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MICROECONOMICS(3 credits, as of 2002)Claroom Lecture Notes(As a minimum)By Wang Zeke Lnswzk@zsu.edu.cn

Based on Intermediate Microeconomics, by Hal R.Varian, Fifth Edition,referring to Price Theory and Applications, by Jack Hirshleifer and Amihai Glazer, Fourth Edition.You¡¯d better to think it as the First step of academic training in Economics Tips: Eential contents are mainly at or near figures Pay attention to graphically problem-solving We will focus on short-run study, and leave you discrete cases

Chapter 0 Economics

The source of all economic problems is scarcity.Thus problems of trade-off, and choice.Economics, as a way of thinking, as a dismal science.Problems-solutions-hidden consequences.Main decision-making agents: individuals(household), firms, and governments.Objects of economic choice are basically commodities, including goods and services.Main economic activities: consumption, production, and exchange.Microeconomics and macroeconomics: to show the invisible hand and to supplement it.The circular flow of economic activities.The product market and the factor market.The market relation is mutual and voluntary.Positive iues and normative iues.Marginal analysis.Relations between total, average, and marginal magnitudes: MM is the slope of the TM curve;AM is the slope of the ray from the origin to the point at the TM curve.Thus, 1, TM increasing(decreasing)if and only if MM > 0(MM AM(MM

Chapter 1 The Market

The optimization principle: People try to choose what¡¯s best for them.The equilibrium principle: Prices adjust until demand and supply are equal.The demand curve: a curve that relates the quantity demanded to price.The reservation price: one¡¯s maximum willingne to pay for something.From people's reservation prices to the demand curve by horizontal summation.Similarly, the supply curve.Their intersection is the market equilibrium.(A competitive market)Comparative statics is the study of how the equilibrium price and quantity change when the underlying conditions changes.The ceteris paribus principle.Pareto efficiency: a concept to evaluate different ways of allocating resources.A Pareto improvement is a change to make some people better off without hurting anybody else.An economic situation is Pareto efficient or Pareto optimal if there is already no way to make Pareto improvement.Equilibria in the short run(some factors are unchanged)and in the long run.Chapter 2 Budget Constraint

Two goods are often enough to discu.The budget constraint: p1 x1 + p2 x2 ¡Ü m.The budget line and the budget set(the market opportunity set).Fig.The slope of the budget line: dx2 / dx1 = ¨C p1 / p2.How the budget line changes when income increases, or when a price increases.Figs.Rationing.It¡¯s effects on the budget set.Fig.Chapter 3 Preferences

Consider rational agents and their stable preferences.Bundle x is strictly preferred(s.p.), or weakly preferred(w.p.), or indifferent(ind.), to Bundle y.(If x is w.p.to y and y is w.p.to x, we say x is indifferent to y.)Aumptions about Preferences: Completene: x is w.p.to y or y is w.p.to x for any pair of x and y.Reflexivity: x is w.p.to x for any bundle x.Transitivity: If x is w.p.to y and y is w.p.to z, then x is w.p.to z.The indifference sets, the indifference curves.Fig.They cannot cro each other.Perfect substitutes and perfect complements.Goods, bads, neutrals.Satiation.Figs.Well-behaved preferences are monotonic(meaning more is better)and convex(meaning average are preferred to extremes).Figs.The marginal rate of substitution(MRS)measures the slope of the indifference curve.MRS = dx2 / dx1.It is the marginal willingne to pay(how much to give up of x2 to acquire one more of x1).Usually negative.Fig.Convex indifference curves exhibit a diminishing marginal rate of substitution.Fig.Chapter 4 Utility, as a way to describe preferences

Eential ordinal utilities, versus convenient cardinal utility functions: u(x)¡Ý u(y)if and only if bundle x is w.p.to bundle y.Fig.The indifference curves are the projections of contours of the u = u(x1, x2).Fig.Utility functions are indifferent up to any strictly increasing transformation.Examples of utility functions: u(x1, x2)= x1 x2;u(x1, x2)= x12 x22;Fig.u(x1, x2)= ax1 + bx2(perfect substitutes);Fig.u(x1, x2)= min{ax1, bx2}(perfect complements).Fig.Quasilinear preferences: all indifference curves are vertically(or horizontally)shifted copies of a single one, for example u(x1, x2)= v(x1)+ x2.Fig.Cobb-Douglas preferences: u(x1, x2)= x1c x2d , or u(x1, x2)= x1ax21-a with a = c /(c+d);and their log equivalents: u(x1, x2)= c ln x1 + d ln x2 , or u(x1, x2)= a ln x1 +(1¨C a)ln x2.Fig.Marginal utilities, and MRS along an indifference curve.Derive MRS = ¨C MU1 / MU2 by taking total differential along any indifference curve.Chapter 5 Choice of Consumption

Optimal choice is at the point in the budget line with highest utility.The tangency solution of an indifference curve and the budget line: MRS = ¨C p1 / p2.Fig.Basic equations: MU1 / p1 = MU2 / p2 and p1 x1 + p2 x2 = m.(how if negative solutions)Interior and boundary(corner)solutions.Kinky tastes.Multiple tangencies.Figs.Three approaches to the basic equations: Graphical(Tangency);As-one-variable;and *Lagrangian.The optimal choice is the consumer¡¯s demanded bundle.The demand function.Examples: perfect substitutes, perfect complements, goods, bads, and neutrals,convex and concave preferences, Codd-Douglas demand functions.Figs.Chapter 6 Demand

Demand functions: x1 = x1(p1, p2, m), x2 = x2(p1, p2, m).Inferior and ultra-superior goods(by income);Fig.Luxury and neceary goods(by income).Fig.Normal and Giffen goods(by price).Fig.The income expansion path or the income offer curves(x1x2 plane)and the demand curve(p1 ¨C x1 plane).Figs.Substitutes and complements.Codd-Douglas preferences.Quasilinear preferences.Example: Quasilinear preferences lead to vertical(horizontal)income offer curves and vertical(horizontal)Engel curves.Chapter 8 Slutsky Equation

How the optimum moves when the price of a good changes? Decomposition: the total effect = the substitution effect + the income effect.The pivot gives the substitution effect, the shift gives the income effect.Slutsky decomposition, pivoting the budget line around the original choice.Fig.Hicks decomposition, pivoting the budget line around the indifference curve.Fig.The law of demand.Choosing taxes.(Fig.5.9)

Chapter 9 Buying and Selling for a consumer with an endowment ¦Ø

Offer curve and demand curve.A figure review.Labor supply.A graphical discuion.Chapter 12 Uncertainty

Utility functions and probabilities.Expected utility functions, or von Neumann-Morgenstern utility functions: EU = ¦²i piU(si), where pi is the probability the event si occurs.They are indifferent up to any positive affine transformation.Risk aversion and risk loving.Concave vs convex utility.The second derivative.Chapter 14 Consumer¡¯s Surplus

Demand for a discrete good.Reservation prices and consumer¡¯s surplus.Fig.Producer¡¯s surplus.Fig.Calculating gains and loes.The water-diamond paradox.Chapter 15 Market Demand

Adding up demand curves: the horizontal summation principle.Fig.The price elasticity of demand: ¡¡¡¡¡¡¡¡¦Å=(¦¤q / q)/(¦¤p / p)=(p / q)/(¦¤p /¦¤q), or ¡¡¡¡¡¡¡¡¦Å=(dq / q)/(dp / p)=(p / q)/(dp /dq).It is normally negative.So, very often people turn to consider its absolute value |¦Å|.A commodity has an elastic(inelastic, unit)demand if |¦Å| > 1(|¦Å|

Chapter 16 Partial Equilibrium The market supply curve.A competitive market.The equilibrium.Pareto efficiency.Fig.Market surplus and market shortage.Fig.Shortage is not scarcity.Two special cases: of a vertical supply and of a horizontal supply.Figs.Algebra of the equilibrium: D(p)= S(p).Comparative statics.Shifting both curves.Taxes.Distinguish Pp , the price paid by consumers, Pr , the price received by producers, Pl , the list price, and Po , the original price.The two ways to analyze the effect of a tax(imposed on demand or imposed on supply)are equivalent.Algebra of the equilibrium with a tax: D(pp)= S(pr), and pp = pr + T.Who bears the burden of a tax? The one with le elasticity shares more burden.Paing along a tax.The deadweight lo of a tax.Figs.A subsidy is the opposite of a tax.Chapter 18 Technology

These four chapters focus mainly on resource allocation insider firms.Inputs and outputs.Factors of production: land, labor, capital, raw materials, and so on.Financial capital and physical capital.Technological constraints.A production set: X = input(s), Y = output.Example of one-input-one-output case: production function.Fig.Examples of technology in two-inputs-one-output case(isoquants analysis): fixed proportions, perfect substitutes, Cobb-Douglas.Figs.Aumptions of technology: monotonic(free disposal), convex.Fig.The marginal product, The technical rate of substitution(TRS): with dy = 0, TRS(x1, x2)= dx2 / dx1 = ¨C MP1(x1, x2)/ MP2(x1, x2).Diminishing MP.Diminishing TRS.The long run(LR)and the short run(SR).Returns to scale: increasing, decreasing, and constant.Chapter 19 Profit Maximization

The organization of firms.Proprietorships, partnerships, or corporations.Profits and stock market value.Fixed and variable factors.SR profit maximization: ¦Ð= pyw2x2, y = ¦Ð/ p + w2x2 / p + w1x1 / p describes isoprofit lines, max x1¦Ð gives pMP1 = w1.Fig.Cobb-Douglas case.Optimum lies on the tangency of an isoprofit line and the production function.Fig.Comparative statics: Increasing p increases x1 and then y.Increasing w1 reduces x1, and thus the factor demand curve follows.Figs.y

y w1 Low p High p High w1 Low w1

x1 x1 x1

LR: both x1 and x2 are variable.Profit maximization and(constant)returns to scale.Exercise: Max xi¦Ð based on production function y = f(x1, x2)to derive factor demand xi = xi(p, w1, w2), and then the firm supply function y = g(p, w1, w2).Chapter 20 Cost Minimization

Basic model: min x1, x2 w1 x1 + w2 x2 subject to f(x1 , x2)= y gives c(w1 , w2 , y).Isocost lines: x2 = C/w2 ¨C w1x1/w2.Tangency of an isocost line and an isoquant.¨C MP1(x1, x2)/ MP2(x1, x2)= TRS(x1, x2)= ¨C w 1 / w 2 or Fig.Minimizing costs for y = min{ax1 , bx2};y = ax1 + bx2;and y = x1a x2b.Returns to scale and the cost function.Fixed and variable costs.Total, average, and marginal costs.FC, VC;TC, AC, MC, and AVC.MC > AC(

Chapter 21 Cost Curves

A misleading formula: AVC(1)= MC(1).Should be MC(0)= AVC(0).The area under MC gives VC: ¡ÒMC = VC.Division Fig.of

output

among

plants

of

a MP1(x1, x2)/ w 1 = MP2(x1, x2)/ w 2.firm.Typical cost curves.Example: c(y)= y 2 + 1.LR and SR cost curves.Chapter 22 Supply of a competitive firm

These six chapters focus on the profit-maximizing output decision of firms.The technology description and the cost-minimization are already done with only cost functions left.With¦Ð(y)= R(y)¨C C(y), we have the following Basic Equation for firm supply decision: MC = MR.It¡¯s in fact FOC.SOC is(MC)¡¯ =(MR)¡¯.Pure competition.Firm as a Price Taker.Thus R = py, and then MR = p.The supply decision.FOC: MC(y*)= p.SOC: MC ¡¯(y*)¡Ý 0.The demand curve facing a competitive firm.Fig.The firm¡¯s supply curve is the upward-sloping part of MC that lies above the AVC curve.The part of MC is also seen as the inverse supply function.Fig.Three equivalent ways to measure the producer¡¯s surplus(= R ¨C VC =¦Ð + FC).Example: c(y)= y 2 + 1.LR: p = MC(y, k(y))vs SR: p = MC(y, k).Chapter 23 Industry Supply

Horizontal summation gives the industry supply.Entry and exit.The ¡°zero profit¡± theorem.Free entry vs barriers to entry.Chapter 24 Monopoly

The market demand curve facing a monopolist coincides with its AR curve.Fig.The marginal revenue curve MR.AR and MR.Fig.With MR = dR / dy = p(y)[ 1 + 1 /¦Å(y)], from the basic equation MR = MC we have p(y)= MC(y)/ [1 ¨C 1 / |¦Å(y)| ].The market price is a markup over marginal cost, and 1 / [1 ¨C 1 / |¦Å(y)| ] is called the markup.Two equivalent ways to determine the equilibrium: MC = MR, or AR = MC /(1¨C |¦Å|).Figs.FOC: MC = MR.SOC: MC¡¯ ¡Ý MR¡¯.The impact of taxes on a monopoly.Inefficiency of monopoly.Deadweight lo of monopoly.Natural monopoly.Figs.What causes monopolies: by nature or by permiion.The minimum efficient scale factor.Regulation of monopoly: AC = AR.Chapter 25 Monopoly Behavior

Price discriminations of first-degree(perfect), of second-degree(bulk discounts), and Price discrimination of third-degree(market segmentation, Figs.): MC(y1+y2)= mr1(y1)= mr2(y2)gives p1 [ 1 ¨C 1 / |¦Å1(y1)| ] = p2 [ 1 ¨C 1 / |¦Å2(y2)| ].Graphical analysis and Equation solutions.Chapter 27 Oligopoly, mainly Duopoly

Quantity or price competitions.Identical products: p = p(Y), Y = y1 + y2.Sequential games.Backward solution.Quantity leadership: Stackelberg model.max y2 p(y1+ y2)y2 ¨C c2(y2), or MR2 = p(y1+y2)+ y2 dp / dy2 = MC2 gives the follower¡¯s reaction function y2 = f 2(y1);then max y1 p(y1+ f2(y1))y1 ¨C c1(y1)determines y1.Example: p(y1 + y2)= a ¨C b(y1 + y2), c = 0.Figures 26.1 and 26.2.Price leadership: The leader sets p first, then max y2 py2 ¨C c2(y2)gives S2(p).Now, the leader goes as a monopolist facing the residual demand R(p)= D(p)x2 plane), and the Engel curve(m ¨C x1 plane).Figs.The price offer curve(x1x1(p1, m)= [x1(p1¡¯, m¡¯)x1(p1¡¯, m¡¯)].* The Slutsky equation: x1s(p1, p2 , x1*, x2 *)¡Ô x1(p1, p 2 , p1x1*+ p2x2*), thus x1(p1, p2 , m*)/ p1 = x1s(p1, p2 , x1*, x2*)/ p1x1)¦¤x1m / ¦¤m.Labor supply.A graphical discuion.Chapter 10 Intertemporal Choice

Suppose for example in a 3-period model, the consumption is ck and the interest rate is rk in period k, then the present value of the consumptions is c1 + c2 /(1+r1)+ c3 /(1+r1)(1+r2).The responses to an interest rate increasing of a lender and a borrower.Chapter 11 Aet Markets

Aets are goods that provide a flow of services over time.Aets that provide a monetary flow are called financial aets.The no arbitrage condition: in equilibrium, there should be no opportunities to realize a sure return by buying some of one aet and selling some of another.Aets with consumption returns: The housing example.Taxation of aet returns.The dividend(interest)return vs capital gains.Municipal bonds.Financial institutions.Chapter 12 Uncertainty

A contingent consumption plan: a specification of what will be consumed in each different(future)state of nature.Utility functions and probabilities.Expected utility functions, or von Neumann-Morgenstern utility functions: EU = ¦²i piU(si), where pi is the probability the event si occurs.They are indifferent up to any positive affine transformation.Risk aversion and risk loving.Concave vs convex utility.The second derivative.Diversification.Risk spreading.The stock market.Chapter 13 Risky Aets

Mean-variance utility: if a random variable w takes values ws for s = 1,¡-, S with probability ¦Ðs , then the mean of the probability distribution is ¦Ìw = ¦²¦Ðs ws , and the variance is ¦Òw2 = ¦²¦Ðs(ws ¨C¦Ìw)2 while its square root ¦Òw is the standard deviation.The aociated utility is then u(¦Ìw , ¦Òw2)or u(¦Ìw , ¦Òw).A simple portfolio problem: if 1-x :==>(r f), and x :==>(m s , p s;r m , s m), then we have r x = ¦²s(x m s +(1-x)r f)¦Ðs = x ¦²s m s ¦Ðs +(1-x)r f ¦²s¦Ðs = x r m +(1-x)r f and ¦Òx2 = x 2 ¦Òm 2.Thus, between risk and return, MRS =(r mr f), and thus r i = r f + b i(r mr f)as the market line(to ranking mutual funds).Chapter 14 Consumer¡¯s Surplus

Demand for a discrete good.Reservation prices and consumer¡¯s surplus.Fig.Producer¡¯s surplus.Fig.Calculating gains and loes.The water-diamond paradox.Compensating and Equivalent Variations(coinciding if quasilinear utilities).Chapter 15 Market Demand

One can think of the market demand as the demand of some ¡°representative consumer¡±.Adding up demand curves: the horizontal summation principle.Fig.The price elasticity of demand: ¡¡¡¡¡¡¡¡¦Å=(¦¤q / q)/(¦¤p / p)=(p / q)/(¦¤p /¦¤q), or

¡¡¡¡¡¡¡¡¦Å=(dq / q)/(dp / p)=(p / q)/(dp /dq).It is normally negative.So, very often people turn to consider its absolute value |¦Å|.A commodity has an elastic(inelastic, unit)demand if |¦Å| > 1(|¦Å|

Chapter 17 Auction

A topic in Economics of Information.Private-value auctions and common-value auctions.Four types of auctions according to bidding rules:(Progreive)English auction, and its minimal bid increment(Degreive)Dutch auction First price sealed bid auction FPSB auction Second price sealed bid auction SPSB auction, or Vickrey auction Auction Design: Pareto efficiency and Profit maximization.English auction and Vickrey auction are truth-telling.Winner¡¯s Curse.Seller¡¯s Curse.Reservation price.Collusion.Chapter 18 Technology

These four chapters focus mainly on resource allocation insider firms.Inputs and outputs.Factors of production: land, labor, capital, raw materials, and so on.Financial capital and physical capital.Technological constraints.A production set: X = input(s), Y = output.Example of one-input-one-output case: production function.Fig.Examples of technology in two-inputs-one-output case(isoquants analysis): fixed proportions, perfect substitutes, Cobb-Douglas.Figs.Aumptions of technology: monotonic(free disposal), convex.Fig.The marginal product, The technical rate of substitution(TRS): with dy = 0,TRS(x1, x2)= dx2 / dx1 = ¨C MP1(x1, x2)/ MP2(x1, x2).Diminishing MP.Diminishing TRS.The long run(LR)and the short run(SR).Returns to scale: increasing, decreasing, and constant.Chapter 19 Profit Maximization

The organization of firms.Proprietorships, partnerships, or corporations.Profits and stock market value.Fixed and variable factors.SR profit maximization: ¦Ð= pyw2x2, y = ¦Ð/ p + w2x2 / p + w1x1 / p describes isoprofit lines, max x1¦Ð gives pMP1 = w1.case.Optimum lies on the tangency of an isoprofit line and the production function.Fig.Comparative statics: Increasing p increases x1 and then y.Increasing w1 reduces x1, and thus the factor demand curve follows.Figs.Fig.Cobb-Douglas

y

y w1 Low p High p High w1 Low w1

x1 x1 x1

LR: both x1 and x2 are variable.Profit maximization and(constant)returns to scale.* Revealed profitability.Weak axiom of profit maximization WAPM gives ¦¤p¦¤y ¨C¦¤w 1¦¤x 1 ¨C¦¤w 2¦¤x 2 ¡Ý 0.Exercise: Max xi¦Ð based on production function y = f(x1, x2)to derive factor demand xi = xi(p, w1, w2), and then the firm supply function y = g(p, w1, w2).Chapter 20 Cost Minimization

Basic model: min x1, x2 w1 x1 + w2 x2 subject to f(x1 , x2)= y gives c(w1 , w2 , y).Isocost lines: x2 = C/w2 ¨C w1x1/w2.Tangency of an isocost line and an isoquant.¨C MP1(x1, x2)/ MP2(x1, x2)= TRS(x1, x2)= ¨C w 1 / w 2 or MP1(x1, x2)/ w 1 = MP2(x1, x2)/ w 2.Fig.Minimizing costs for y = min{ax1 , bx2};y = ax1 + bx2;and y = x1a x2b.* Revealed cost minimization.Weak axiom of cost minimization WACM.¦¤w 1¦¤x 1 +¦¤w 2¦¤x 2 ¡Ü 0.Returns to scale and the cost function.Fixed and variable costs.Total, average, and marginal costs.FC, VC;TC, AC, MC, and AVC.MC > AC(

Chapter 21 Cost Curves

A misleading formula: AVC(1)= MC(1).Should be MC(0)= AVC(0).The area under MC gives VC: ¡ÒMC = VC.Division Fig.of

output

among

plants

of

a

firm.Form MC based on mc1 and mc2 by horizontal summation.Typical cost curves.Example: c(y)= y 2 + 1.LR and SR cost curves.Chapter 22 Supply of a competitive firm

These six chapters focus on the profit-maximizing output decision of firms.The technology description and the cost-minimization are already done with only cost functions left.With¦Ð(y)= R(y)¨C C(y), we have the following Basic Equation for firm supply decision: MC = MR.It¡¯s in fact FOC.SOC is(MC)¡¯ =(MR)¡¯.Pure competition.Firm as a Price Taker.Thus R = py, and then MR = p.The supply decision.FOC: MC(y*)= p.SOC: MC ¡¯(y*)¡Ý 0.The demand curve facing a competitive firm.Fig.The firm¡¯s supply curve is the upward-sloping part of MC that lies above the AVC curve.The part of MC is also seen as the inverse supply function.Fig.Three equivalent ways to measure the producer¡¯s surplus(= R ¨C VC =¦Ð + FC).Example: c(y)= y 2 + 1.LR: p = MC(y, k(y))vs SR: p = MC(y, k).LR supply curve is the part of LMC above LAC

Chapter 23 Industry Supply

Horizontal summation gives the industry supply.Entry and exit.The ¡°zero profit¡± theorem.Free entry vs barriers to entry.Industry equilibrium with free entry, and the LR industry supply curves with free entry.Taxation in SR and in LR.Fixed factors and economic rent.Rent seeking.Energy policy: Two-tiered oil pricing;Price control;The entitlement program.Economists versus lobbyists.Chapter 24 Monopoly

The market demand curve facing a monopolist coincides with its AR curve.Fig.The marginal revenue curve MR.AR and MR.Fig.With MR = dR / dy = p(y)[ 1 + 1 /¦Å(y)], from the basic equation MR = MC we have p(y)= MC(y)/ [1 ¨C 1 / |¦Å(y)| ].The market price is a markup over marginal cost, and 1 / [1 ¨C 1 / |¦Å(y)| ] is called the markup.Two equivalent ways to determine the equilibrium: MC = MR, or AR = MC /(1¨C |¦Å|).Figs.FOC: MC = MR.SOC: MC¡¯ ¡Ý MR¡¯.The impact of taxes on a monopoly.Inefficiency of monopoly.Deadweight lo of monopoly.Natural monopoly.Figs.What causes monopolies: by nature or by permiion.The minimum efficient scale factor.Regulation of monopoly: AC = AR.Chapter 25 Monopoly Behavior

Price discriminations of first-degree(perfect), of second-degree(bulk discounts), and Price discrimination of third-degree(market segmentation, Figs.): MC(y1+y2)= mr1(y1)= mr2(y2)gives p1 [ 1 ¨C 1 / |¦Å1(y1)| ] = p2 [ 1 ¨C 1 / |¦Å2(y2)| ].Graphical analysis and Equation solutions.* Monopolistic competition from product differentiation.Most prevalent but most difficult to analyze.A location model of product differentiation.Cartels.Chapter 26 Factor Markets

Let MRP x be the marginal revenue product, and pMP x the value of the marginal product.R(x)= p(f(x))f(x)leads to MRP x = MRy¡ÁMPx = p(y)[1 ¨C 1 / |¦Å(y)| ] MPx.For monopolist, MRP x£¼ pMP x.Thus instead of pMP = w, its factor demand is MRP = w.If a firm is a competitor in its output market and a monopsolist in its factor market with the inverse factor supply w(x), then maximizing pf(x)¨C w(x)x gives pf ¡¯(x)= MCx = w(x)+ w ¡¯(x)x = w(x)[ 1 + 1 / ¦Ç].Thus employ le of the factor.The minimum wage in a competitive and in a monopsonized labor market.An integrated monopolist will always produce more than an upstream-downstream pair of monopolists, due to double markup.Chapter 27 Oligopoly, mainly Duopoly

Quantity or price competitions.Identical products: p = p(Y), Y = y1 + y2.Sequential games.Backward solution.Quantity leadership: Stackelberg model.max y2 p(y1+ y2)y2 ¨C c2(y2), or MR2 = p(y1+y2)+ y2 dp / dy2 = MC2 gives the follower¡¯s reaction function y2 = f 2(y1);then max y1 p(y1+ f2(y1))y1 ¨C c1(y1)determines y1.Example: p(y1 + y2)= a ¨C b(y1 + y2), c = 0.Figures 26.1 and 26.2.Price leadership: The leader sets p first, then max y2 py2 ¨C c2(y2)gives S2(p).Now, the leader goes as a monopolist facing the residual demand R(p)= D(p)MC1(x1)= MC2(x2).Or the market incentive to merger.The tragedy of the commons: with falling AP, AP(c)= a vs MP(c)= a.Chapter 33 Law and Economics Crime and punishment.maxx B(x)-¦Ð(e)F.So, high fines / low enforcement combination.Liability law.minx c(x)+ L(x).Strict liability vs negligence rule.Chapter 34 Information Technology

No need for a new kind of economics.Economics is primarily about people, not goods.Network externalities.Market with three equilibria.Growth takes off after a critical ma.Huge fixed cost and negligible variable cost.For a digital product, it's easy to make copies as good as the original.Copyright.Zero-profit and maximization of [1¨C¦Ð(x)]px ¨C¦Ð(x)Fine gives, for x*, that x = ¦Ð(x)[1¨C¦Ð(x)] /¦Ð¡¯(x)and p* =¦Ð(x*)F / [1¨C¦Ð(x*)] x*.Let K be the development costs, we need ¦ÐF ¡Ý(1¨C¦Ð)(x* / D(p*))K.Sharing intellectual property.Modeling example for video industry.Chapter 35 Public Goods

Public good is a good that must be provided in the same amount to all the affected consumers.Provision of a TV set by roommates in a dormitory: simply ¡Æri ¡Ý¡Æg i = c.Private provision of the public good.Free riding.Different levels of the public good: MRS1 + MRS2 = MC(G).Quasilinear case.A command system and a voting system.The ¡°paradox of voting¡±.Demand revelation.The pivotal agent approach.The Clarke tax.Chapter 36 Asymmetric Information

Common knowledge and private information.Asymmetric information.Akerlof model: the market of ¡°lemons¡±.Quality choice.Adverse selection as a hidden information problem.Moral hazard as a hidden action problem.Signaling.Spence model.Graph to show separating equilibria vs pooling equilibria.Incentive systems.Participation constraint: s(f(x))¨C c(x)¡Ý u^, where x stands for effort while c the cost.max x f(x)¨C s(f(x))= f(x)¨C c(x)¨C u^ gives MP(x*)= MC(x*).Incentive compatibility constraint then follows: s(f(x*))¨C c(x*)¡Ýs(f(x))¨C c(x)for all x.Efficient and equivalent ways to implement: Rent: R = f(x*)¨C c(x*)¨C u^;Wage: s(x)= MP(x*)x + K;Take-it-or-leave-it: pay B* = c(x*)+ u^ if x = x*.The residual claimant to the output.Shareholders vs bondholders.Sharecropping s(x)= ¦Áf(x)+ F gives ¦ÁMP(x)= MC(x), and thus is not efficient.However, a drastic change if asymmetric information.