3 Goal of the class Teach you to think like a micro-economist Labor market issuesIndustrial organizationPublic policiesInternational tradeDerive the major concepts and intuitions from introductory microeconomicsWe will emphasize analytic logic and mathematical rigor.
4 Class will cover: Consumer demand Firm production Describe consumer preferenceDerive consumer demandMarket vs. individual demandConsumer welfareFirm productionProduction technologyFirm choice of input and outputCost and profitHow demand meets supply?Exchange economyMarket structureMarket failures: monopoly, asymmetric info, externalityPolicy interventions
5 Example: rental market in College Park Product definition:one bedroom aptoff-campus rentalin College parkPlayers:tenants, landlords, city government? University?Actions and incentivesTenants: reservation price/willingness to payLandlords: cost, earn money if possibleMarket outcomes:price, vacancy rate, tax revenue?
6 Monthly rentsupplyequilibriumdemandUnits availableWhy is the demand downward sloping?
7 When will we observe a fixed supply? Monthly rentsupplyequilibriumdemandWe 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 availableWhen will we observe a fixed supply?
8 Market scenario 1: convert some apartments to condos supplyMonthly rentdemandUnits availableBoth demand and supply get reduced, the effect on market equilibrium price is unclear
9 Market scenario 2: impose $50/month tax on landlord supplyMonthly rentdemandUnits availableNo change in demand and supply thus no change in priceONLY TRUE with fixed supplyWhat happens if the supply is not fixed?
10 Market scenario 3: non-discriminating monopoly supplyMonthly rentdemandUnits availableThe monopolist may want to restrict the supply so that he can charge higher price not efficient from the society point of viewWhat if the monopolist can charge different price on different tenants?
11 Market scenario 4: rent control supplyMonthly rentdemandUnits availableKeep the price down, but create excessive demandHow 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 preferenceYou know how to derive the supply decision of each firmYou know how to compute market equilibrium under different market structuresYou can compute who gains and who loses by how much under a simple policy intervention
13 Syllabus on my personal website http://kuafu.umd.edu/~ginger/ click on Econ326Also available on elms.umd.edu
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 7EvaluationThree problem sets, 10 points eachTwo midterms, 20 points eachOne cumulative final, 30 pointsFive random in-class quizzes, 2 bonus points eachTotal 110 pointsConversely, 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
17 Important datesSept. 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 examNo curvesThere will be 5 in-class quizzes at unannounced dates.
18 Exam policiesIf you miss exams for reasons in line with university policy, you can take makeup exams or roll over your missed points to finalFor 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 setsHard copy distributed in class, soft copy available on elmsYou 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 sessionsCollaborative 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 HouseOffice HoursMonday 2:15-3:15pm, Friday 2-3pmOffice PhoneChange of office hours for Sumedha
21 Teaching StylePower point lecture notes are posted on elms (subject to update)More details and examples may be covered during the classHandouts, problem sets, answer keys will be posted on elms. I will also distribute handouts and problem sets in classGraded work will be returned in TA sessions
22 Expectation on You Attend the class Read related textbook chapters Mute your cell phone at leastIf you have to use your computer, make sure it is muted and you do not bother othersRead related textbook chaptersdate-specific chapter numbers are available in syllabusAttend TA sessions (will be very useful)Sharpen your calculusAsk for help EARLY if you encounter difficultyFeel free to give us feedback any time so we can improve during the class
23 Lecture 2 Utility Theory Consumer preferences Constructing Indifference curvesProperties of Indifference curvesTextbook chapter
24 Intuition of consumer theory How does a consumer choose the best things that she can afford?What is the bestAfford budget constraintHow to choose constrained optimizationExamples:Individual choice of work timeApple rolls out iphone4Tax cut at the end of 2010
25 Axioms of preferences Completeness Transitivity Non-satiation: A > B, B > A, A ~ B for all bundles A, BTransitivityA > B and B > C => A > COtherwise we won’t be able to tell which bundle is the bestNon-satiation:more is preferred to less. Goods are always “good”Counter examples: bad (dislike), neutral goods (indifferent)Balance:averages preferred to extremesAlso 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 Utilitythe increase in utility you get when you consume one more unit of good XUnits of ApplesTotal utility(TU)Marginal Utility (MU)155-0=5299-5=431212-9=341414-12=21515-14=1One common property: Diminishing marginal utility
28 Show MU in graphTotal Utility UUnits of apples (X)
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 FunctionUtility 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+5lnYU=X0.5Y0.5 vs U=XYU=XY vs U=lnX+lnYU=X+Y2 vs U=X+YNote:monotonic transformation does not change the order of preference,it may change the property of MUIt 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)YYXX
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 levelIndifference curves never cross each other
34 Axioms of preferences Completeness Transitivity Non-satiation: A > B, B > A, A ~ B for all bundles A, BTransitivityA > B and B > C => A > COtherwise we won’t be able to tell which bundle is the bestNon-satiation:more is preferred to less. Goods are always “good”Counter examples: bad (dislike), neutral goods (indifferent)Balance:averages preferred to extremesAlso called convex preference
35 Examples of indifference curves U(X, Y)=X * YYpointXYU12439165678I1=4, I2=9, I3=16XTypical convex preferenceSatisfy all four axioms of preference
36 Examples of indifference curves U(X, Y)=X + YYpointXYU124368575347I1=2, I2=4, I3=58216XPerfect substitutesViolate “balance” because avg is not better than extremesMUx is a constant (not diminishing), so is MUY
37 Examples of indifference curves U(X, Y)=min(X, Y)YpointXYU12345678I1=2, I2=4, I3=5XPerfect complementsViolate “non-satiation” sometimesU is not always differentiable, MU is not well defined at the kinks
38 Lecture 3 Marginal rate of substitution Properties of indifference curvesShape of indifference curvesSpecial examplesTextbook Chapter 3.1 & 3.2Assign 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) YASlope = - MRS at point AX
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=XYU=lnX + lnYU=X+YU=X+Y2U=(X+1)(Y+2)U=X2 Y2Which 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 slopingViolate non-satiation if upward slopingIndifference curves never crossViolate transitivity if they crossIndifference curves are convexViolate balance if they are concave or linearDraw 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 bananasLike apples up to a satiation levelLike apples, but dislike bananasLike apples, but indifferent to bananasMust eat one apple with one bananaDislike apples, dislike bananasLike both apples and bananas up to a satiation level
50 Must eat one apple with one banana (perfect complements) bananasULocus lineWhat 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) bananasUWhat 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)
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 = IRearrange: Y = I/ Py + (- Px / Py ) * Xinterceptslope
55 Graph budget constraint YI/PySlope = - Px / PyI/PxXPx/Py = the rate at which Y is traded for X in the marketplaceUnlike 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 cardsBakugan ball is $5 eachPokemon card is $2 eachDraw his budget line
57 What happens with income tax cut? Tax cut more incomeI/PxI/PyXYSlope = - Px / PyDoes 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 increasesI/PxI/PyXYSlope = - Px / PyDoes 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 = $2000Two goods: X=food, Y=health carePrices: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=1000Step 2: if Y=500, $1500 left for food 1500/2=750Step 3: if Y<500, price ratio is 2/1Step 4: if Y>500, price ratio is 2/0.2=10Step 5: if all income is used for health care, we can buy 500+( )/0.2=8000Slope = -Px /Py = -25007501000X (food)
61 Example 2: 1979 food stamp program Income I=2000Two goods: food (X), other (Y)Px =1, Py = 1A household is granted $200 food stampBut the food stamp can only be used for food
62 What happens if there is a black market to trade food stamps? other200020002200foodWhat happens if there is a black market to trade food stamps?
64 #1: no financial marketY (tomorrow)2*III2*IX (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 savingX (today)
67 Recap so far Indifference curves describe consumer preference Budget constraints describe what consumers can affordPut the two together to determine the best bundle one can afford
68 Graphical presentation YMRS > Px/PyI/PyASlope = - Px / PyCBMRS < Px/PyI/PxXPx/Py = the rate at which Y is traded for X in the marketplaceMRS = 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 PrincipleMRS = the rate at which the consumer is willing to trade Y for one extra unit of XPx / Py = the rate at which Y is traded for X in the market placeMRS = Px / Py MUx /Px = MUy /Py
70 Mathematical derivation Max U(X, Y) by choosing X and YSubject to I = Px * X + Py * YDefine Lagrangian functionL = U(X,Y) + λ (I – Px * X – Py * Y)λ is an additional variable, now need to choose X, Y, λ
72 We get the equal marginal principle back! λ is the shadow price of the budget constraintTell 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 = $2Price of clothes =$1Income=100Answer: F=25, C=50
74 Lecture 5 Consumer’s optimal choice Cobb-Douglas utility Inner solution, corner solutionCobb-Douglas utilityPrice and consumer choiceIncome and consumer choiceNormal, inferior and giffen goodsTextbook Chapter 4 appendix,
75 Typically: Inner solution At the optimal choice:MRS = Px/PyI=Px * X + Py * YI/PyI/PxX
76 I/PxI/PyXYWhat if the equal marginal principle cannot be satisfied? corner solutionSpend every penny:I=Px * X + Py * YCheck which corner gives higher utilityU
77 Example 1 of corner solution: perfect substitutes U=X+2YPx=10Py=10Income=1000YU100100X
78 Example 2 of corner solution: perfect complements 100XYU=min(X,2Y)Px=10Py=10Income=1000
79 Demand Optimal choice Properties: X=f(Px, Py, Income) Homogenous degree of zeroTypically depends on income, own price, price of other goods
80 Special example: Cobb-Douglas Utility Two equationsSolve 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 goodsHomothetic preferences:MRS only depends on the ratio of X and YFixed share of income for each good
82 Graph consumer choice in response to: Price changesIncome changes
84 Two goods:food, clothingIncome increasesNote 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 goodsConsumers 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 curveNormal 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 goodsNormal and inferior goods are defined by how consumer choice changes in response to income changeGiffen goods depend on price changeTypical goods have downward sloping demand curveGiffen 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 6Decompose income and substitution effects in response to price changeSlusky EquationTextbook chapter:Handout #1: an example
90 Food price fallsInitial choice A new choice BImaginary D: same utility as A, but face new price
95 Example 2: Introduction of health insurance X=food, Y=health care, Px=$2, Py=$1 if no insurance, Income=2000Benchmark: no insuranceScenario #1: insurers pay 80% of the cost of any medical serviceScenario #2: insurers pay 80% after $500 deductible
96 10000Y (health care)A: choice with no insuranceC: choice with insuranceA to B: substitution effectB to C: income effectSlope = -Px /Py = -2/0.2=-10CBASlope = -Px /Py = -21000X (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 deductibleY (health care)8000Slope = -Px /Py = -2/0.2=-10Slope = -Px /Py = -25007501000X (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 elasticityTextbook chapter:
99 Individual demand A consumer’s optimal choice of a good depends on The price of this goodThe price of other goodsIncome
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=100-2PWhat is demand elasticity at p=10,20,30?At what price is the demand isoelastic?P50Demand elasticity changes along the demand curve.What kind of demand curve has constant demand elasticity?Q100
112 Special cases P Q Completely inelastic demand Infinitely elastic demandQ
115 More on cross elasticity X and Y are substitutesIf an increase in Px leads to an increase in the quantity demanded of Y.X and Y are complementsIf an increase in Px leads to a decrease in the quantity demanded of Y.X and Y are IndependentIf Px does not affect the quantity demanded of YCobb-Douglas utility independent goods
116 Consumer surplusIndividual consumer surplus = difference between what a consumer is willing to pay for a good and the amount actually paidTotal consumer surplus= sum of individual consumer surplusFor 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 curveIncome and substitution effectsSum of Individual demand=market demandDemand elasticity, income elasticity, cross elasticityConsumer surplus
120 Lecture 11 Risk and Consumer behavior Describe riskPreferences towards riskDemand for risky assets
121 Risk, Uncertainty, and Profit, by Frank Knight (1921) Risk: random events that can be quantified in probabilityUncertainty: random events that cannot be quantified in probabilityToday we focus on “risk” only
122 Describe riskOutcome: a random event is associated with multiple outcomes, for instance:head/tail when we flip a coingain/loss when we invest in a risky assetHealthy or sick in the futureProbability: likelihood that a given outcome will occurPayoff: value associated with a possible outcome
123 Describe riskExpected value: probability-weighted average of the payoffs associated with all possible outcomesE(X)=Prob1*X1+ Prob2*X2 +…+ Probn*XnVariance: Extent to which possible outcomes of a risky event differVar(X)= Prob1*(X1-E(X))2+ Prob2*(X2 -E(X))2 +…+ Probn*(Xn -E(X))2Standard deviation: square root of variance, same unit as X
124 ExampleJob1:50% probability with income $200050% probability with income $1000Job299% probability with income $15101% probability with income $1500Calculate expected values, variance, standard deviation
126 Preferences toward risk For outcome Xi, utility = U(Xi)Expected utilityEU=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 $30,00050% prob with income $10,000
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)UHow 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 relatedMost effective if the activities are negatively correlated (examples?)InsurancePay insurance premium to avoid risky outcomesActuarially fair: the insurance premium is equal to the expected payout
134 Choosing between risk and return Risk free asset: RfAsset with market risk: Rm, m( Rm – Rf )Portfolio p: Rp= Rf * pm
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?payoffProb (investment A)Prob (investment B)$3000.100.30$2500.800.40$200For investment A, EX=0.1* * *200=250, stdev=sqrt(0.1*50^2+0.8*0^2+0.1*50^2)=22.36For investment B, EX=0.3* * *200=250, stdev=sqrt(0.3*50^2+0.4*0^2+0.3*50^2)=38.73Jill 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 functionAverage product, marginal productLaw of diminishing marginal returnMalthus and the food crisisProduction with two inputsIsoquant curveMarginal rate of technical substitutionReturns to scale
138 Technology of Production Production function: shows the highest output that a firm can produce for each specified combination of inputsSingle 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 changedLong-run: time needed to make all production inputs variable.
139 Single-input production q=F(L) Average product: q /LMarginal product: dq /dLLqAvg productq/LMarginal product dq/dL110230360480595
141 Marginal Product (MP) and Average Product (AP) Total product q = q (L)Marginal Product = dq / dLAverage Product = q / LQuestion: How does AP change with L?𝑑(𝐴𝑃) 𝑑𝐿 = 𝑑 𝑞 𝐿 𝑑𝐿 =− 𝑑𝑞 𝑑𝐿 ∙𝐿−𝑞 𝑑𝐿 𝑑𝐿 𝐿 2 = 𝑀𝑃−𝐴𝑃 𝐿If MP>AP, AP increases with LIf MP<AP, AP decreases with LAP=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 improvementExample: 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 outputSimilar 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 / MPkMRTS = - slope of isoquant curveDiminishing MRTSSimilar to MRS in consumer utility
145 ExamplePlot isoquant curve for K=2, L=1, calculate marginal product of labor, marginal product of capital and MRTS at this pointq=3KLq=3K+Lq=min(3K, L)
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 OrdinalConsumer utility is ordinal because we only care about the relative preference on bundles and it is hard to compare utility across individualsProduction function is cardinal because the absolute scale mattersCobb-Douglas production:𝑞=𝐴∙ 𝐾 𝛼 ∙ 𝐿 𝛽𝐴: technological factor𝛼+𝛽: return to scale
150 Returns to scaleRate at which output increases as ALL inputs are increased proportionallyNote it is different from marginal productIt is a property of a given production function, also different from technological improvementSimple rule of thumb: will the output double when all the inputs double?q more than double Increasing returns to scaleq exactly double Constant returns to scaleq less than double Decreasing returns to scale
151 Constant return to scale Increasing return to scale Example of constant returns to scale: lawn mowingincreasing returns to scale: specializationdecreasing 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 𝛽Suppose K increases to xK, L increases to xLLet q’ denote the new production by xK and xL𝑞 ′ =𝐴∙ 𝑥𝐾 𝛼 ∙ 𝑥𝐿 𝛽= 𝑥 𝛼+𝛽 ∙𝐴∙ 𝐾 𝛼 𝐿 𝛽= 𝑥 𝛼+𝛽 ∙𝑞If 𝛼+𝛽<1, decreasing returns to scaleIf 𝛼+𝛽=1, constant returns to scaleIf 𝛼+𝛽>1, increasing returns to scale
153 Example: are these production functions decreasing, increasing or constant returns to scale? q=3KLq= K0.5L0.3q=0.5lnK + 0.8lnLq=3K+Lq=min(3K, L)q= 3KL + 3KL2Answer: (1) increasing (2) decreasing (3) undetermined (4) constant (5) constant (6) increasing
154 Lecture 14, 15 and 16 Cost functions Firm decisionGiven production technologyGiven input prices of input firm decides on optimal choice of inputs cost functionShort runLong run
155 Cost w = wage rate r = capital rental cost Both could be opportunity costCost function C (q) = w*L(q) + r*K(q)Firm’s decision does not include “sunk cost” after the cost is sunkExample?
156 Fixed vs. Variable Cost w = wage rate r = capital rental cost In the long run when every input is variable𝐶 𝑞 =𝑤∗𝐿 𝑞 +𝑟∗𝐾(𝑞)In the short run, if K is fixed at 𝐾 ,𝐶 𝑞 =𝑤∗𝐿 𝑞 +𝑟∗ 𝐾Variable costfixed 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∗ 𝐾Example: 𝑞= 𝐾 ∙ 𝐿 0.5𝐶=𝑤∗𝐿+𝑟∗ 𝐾 =𝑤∗ 𝑞 𝐾 𝑟∗ 𝐾The 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 generallyTotal production functionTotal cost function
159 Marginal cost (MC) and avg cost (AC) Total cost functionMarginal cost MC = dC/dqAverage Variale cost = VC/qAverage total cost = TC/q = (VC + FC)/qWhen 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, 𝐿The 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)=0𝑤 𝑟 = −𝜆 𝜕𝐹 𝜕𝐿 −𝜆 𝜕𝐹 𝜕𝐾 = 𝑀𝑃 𝐿 𝑀𝑃 𝐾 =𝑀𝑅𝑇𝑆The 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
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 laborIf 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 LOptimal inputs are at the kink of the isoquant curve
165 Follow the previous example 𝑞= 𝐾 ∙ 𝐿 0.5In the short run when K= 𝐾 , we find𝐶=𝑤∗𝐿+𝑟∗ 𝐾 =𝑤∗ 𝑞 𝐾 𝑟∗ 𝐾In the long run when both L and K are variable:𝐶=𝑤∗ 𝑟𝑞 𝑤 𝑟∗2 𝑤 𝑞 2 𝑟
169 Exercise Production function q=10KL Wage w=10, rental cost of capital r=20Total, 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 marketProfit maximization of competitive firmsTotal revenue, marginal revenueChoice of output given market prices
171 Perfectly competitive market Homogenous goodsmust charge same priceFree entry and exit of producersPrice-taking:numerous firms in the market so no firm's individual supply decision affects price.All firms face perfectly elastic demandAny example that violates the above assumption(s)?
172 Demand curve faced by a competitive firm (perfectly elastic) Individual firms vs. the industryDemand 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 profitTotal profit = total revenue – total cost𝜋 𝑞 =𝑇𝑅 𝑞 −𝑇𝐶 𝑞The firm chooses q to maximize total profit
175 Algebraically: Choose q in order to maximize First order condition: 𝑑𝜋 𝑑𝑞 = 𝑑𝑇𝑅(𝑞) 𝑑𝑞 − 𝑑𝑇𝐶 𝑞 𝑑𝑞 =𝑀𝑅−𝑀𝐶=0At the optimal choice of q, MR=MC𝜋 𝑞 =𝑇𝑅 𝑞 −𝑇𝐶 (𝑞)
176 For a competitive firm, price-taking implies: 𝑇𝑅 𝑞 =𝑝∙𝑞𝑀𝑅 𝑞 =𝑝At the optimal choice of q𝑀𝑅=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.
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=100MC=1+qIn the short run, q=9The total profits = p*q-100-q-0.5q^2At the optimal choice of output, MC=MR=p=1+q q=p-1Plug 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?
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 runCan shut down and exit the market if the expected profit is lower than the fixed costShort run production: q1Long run production: q3Long 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 profitZero economic profit represents a competitive return for the firm’s investment of financial capitalThe 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 industryAll firms face same costEvery firm is small as compared to the marketLong run supply curve is horizontal
189 The industry’s long run supply curve increasing cost industryThe prices of some or all inputs increase as the industry expandsLong 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 industryThe 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/𝑃In 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 ExerciseSuppose 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=25At 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 supplyConsumer surplusProducer surplusDead weight lossConsequence of price regulations
194 Competitive market equilibrium Every consumer is a price-taker and a utility-maximizerEvery firm is a price-taker and a profit- maximizerFree entry and exitDemand 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 𝑑𝑥Producer 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 welfareSuppose 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=1633.5With 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 welfarePrice regulation will also generate a redistribution between consumers and producersWhat 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 inelasticWith 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 licensesTrade barriersAt world price, buy Qs from domestic, and import Qd-QsIf import is not allowed, price rises to P0How 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-QsIf 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 boxDetermination of trade price and trade amountContract curveTextbook: Chapter 16
206 Edgeworth box 2 individuals No production, exchange only Every one is price taker
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 YUtility: 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 = MCMonoposony: 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 takerMonopoly: one seller, non price takerMonoposony: one buyer, non price takerAsymmetric informationExternality
214 Monopoly Keep market demand as given A single seller (or a group of colluding sellers)Maximize profit by choosing output𝜋=𝑝 𝑞 ∙𝑞−𝑇𝐶(𝑞)Total revenue Total costFirst order condition:𝑀𝑅=𝑝+ 𝑝 ′ 𝑞 ∙𝑞=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 =𝑀𝐶Rewrite it, we get𝑝−𝑀𝐶 𝑝 =− 1 𝜀Mark upInverse 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 powerMonopolist 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=4Competitive: P=MC=100-Q=4 Q=96, P=4Monopoly:MR=100-2QMR=MC 100-2Q=4 Q=48, P=100-Q=52Change of CS:CS of competitive = 0.5*(100-4)*96=4608CS of monopoly =0.5*(100-52)*48=1152CS is reduced by 3456Change of PS:PS of competitive: 0PS of monopoly: (52-4)*48=2304Total welfare change = =1152Note: 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= QMarginal cost =$2If we grant X years of monopoly power for the inventor, what should X be?MR= Q=2 Q=490000, P=51Variable profit = *(51-2)=24.01 million per monthX=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 consumersNo arbitrage
221 Types of Price discrimination 1st degreecharge each consumer their maximum willingness to pay2nd degreedon’t know who is willing to pay more, offer a menu of deals to sort out consumers3rd degree: offerdifferent prices according to consumers’ observable attributes (age, gender, …)Can you think of examples for each?
223 Third degree of price discrimination Profit maximization leads to:𝑀𝑅 1 = 𝑀𝑅 2 =𝑀𝐶Which type of consumers get charged more?Who benefits from price discrimination?Who loses?Less elastic consumers get charged more, they lose from price discriminationMore 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 𝑁𝑌𝑄 𝐿𝐴 =100−0.50 𝑃 𝐿𝐴Cost of production:𝐶=100+40𝑄 𝑤ℎ𝑒𝑟𝑒 𝑄= 𝑄 𝐿𝐴 + 𝑄 𝑁𝑌Price 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=140MR of LA=200-4QLA=MC=40 QLA=40, PLA=120If P must be the same, Q= P, which can be written as P=(160-Q)/0.75MR= 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-takersDemand = supplyP=MCMonopolyBuyers are price takers, but the seller is notMR=MC>PSeller 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 priceThis power is only useful when demand is downward sloping (rather than horizontal)Monopsony:one buyer vs. competitive sellersThe buyer realizes his power to set market priceThis power is only useful when supply is upward sloping (rather than horizontal)
227 >𝑀𝐶 if MC is upward sloping MathematicallyMonopsony tries to maximize𝑁𝑒𝑡 𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠 𝑓𝑟𝑜𝑚 𝑏𝑢𝑦𝑖𝑛𝑔 𝑞=𝑇𝑜𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑞 −𝑇𝑜𝑡𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑞=sum of WTP for each unit −p∙𝑞First order condition:𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑞 =𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑞 inverse demand p(q)=𝑀𝐶+ 𝑑𝑀𝐶(𝑞) 𝑑𝑞 ∙𝑞Willingness 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
229 Compare monopsony with monopoly Monopoly pushes price to demand curveMonopoly is more powerful if demand is inelasticMonopsony pushes price to supply curveMonopsony is more powerful if supply is inelastic
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+0.2QCalculate P and Q in competitive equilibriumCalculate P and Q in monopsony equilibriumWelfare consequence of monopsonyCompetitive equilibrium: demand = supply Q=80+0.2Q 420=0.3Q Q=1400, P=360, CS=98000, PS=196,000, total welfare=294,000Monopsony: 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 competitionHomogenous goodsEvery one is price takerFree entry and exitWe talked about two extremes: perfect competition and monopoly (monopsony)Between the two extremes:Monopolistic competitionOligopoly
233 Monopolistic competition large number of small firmsfreedom of entry and exitperfect infoDifferentiated productsWhat does this imply?Every firm faces downward sloping demand have some power is setting price above MCEvery 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 lossP>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 goodsSimplest caseduopoly (i.e. only two sellers)Each aware of the existence of the other firmCompete instead of collude each firm has market power less than monopolistExamples?
237 Nash EquilibriumEach 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 simultaneouslyeach firm treats the output level of its competitor as fixed when deciding its own output
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 −0First order condition with respect to Q1 while taking Q2 as given:𝑑 𝜋 1 𝑑 𝑄 1 =30−2 𝑄 1 − 𝑄 2 =0Firm 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 −0First order condition with respect to Q2 while taking Q1 as given:𝑑 𝜋 2 𝑑 𝑄 2 =30− 𝑄 1 −2 𝑄 2 =0Firm 1’s reaction curve:𝑄 2 =15− 𝑄 1 /2
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 advantageDifference between Cournot and Stackelberg modelsThe 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 firmsFirm 1 chooses Q1 first, firm 2 chooses Q2 nextFirm 2’s best choice of Q2 given Q1 firm 2’s reaction curve 𝑄 2 =15− 𝑄 1 /2Firm 1 anticipates firm 2’s reaction curve𝜋 1 =𝑃∙ 𝑄 1 − 𝐶 1 =(30− 𝑄 1 - 𝑄 2 )∙ 𝑄 1 − 0=(30− 𝑄 𝑄 1 /2)∙ 𝑄 1First order condition: 15− 𝑄 1 =0𝑄 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 firmsAs long as the other firm charges above MC, this firm has incentive to undercutAt 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 TheoryNash 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 adoptPrisoner’s dilemmaConfessNot 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 unstableAny other example?
252 Pure strategy vs. Mixed strategy Example: Inspection game Mixed: randomize between strategiesExample: Inspection gameNo pure strategy equilibrium, the only equilibrium is 50% probability detect, 50% probability complyDetectNot DetectComply-5,-5-5,0Not comply-10, 50, 0Suppose probability of detect is Pd, probability of comply is PcGiven 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=0.5Given 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 SelectionProblemsolutionMoral HazardSolutionAdverse selection and Moral Hazard
254 Recall: Reasons for market failure Imperfect competitionMonopoly, monopsony, oligopoly,monopolistic competitionAsymmetric informationSituation in which a buyer and a seller possess different information about a transaction.Externality
255 The market for lemonsSuppose 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….)0.250.51
256 Adverse selectionCause: Products of different qualities are sold at a single price because sellers observe product quality but buyers do notConsequence: 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 warrantyBlanket return policyHyundai offers 10-year warrantySignalingworkers may signal their ability by educationReputationReputable restaurants (e.g. McDonald) have more to lose if they cheatThird party certificationUnraveling results
258 Moral hazard One party engage in hidden actions This action affects the probability or magnitude of a payment associated with an eventExample: principal-agent problem
259 Solutions to principal-agent problem Close monitoringIncentive contractTextbook example: revenue from making watchesCost of low effort=0, cost of high effort=10,000What kind of contract can solicit high effort?Bad Luck (50%)Good Luck (50%)Low effort (a=0)$10,000$20,000High 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=1000At high effort, expected wage is ( )*0.5+( )*0.5=12000The net gain to the worker with high effort = =2000>1000, so the worker will commit to high effortWhen the worker engages in high effort, the principal’s net gain = 20000* * =18000.
261 Adverse selection and moral hazard They are differentAdverse selection: info asymmetry before contractMoral hazard: info asymmetry after contractThey can co-existUnsecured consumer creditInsuranceEmployment
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 priceNegative externalityExamples?Positive externality
264 Inefficiency of negative externality MC: marginal cost facing the producerMSC: marginal social cost of production facing the whole societyMSC-MC=marginal external costExternality over production
265 Solution Restrict production in light of negative externality Emission standardHow can EPA know the optimal standard?Enforcement cost is highCharge emission feeTradeable emissions permits
266 Example: Chapter 18 Exercise #6 Demand for paper: Qd=160, PSupply for paper: Qs=40, PMarginal external cost of effluent dumpting: MEC=0.0006QsCalculate 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=100,000Under perfect competition, MC is the supply curve. Qs=40, P P=0.0005Qs -20= MCTo account for marginal external cost, MSC=MC+MEC=0.0006Qs Qs-20=0.0011Qs-20Rewrite the demand: P= QdAt 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 landscapingMB=Marginal benefits for the home ownerMarginal social benefits=MB+marginal external benefit for neighborsPositive externality under provision of public goods
268 Public goodsDefinition: the marginal cost of provision to an additional consumer is zero and people cannot be excluded from consuming itTwo properties:Nonrival: zero cost to additional consumersNonexclusive: cannot exclude people from using the public goodsExamples: national defense, light house, air quality, informationPrivate 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 problemProducer’s problemMarket equilibriumExtrasuncertainty, game theory, asymmetric information, externalityThe 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 problemHow does consumer choice change in response to changes in price or income?Derive individual demand and market demandCalculate demand elasticitySpecial cases: perfect substitutes and perfect complements
272 Producer’s problem Production function and related concepts Solve firm’s cost minimization problemHow does firm’s choice change in light of production change or input price change?Cost function and related conceptsDerive individual and market supply in perfect equilibrium