separately and simultaneously each firm treats the output level of its competitor as fixed when deciding its own output

239 Solve Cournot equilibrium
Reaction curves: 𝑄 1 = 𝑓 1 𝑄 2 , 𝑄 2 = 𝑓 2 𝑄 1

240 Example: textbook p453 Market demand: P=30-Q MC=0 for both firms
How much to produce in Cournot equilibrium? What is the market price? What if the two firms collude so they together act like a monopolist? Compare these two cases with competitive equilibrium

241 Cournot: firm 1’s point of view
𝜋 1 =𝑃∙ 𝑄 1 − 𝐶 1 =(30− 𝑄 1 - 𝑄 2 )∙ 𝑄 1 −0 First order condition with respect to Q1 while taking Q2 as given: 𝑑 𝜋 1 𝑑 𝑄 1 =30−2 𝑄 1 − 𝑄 2 =0 Firm 1’s reaction curve: 𝑄 1 =15− 𝑄 2 /2

242 Cournot: firm 2’s point of view
𝜋 2 =𝑃∙ 𝑄 2 − 𝐶 2 =(30− 𝑄 1 - 𝑄 2 )∙ 𝑄 2 −0 First order condition with respect to Q2 while taking Q1 as given: 𝑑 𝜋 2 𝑑 𝑄 2 =30− 𝑄 1 −2 𝑄 2 =0 Firm 1’s reaction curve: 𝑄 2 =15− 𝑄 1 /2

243 Put the two together: 𝑄 1 = 𝑄 2 =10 𝑃=30−𝑄=30− 10+10 =10
𝑄 1 =15− 𝑄 2 /2 𝑄 2 =15− 𝑄 1 /2 𝑄 1 = 𝑄 2 =10 𝑃=30−𝑄=30− =10

244 Compare to monopoly if the two firms collude
MR=P+P’(Q)*Q=30-Q-Q=30-2Q MR=MC  30-2Q=0  Q=15 The two firms together produce 15, so each produce 7.5. P=30-Q=15.

245 Compare to perfect competition
P=MC  30-Q=0  Q=30, P=0.

246 Graphically

247 Difference between Cournot and Stackelberg models
Variation 1: What if the two firms do not choose output simultaneously? Stackelberg model: One firm sets its output before other firms do.  first move advantage Difference between Cournot and Stackelberg models The leading firm will consider how the other firms adjust output according to his choice of output

248 Continue the previous example
Demand: P=30-Q, MC=0 for both firms Firm 1 chooses Q1 first, firm 2 chooses Q2 next Firm 2’s best choice of Q2 given Q1  firm 2’s reaction curve 𝑄 2 =15− 𝑄 1 /2 Firm 1 anticipates firm 2’s reaction curve 𝜋 1 =𝑃∙ 𝑄 1 − 𝐶 1 =(30− 𝑄 1 - 𝑄 2 )∙ 𝑄 1 − 0=(30− 𝑄 𝑄 1 /2)∙ 𝑄 1 First order condition: 15− 𝑄 1 =0 𝑄 1 =15, 𝑄 2 =7.5, 𝑃=7.5.

249 Demand: P=30-Q, MC=0 for both firms
Variation 2: What if the two firms choose price instead of output simultaneously? Demand: P=30-Q, MC=0 for both firms As long as the other firm charges above MC, this firm has incentive to undercut At the end, each charges MC and earns zero profit! This is called Bertrand competition! What if the two firms have different cost, say MC1=10, MC2=0?  firm 2 takes the whole market, and charges slightly under 10

250 Simple Game Theory Nash Equilibrium: no one has incentive to deviate given the other parties’ strategy. Dominant strategy: it is the player’s best strategy no matter what strategy the other players adopt Prisoner’s dilemma Confess Not confess -10, -10 -5, -15 -15, -5 -6, -6

251 Examples of prison’s dilemma
Two firms collude  each has incentive to secretly cut price or expand output  collusion is fundamentally unstable Any other example?

252 Pure strategy vs. Mixed strategy Example: Inspection game
Mixed: randomize between strategies Example: Inspection game No pure strategy equilibrium, the only equilibrium is 50% probability detect, 50% probability comply Detect Not Detect Comply -5,-5 -5,0 Not comply -10, 5 0, 0 Suppose probability of detect is Pd, probability of comply is Pc Given Pd, the regulated must be indifferent between comply and not comply (otherwise one won’t randomize between the two). This implies -5=-10*Pd+0*(1-Pd)  Pd=0.5 Given Pc, the inspector must be indifferent between detect or not detect -5*Pc+(5)*(1-Pc)=0  Pc=0.5.

253 Lecture 25 Asymmetric Information
Adverse Selection Problem solution Moral Hazard Solution Adverse selection and Moral Hazard

254 Recall: Reasons for market failure
Imperfect competition Monopoly, monopsony, oligopoly, monopolistic competition Asymmetric information Situation in which a buyer and a seller possess different information about a transaction. Externality

255 The market for lemons Suppose used car quality is uniformly distributed between 0 (completely dysfunctional) and 1 (same as brand new) Suppose a typical buyer is willing to pay X for quality X. Problem: the buyer cannot observe car quality before purchase (no test drive….) 0.25 0.5 1

256 Adverse selection Cause: Products of different qualities are sold at a single price because sellers observe product quality but buyers do not Consequence: too much of the low quality product (so called “lemons”) and too little of the high quality product (so called “peaches”) are sold. Other examples?

257 Solutions to adverse selection
Return and warranty Blanket return policy Hyundai offers 10-year warranty Signaling workers may signal their ability by education Reputation Reputable restaurants (e.g. McDonald) have more to lose if they cheat Third party certification Unraveling results

258 Moral hazard One party engage in hidden actions
This action affects the probability or magnitude of a payment associated with an event Example: principal-agent problem

259 Solutions to principal-agent problem
Close monitoring Incentive contract Textbook example: revenue from making watches Cost of low effort=0, cost of high effort=10,000 What kind of contract can solicit high effort? Bad Luck (50%) Good Luck (50%) Low effort (a=0) $10,000 $20,000 High effort (a=1) $40,000

260 Incentive contract Any fixed wage does not yield high effort.
Let wage conditional on revenue. Consider: w=max(R-18000,0) At low effort, expected wage is 0*0.5+( )*0.5=1000 At high effort, expected wage is ( )*0.5+( )*0.5=12000 The net gain to the worker with high effort = =2000>1000, so the worker will commit to high effort When the worker engages in high effort, the principal’s net gain = 20000* * =18000.

261 Adverse selection and moral hazard
They are different Adverse selection: info asymmetry before contract Moral hazard: info asymmetry after contract They can co-exist Unsecured consumer credit Insurance Employment

262 Lecture 26: Externality Definition Negative externality
Positive externality Solutions

263 Externality Definition: Negative externality Positive externality
Action by either a producer or a consumer which affects other producers or consumers but is not accounted for in the market price Negative externality Examples? Positive externality

264 Inefficiency of negative externality
MC: marginal cost facing the producer MSC: marginal social cost of production facing the whole society MSC-MC=marginal external cost Externality  over production

265 Solution Restrict production in light of negative externality
Emission standard How can EPA know the optimal standard? Enforcement cost is high Charge emission fee Tradeable emissions permits

266 Example: Chapter 18 Exercise #6
Demand for paper: Qd=160, P Supply for paper: Qs=40, P Marginal external cost of effluent dumpting: MEC=0.0006Qs Calculate P and Q assumption no regulation on the dumping of effluent. Determine the socially efficient P and Q. Without accounting for the marginal external cost of effluent, Qs=Qd  P= P  =4000P  P=30, Q=100,000 Under perfect competition, MC is the supply curve. Qs=40, P  P=0.0005Qs -20= MC To account for marginal external cost, MSC=MC+MEC=0.0006Qs Qs-20=0.0011Qs-20 Rewrite the demand: P= Qd At the equilibrium, MSC=P, Qd=Qs  Q-20= Q  Q=100  Q=62500, P=48.75

267 Inefficiency of positive externality
Consider home repair and landscaping MB=Marginal benefits for the home owner Marginal social benefits=MB+marginal external benefit for neighbors Positive externality  under provision of public goods

268 Public goods Definition: the marginal cost of provision to an additional consumer is zero and people cannot be excluded from consuming it Two properties: Nonrival: zero cost to additional consumers Nonexclusive: cannot exclude people from using the public goods Examples: national defense, light house, air quality, information Private provision of public goods suffers from the free-riding problem

269 A comprehensive example
Stephen J. Dubner and Steven D. Levitt’s blog on 4/20/2008 titled “Not so-free ride” zine/20wwln-freakonomics- t.html?pagewanted=1

270 Course overview Three main blocks Extras
Consumer’s problem Producer’s problem Market equilibrium Extras uncertainty, game theory, asymmetric information, externality The review below focuses on the most basic points that you should master, it is not meant to be exhaustive of all materials subject to testing

271 Consumer’s problem Utility function Budget constraint
Write out and solve consumer’s utility maximization problem How does consumer choice change in response to changes in price or income? Derive individual demand and market demand Calculate demand elasticity Special cases: perfect substitutes and perfect complements

272 Producer’s problem Production function and related concepts
Solve firm’s cost minimization problem How does firm’s choice change in light of production change or input price change? Cost function and related concepts Derive individual and market supply in perfect equilibrium

273 Market equilibrium Perfect competition (demand = supply, price=MR=MC)
2-person exchange economy (Edgeworth box) Monopoly (MR=MC<price) uniform pricing, price discrimination Monoposony (ME=WTP>Price) Duopoly (Cournot, Bertrand, Stackelberg) Monopolistic competition

274 Extras Uncertainty Expected value, expected utility and risk preferences Simple game theory Concept of Nash Equilibrium, dominant strategy, mixed strategy Simple examples in class Asymmetric Information Adverse selection Moral hazard Externality Negative externality Positive externality, public goods, free-riding

275 Course evaluation please OPEN in the last two weeks of the semester Thank you!

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