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Econ326 Intermediate Microeconomics Fall 2011 Instructor: Ginger Z. Jin http://kuafu.umd.edu/~ginger TA: Aaron Szott Lecture 1 Course introduction Syllabus Teaching style and expectations Textbook Chapter 1, 2.1-2.3 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. Class will cover: Consumer demand ◦ ◦ ◦ ◦ 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 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? Monthly rent supply equilibrium demand Units available Why is the demand downward sloping? Monthly rent supply equilibrium demand Units available When will we observe a fixed supply? 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 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? 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? Market scenario 4: rent control supply Monthly rent demand Keep the price down, but create excessive demand How to allocate the limited supply to excessive demand? lottery, ration, allow secondary market trade? Units available 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 Syllabus on my personal website http://kuafu.umd.edu/~ginger/ click on Econ326 Also available on elms.umd.edu 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. Syllabus ◦ Textbook: 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 Fixed grade definition (No curve, no rounding) F: D: D+ C-: C: C+: B-: B: B+: A-: A: A+: <40 [40,45) [45,50) [50,55) [55,60) [60,65) [65,70) [70,75) [75,80) [80,90) [90,100) [100,110]. Important dates Sept. 8: Sept. 22 Oct. 4 Oct. 11 Oct. 28 Nov. 8 Nov. 15 Dec. 8 ???? Handout problem set 1 Problem set 1 due Midterm 1 Handout problem set 2 Problem set 2 due Midterm 2 Handout problem set 3 Problem set 3 due Final exam There will be 5 in-class quizzes at unannounced dates. 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 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. Teaching Assistant: Aaron Szott Office: ◦ 0124F Cole Field House Office Hours ◦ Monday 2:15-3:15pm, Friday 2-3pm Office Phone ◦ 301-305-9259 Change of office hours for Sumedha 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 Expectation on You Attend the class ◦ 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 Lecture 2 Utility Theory Consumer preferences Constructing Indifference curves Properties of Indifference curves Textbook chapter 3.1-3.2 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 Axioms of preferences Completeness ◦ 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 Utility Definition of Utility ◦ Numerical score representing the satisfaction that a consumer gets from a given basket of goods. In what unit? ◦ ordinal versus cardinal 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) 0 0 1 5 5-0=5 2 9 9-5=4 3 12 12-9=3 4 14 14-12=2 5 15 15-14=1 One common property: Diminishing marginal utility Show MU in graph Total Utility U Units of apples (X) Exercise: compute MU, diminishing MU? U=5(X+1) U=5ln(X+1) U=X0.3 U=100-X2 U=X0.4Y0.6 Ordinal vs Cardinal Ordinal Utility ◦ 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 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: 1. monotonic transformation does not change the order of preference, 2. it may change the property of MU 3. It does NOT change the relative tradeoff between two goods (MUx vs MUy) How to graph utility of two goods U(X,Y) U(X,Y) Y Y 0 X 0 X 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 Axioms of preferences Completeness ◦ 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 Examples of indifference curves U(X,Y)=X * Y point X Y U 1 1 1 1 2 2 2 4 3 3 3 9 4 4 4 16 5 1 4 4 6 4 1 4 7 2 3 6 8 3 2 6 Y Typical convex preference Satisfy all four axioms of preference X Examples of indifference curves U(X,Y)=X + Y point X Y U 1 1 1 2 2 2 2 4 3 3 3 6 4 4 4 8 5 1 4 5 6 4 1 5 7 2 3 5 8 3 2 5 Y 5 7 3 4 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 Examples of indifference curves U(X,Y)=min(X, Y) point X Y U 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 1 4 1 6 4 1 1 7 2 3 2 8 3 2 2 Y X Perfect complements Violate “non-satiation” sometimes U is not always differentiable, MU is not well defined at the kinks 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 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) Marginal rate of substitution (MRS) Y A Slope = - MRS at point A X Diminishing MRS (MRS of X for Y diminishes with X) Y A lot of Y relative to X Not much Y rel to X X Consistent with diminishing marginal utility 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) 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? 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 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 Like apples and bananas bananas U apples Like apples up to a satiation level bananas U What happens if one likes both apple and banana up to a satiation level? apples Like apples but dislike bananas bananas U What if one dislikes both apples and bananas? apples Like apples but indifferent to bananas bananas U apples 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 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 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) Lecture 4: Budget constraints ◦ definition ◦ Shocks to consumer budget ◦ Kinked consumer budget Textbook Chapter 3.1 & 3.2 Budget constraints Definition: ◦ 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 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 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 What happens with income tax cut? Tax cut more income Y I/Py • Does the intercept on Y change? • Does the intercept on X change? • Does the slope of the budget line change? Slope = - Px / Py I/Px X What happens if gasoline price goes up? (assume gasoline is X) Px increases Y I/Py • Does the intercept on Y change? • Does the intercept on X change? • Does the slope of the budget line change? Slope = - Px / Py I/Px X 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%) Y (health care) 8000 Slope = -Px /Py = -2/0.2=-10 Slope = -Px /Py = -2 500 750 1000 X (food) 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 other 2000 2000 2200 food What happens if there is a black market to trade food stamps? Example 3: role of financial market #1: no financial market Y (tomorrow) 2*I I I 2*I X (today) Y (tomorrow) #2: a financial market allows saving and borrowing at interest rate r The opportunity cost of not saving today makes one feel as if today’s price is increased to (1+r). X (today) Y (tomorrow) Now we have a kink due to the asymmetric terms of borrowing and saving X (today) 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 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 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 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 Mathematical derivation 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 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 Lecture 5 Consumer’s optimal choice ◦ Inner solution, corner solution Cobb-Douglas utility Price and consumer choice Income and consumer choice Normal, inferior and giffen goods Textbook Chapter 4 appendix, 4.1-4.4 Typically: Inner solution Y I/Py At the optimal choice: MRS = Px/Py I=Px * X + Py * Y I/Px X What if the equal marginal principle cannot be satisfied? corner solution Y I/Py U Spend every penny: I=Px * X + Py * Y Check which corner gives higher utility I/Px X Example 1 of corner solution: perfect substitutes Y U 100 100 U=X+2Y Px=10 Py=10 Income=1000 X Example 2 of corner solution: perfect complements U Y U=min(X,2Y) Px=10 Py=10 Income=1000 100 100 X Demand Optimal choice ◦ X=f(Px, Py, Income) Properties: ◦ Homogenous degree of zero ◦ Typically depends on income, own price, price of other goods Special example: Cobb-Douglas Utility Two equations Solve for two unknowns (X and Y) 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 Graph consumer choice in response to: Price changes Income changes Two goods: food, clothing Price of food drops Two goods: food, clothing Income increases Note that incomeconsumption curve is not necessarily linear Normal goods ◦ 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? Hamburger is a normal good from A to B, but an inferior good from B to C Engel curve 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. Lecture 6 Decompose income and substitution effects in response to price change Slusky Equation Textbook chapter: 4.3-4.4 Handout #1: an example Food price falls Initial choice A new choice B Imaginary D: same utility as A, but face new price Slusky Equation Total effects Substitution effects Income effects What if X is an inferior good? income effect works against the substitution effect What if X is a Giffen good? income effect works against and more than cancels off the substitution effect Example 1: 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 10000 Y (health care) A: choice with no insurance C: choice with insurance Slope = -Px /Py = -2/0.2=-10 C A to B: substitution effect B to C: income effect B A Slope = -Px /Py = -2 1000 Scenario #1: insurers pay 80% of the cost of any medical service X (food) 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? Lectures 7-8 Application to labor supply Individual and market demand Demand elasticity and cross elasticity Textbook chapter: 4.3-4.4 Individual demand A consumer’s optimal choice of a good depends on ◦ The price of this good ◦ The price of other goods ◦ Income Example Two goods Income C (24w+y)/Pc C* L* 24 24+y/w L w 1 0.5 4.8 8 24 L Pc 1 0.5 19.2 42.7 C More generally: Market demand Q(P)= sum of individual demand Qi(P) Textbook example of market demand How to summarize market demand? Meaning of demand elasticity Classify demand by demand elasticity Market demand Q(P) P If you are the producer, why do you want to know demand elasticity? 50 Example: ◦ Q=100-2P 100 ◦ What is demand elasticity at p=10,20,30? ◦ At what price is the demand isoelastic? Q Special cases P Completely inelastic demand Infinitely elastic demand Q Other elasticities Example 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 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 Total Consumer Surplus = ½ *(20-14)*6500=19,500 Textbook example of market demand Calculate the demand elasticity of total demand and total consumer surplus at p=18. To summarize Consumer preference (utility function) Budget Constraint optimal choice X=X(Px, Py, I) Income-consumption curve, priceconsumption curve, engel curve, demand curve Income and substitution effects Sum of Individual demand=market demand Demand elasticity, income elasticity, cross elasticity Consumer surplus Lecture 11 Risk and Consumer behavior Describe risk Preferences towards risk Demand for risky assets 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 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 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 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 Job1 is riskier 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)) 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 Risk averse (EU(X)?, U(E(X))?) Risk neutral (EU(X)?, U(E(X))?) Risk loving (EU(X)?, U(E(X))?) Risk premium: maximum amount of money that a risk averse person will pay to avoid taking the risk 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? How to reduce risk? Diversification ◦ 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 Choosing between risk and return Risk free asset: Rf Asset with market risk: Rm, m ( Rm – Rf ) Portfolio p: Rp= Rf +-------------- * p m Choice of a risk averse person Exercise: Chapter 5, Question 7 Suppose two investments have the same three payoffs, but the probability of each payoff differs: payoff Prob (investment A) Prob (investment B) $300 0.10 0.30 $250 0.80 0.40 $200 0.10 0.30 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? Lectures 12, 13 Technology of production ◦ ◦ ◦ ◦ 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 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. Single-input production q=F(L) Average product: q /L Marginal product: dq /dL L q 0 1 2 3 4 5 0 10 30 60 80 95 Avg product q/L Marginal product dq/dL Graphically: 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? ∙ − () − = =− = 2 If MP>AP, AP increases with L If MP<AP, AP decreases with L AP=MP at the maximum of AP 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 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 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 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) Diminishing MRTS Special case #1: K and L are perfect substitutes if production function is linear, MRTS is always a constant 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)) 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: = ∙ ∙ : technological factor + : return to scale 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 Constant return to scale Increasing return to scale Can you think of any real-world examples that have constant, increasing or decreasing returns to scale? Cobb-Douglas production Why does + represent returns to scale? = ∙ ∙ Suppose K increases to xK, L increases to xL Let q’ denote the new production by xK and xL ′ = ∙ ∙ = + ∙ ∙ = + ∙ If + < 1, decreasing returns to scale If + = 1, constant returns to scale If + > 1, increasing returns to scale 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 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 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? Fixed vs. Variable Cost w = wage rate r = capital rental cost In the long run when every input is variable = ∗ + ∗ () In the short run, if K is fixed at , =∗ +∗ Variable cost fixed cost How to determine cost with only one variable input? = , = −1 (, ) =∗+∗ = ∗ −1 , + ∗ Example: = ∙ 0.5 =∗+∗ =∗ 2 +∗ More generally Total production function Total cost function 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 How to determine cost with two variable inputs? Choose L and K in order to minimize = ∗ + ∗ Subject to = , Define Lagrangian function = + − − , First order conditions =+ =0 =+ =0 = − (, ) = 0 − = = = − Graphically: Isoquant curve at q Isocost curves Special case 1: when K and L are perfect substitutes, we may get corner solutions If > , capital is cheaper, hire all capital and zero labor If < , labor is cheaper, hire all labor and zero capital 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 Follow the previous example = ∙ 0.5 In the short run when K = , we find 2 =∗+∗ =∗ +∗ In the long run when both L and K are variable: =∗ 2 3 +∗2 1 2 3 Long run AC and MC Inflexibility of short run Short run and long run costs 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? 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 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)? Individual firms vs. the industry Demand curve faced by a competitive firm (perfectly elastic) Demand curve faced by the industry Profit-maximizing firms We assume a for-profit firm aims to maximize profit Total profit = total revenue – total cost = − The firm chooses q to maximize total profit Graphic illustration of profit maximization Algebraically: Choose q in order to maximize = − () First order condition: () = − = − = 0 At the optimal choice of q, MR=MC For a competitive firm, price-taking implies: = ∙ = At the optimal choice of q = =⇒ = About fixed cost = () − 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. Graphic example 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? Short run supply curve of a competitive firm How will the supply curve change in the long run? Industry supply curve in the short run 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 = − =0 = − = − Producer surplus for a firm Producer surplus for the industry in the short run 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 Long run competitive equilibrium for the industry – three conditions 1. All firms are maximizing profit. 2. 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 3. The price of the product is such that the quantity supplied by the industry is equal to the quantity demanded by consumers. Continue the previous example for the whole industry start with p=40 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 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 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 Price elasticity of supply / = / • In a constant cost industry, is infinitely large. • In an increasing cost industry, is positive and finite, with magnitude depending on the extent to which input costs increase as the market expands. Exercise Suppose that a competitive firm has a total cost function = 450 + 15 + 22 . 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 . Lecture 18 Competitive market equilibrium Demand equal to supply Consumer surplus Producer surplus Dead weight loss Consequence of price regulations Competitive market equilibrium Every consumer is a price-taker and a utility-maximizer Every firm is a price-taker and a profitmaximizer Free entry and exit Demand equal to supply Consumer surplus and producer surplus Consumer surplus = sum of (consumer willingness to pay – price paid) over all units sold = 0 − Producer surplus = sum of (market price – marginal cost) over all units sold = 0 − Price control #1: impose a maximum price that is below the market clearing price 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. 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? 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 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 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? 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? What about we impose a lump sum tax on gasoline? Changes in CS? Changes in PS? Gov revenue? Impact of tax depend on demand and supply elasticity Lecture 19 Exchange economy Edgeworth box Determination of trade price and trade amount Contract curve Textbook: Chapter 16 Edgeworth box 2 individuals No production, exchange only Every one is price taker Contract curve 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. Competitive equilibrium 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? Lecture 20 First welfare theorem Reasons for market failure Monopoly: Marginal revenue = MC Monoposony: Marginal expenditure = MC 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. 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 Monopoly Keep market demand as given A single seller (or a group of colluding sellers) Maximize profit by choosing output = ∙ − () Total revenue Total cost • First order condition: = + ′ ∙ = Marginal revenue < price restrict supply Monopoly choice competitive choice MC The Principle of Monopoly pricing = 1+ + ∙ = 1+ = 1 1 + ∙ = = Rewrite it, we get − 1 =− Mark up Inverse of demand elasticity 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. 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? Exercise: Drug innovation needs FC=5 billion Demand per month P=100-0.0001Q Marginal cost =$2 If we grant X years of monopoly power for the inventor, what should X be? 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? 1. The seller has some market power (i.e. facing downward demand) 2. Sellers can distinguish different types of consumers 3. No arbitrage 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? Third degree of price discrimination Two types of demand: 1 = 1 1 2 = 2 2 Monopolist’s profit: = 1 1 + 2 2 − 1 + 2 Profit maximization leads to: 1 = 2 = Third degree of price discrimination Profit maximization leads to: 1 = 2 = Which type of consumers get charged more? Who benefits from price discrimination? Who loses? 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: = 60 − 0.25 = 100 − 0.50 Cost of production: = 100 + 40 ℎ = + Price and quantity with price discrimination? What if the firm must charge the same price for NY and LA? Recap on competitive equilibrium and monopoly Competitive equilibrium: ◦ 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) 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) Mathematically Monopsony tries to maximize = − = sum of WTP for each unit − p ∙ First order condition: = Willingness to pay for the marginal unit of q = inverse demand p(q) [ ∙ ] [() ∙ ] = () = + ∙ > if MC is upward sloping inverse demand p(q) = + () ∙ Graphically -> marginal expenditure >MC -> supply curve MC -> demand curve Compare monopsony with monopoly Monopoly pushes price to demand curve Monopsony pushes price to supply curve Monopoly is more powerful if demand is inelastic Monopsony is more powerful if supply is inelastic Monopsony leads to dead weight loss 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=500-0.1Q 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 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 Monopolistic competition large number of small firms freedom of entry and exit perfect info Differentiated products What does this imply? 1. Every firm faces downward sloping demand have some power is setting price above MC 2. Every firm earns zero economic profit Monopolistic competition in shortrun and long-run Short run Long run 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 Oligopoly a market structure in which ◦ 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? 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 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 Solve Cournot equilibrium Reaction curves: 1 = 1 2 , 2 = 2 1 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 Cournot: firm 1’s point of view 1 = ∙ 1 − 1 = (30 − 1 - 2 ) ∙ 1 − 0 First order condition with respect to Q1 while taking Q2 as given: 1 = 30 − 21 − 2 = 0 1 Firm 1’s reaction curve: 1 = 15 − 2 /2 Cournot: firm 2’s point of view 2 = ∙ 2 − 2 = (30 − 1 - 2 ) ∙ 2 − 0 First order condition with respect to Q2 while taking Q1 as given: 2 = 30 − 1 − 22 = 0 2 Firm 1’s reaction curve: 2 = 15 − 1 /2 Put the two together: 1 = 15 − 2 /2 2 = 15 − 1 /2 1 = 2 = 10 = 30 − = 30 − 10 + 10 = 10 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. Compare to perfect competition P=MC 30-Q=0 Q=30, P=0. Graphically 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 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 2 = 15 − 1 /2 Firm 1 anticipates firm 2’s reaction curve 1 = ∙ 1 − 1 = (30 − 1 - 2 ) ∙ 1 − 0 = (30 − 1 -15 + 1 /2) ∙ 1 First order condition: 15 − 1 =0 1 = 15, 2 = 7.5, = 7.5. 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 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 Confess -10, -10 -5, -15 Not confess -15, -5 -6, -6 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? Pure strategy vs. Mixed strategy ◦ Mixed: randomize between strategies Example: Inspection game Detect Not Detect Comply -5,-5 -5,0 Not comply -10, 5 0, 0 No pure strategy equilibrium, the only equilibrium is 50% probability detect, 50% probability comply Lecture 25 Asymmetric Information Adverse Selection ◦ Problem ◦ solution Moral Hazard ◦ Problem ◦ Solution Adverse selection and Moral Hazard 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 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 0.25 0.5 1 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? 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 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 Solutions to principal-agent problem Close monitoring Incentive contract ◦ Textbook example: revenue from making watches Bad Luck (50%) Good Luck (50%) Low effort (a=0) $10,000 $20,000 High effort (a=1) $20,000 $40,000 ◦ Cost of low effort=0, cost of high effort=10,000 ◦ What kind of contract can solicit high effort? 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+(2000018000)*0.5=1000 At high effort, expected wage is (2000018000)*0.5+(40000-18000)*0.5=12000 The net gain to the worker with high effort = 1200010000=2000>1000, so the worker will commit to high effort When the worker engages in high effort, the principal’s net gain = 20000*0.5+40000*0.512000=18000. 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 Lecture 26: Externality Definition Negative externality Positive externality Solutions Externality Definition: ◦ 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 ◦ Examples? 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 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 Example: Chapter 18 Exercise #6 Demand for paper: Qd=160,000-2000P Supply for paper: Qs=40,000+2000P 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. 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 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 A comprehensive example Stephen J. Dubner and Steven D. Levitt’s blog on 4/20/2008 titled “Not so-free ride” http://www.nytimes.com/2008/04/20/maga zine/20wwln-freakonomicst.html?pagewanted=1 Course overview Three main blocks ◦ 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 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 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 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 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 Course evaluation please CourseEvalUM.umd.edu OPEN in the last two weeks of the semester Thank you!