0. Economics
1. The Market
2. Budget Constraint
3. Preferences
4. Utility
5. Choice of Consumption
6. Demand
8. Slutsky Equation
9. Buying and Selling for a consumer with an endowment ω
12. Uncertainty
14. Consumer's Surplus
15. Market Demand
16. Partial Equilibrium 18. Technology
19. Profit Maximization
20. Cost Minimization
21. Cost Curves
22. Supply of a competitive firm
23. Industry Supply
24. Monopoly
25. Monopoly Behavior
27. Oligopoly
28. Game Theory
29. Exchange
30. Production
32. Externalities
36. Asymmetric Information
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 .
Micro economics and macro economics: 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 issues and normative issues .
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 < 0 ) ;
2 , If TM is at maximum or minimum, then MM = 0;
3 , AM increasing (decreasing) if and only if MM > AM ( MM < AM );
4 , If AM is at maximum or minimum, then MM = AM, Or MM cuts AM at the latter's maximum or minimum.
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 willingness 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 discuss. The budget constraint: p 1 x 1 + p 2
x 2 ≤ m.
The budget line and the budget set (the market opportunity set ). Fig.
The slope of the budget line : dx 2 / dx 1 = – p 1 / p 2 .
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 . )
Assumptions about Preferences:
Completeness : 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 cross 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 = dx 2 / dx 1 . It is the marginal willingness to pay ( how much to give up of x 2 to acquire one more of x 1 ). Usually negative. Fig.
Convex indifference curves exhibit a diminishing marginal rate of substitution. Fig.
Chapter 4 Utility
Essential ordinal utilities , versus convenient cardinal utility functions : u ( x ) ≥ 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 ( x 1 , x 2 ). Fig.
Utility functions are indifferent up to any strictly increasing transformation.
Examples of utility functions: u (x 1 , x 2 ) = x 1 x 2 ; u (x 1 , x 2 ) = x 1 2 x 2 2 ; Fig.
u (x 1 , x 2 ) = ax 1 + bx 2 (perfect substitutes); Fig.
u (x 1 , x 2 ) = min{ax 1 , bx 2 } (perfect complements). Fig.
Quasilinear preferences : all indifference curves are vertically (or horizontally) shifted copies of a single one, for example u (x 1 , x 2 ) = v (x 1 ) + x 2 . Fig.
Cobb-Douglas preferences : u (x 1 , x 2 ) = x 1 c x 2 d , or u (x 1 , x 2 ) = x 1 a x 2 1-a with a = c /(c+d); and their log equivalents: u (x 1 , x 2 ) = c ln x 1 + d ln x 2 , or u (x 1 , x 2 ) = a ln x 1 + (1– a) ln x 2 . Fig.
Marginal utilities , and MRS along an indifference curve.
Derive MRS = – MU 1 / MU 2 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 = – p 1 / p 2 . Fig.
Basic equations: MU 1 / p 1 = MU 2 / p 2 and p 1 x 1 + p 2 x 2 = 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: x 1 = x 1 (p 1 , p 2 , m), x 2 = x 2 (p 1 , p 2 , m).
Inferior and ultra-superior goods (by income); Fig.
Luxury and necessary goods (by income). Fig.
Normal and Giffen goods (by price). Fig.
The income expansion path or the income offer curves ( x 1 - x 2 plane ) , and the Engel curve ( m – x 1 plane ) . Figs.
The price offer curve ( x 1 - x 2 plane ) and the demand curve ( p 1 – x 1 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 ω
Offer curve and demand curve . A figure review.
Labor supply . A graphical discussion.
Chapter 12 Uncertainty
Utility functions and probabilities. Expected utility functions , or von Neumann-Morgenstern utility functions :
EU = Σ i p i U(s i ), where p i is the probability the event s i 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 losses. The water-diamond paradox.
Chapter 15 Market Demand
Adding up demand curves: the horizontal summation principle . Fig.
The price elasticity of demand :
ε = ( Δ q / q ) / ( Δ p / p)= ( p / q ) / ( Δ p / Δ q), or
ε = (dq / q ) / (dp / p)= ( p / q ) / (dp /dq).
It is normally negative. So, very often people turn to consider its absolute value | ε |.
A commodity has an elastic ( inelastic , unit ) demand if | ε | > 1 ( | ε | < 1 , | ε | = 1 ).
Elasticity and revenue. R = pq, dR = q dp + p dq, and then
dR / dp = q [ 1 + ε (p) ] where ε ( p ) = ( p dq ) / (q dp). Fig.
Similarly, MR = dR / dq = p (q) [ 1 + 1 / ε (q) ] where ε ( q ) = ( p dq ) / (q dp).
Strikes and profits. The Laffer cu
rve.
Constant elasticity demands. Another way to express elasticity: ε = d ln q / d ln p.
The income elasticity of demand η . With p 1 x 1 + p 2 x 2 = m, we have 1 = p 1 dx 1 /dm + p 2 dx 2 /dm = s 1 η 1 +s 2 η 2 , where s i is the expenditure share of good i .
The arc elasticity vs the point elasticity.
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 P p , the price paid by consumers, P r , the price received by producers, P l , the list price, and P o , 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 ( p p ) = S ( p r ), and p p = p r + T.
Who bears the burden of a tax? The one with less elasticity shares more burden.
Passing along a tax. The deadweight loss 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.
Assumptions of technology: monotonic ( free disposal ), convex . Fig.
The marginal product
The technical rate of substitution (TRS): with dy = 0,
TRS (x 1 , x 2 ) = dx 2 / dx 1 = – MP 1 (x 1 , x 2 ) / MP 2 (x 1 , x 2 ).
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 : π = py - w 1 x 1 - w 2 x 2 , y = π / p + w 2 x 2 / p + w 1 x 1 / p describes isoprofit lines, max x1 π gives pMP 1 = w 1 . Fig. Cobb-Douglas case.
Optimum lies on the tangency of an isoprofit line and the production function. Fig.
Comparative statics: Increasing p increases x 1 and then y. Increasing w 1 reduces x 1 , and thus the factor demand curve follows. Figs.
Exercise: Max xi π based on production function y = f ( x 1 , x 2 ) to derive factor demand x i = x i ( p, w 1 , w 2 ), and then the firm supply function y = g ( p, w 1 , w 2 ).
Chapter 20 Cost Minimization
Basic model : min x1, x2 w 1 x 1 + w 2 x 2
subject to f (x 1 , x 2 ) = y gives c ( w 1 , w 2 , y ).
Isocost lines : x 2 = C/w 2 – w 1 x 1 /w 2 . Tangency of an isocost line and an isoquant.
– MP 1 (x 1 , x 2 ) / MP 2 (x 1 , x 2 ) = TRS (x 1 , x 2 ) = – w 1 / w 2
or
MP 1 (x 1 , x 2 ) / w 1 = MP 2 (x 1 , x 2 ) / w 2 . Fig.
Minimizing costs for y = min{ax 1 , bx 2 }; y = ax 1 + bx 2 ; and y = x 1 a x 2 b .
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 ( < AC) if and only if AC is increasing (decreasing) . MC cuts AC (AVC) at AC's (AVC's) extreme. Long-run and short-run costs.
Fixed and quasi-fixed costs.
Sunk costs are costs that are not recoverable. A special kink of fixed costs.
Chapter 21 Cost Curves
A misleading formula: AVC(1) = MC (1). Should be MC(0) = AVC(0) .
The area under MC gives VC: ∫ MC = VC .
Division of output among plants of a firm. Fig.
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 π (y) = R(y) – 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* ) ≥ 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 – VC = π + 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 / ε (y) ], from the basic equation MR = MC we have
p ( y ) = MC ( y ) / [1 – 1 / | ε ( y ) | ].
The market price is a markup over marginal cost, and 1 / [1 – 1 / | ε ( y ) | ] is called the markup .
Two equivalent ways to determine the equilibrium :
MC = MR , or AR = MC / ( 1– | ε | ). Figs.
FOC: MC = MR. SOC: MC' ≥ MR'. The impact of taxes on a monopoly.
Inefficiency of monopoly. Deadweight loss of monopoly. Natural monopoly . Figs.
What causes monopolies: by nature or by permission. The minimum efficient scale factor.
Regulation of monopoly: AC = AR.
Chapter 25 Monopoly Behavior
Price discri
minations of first-degree (perfect), of second-degree (bulk discounts), and Price discrimination of third-degree ( market segmentation , Figs.):
MC(y 1 +y 2 ) = mr 1 (y 1 ) = mr 2 (y 2 ) gives p 1 [ 1 – 1 / | ε 1 ( y 1 )| ] = p 2 [ 1 – 1 / | ε 2 ( y 2 )| ].
Graphical analysis and Equation solutions .
Chapter 27 Oligopoly
Quantity or price competitions. Identical products: p = p ( Y ), Y = y 1 + y 2 .
Sequential games . Backward solution .
Quantity leadership : Stackelberg model . max y2 p (y 1 + y 2 ) y 2 – c 2 ( y 2 ), or MR 2 = p (y 1 +y 2 ) + y 2 dp / dy 2 = MC 2 gives the follower's reaction function y 2 = f 2 (y 1 ) ; then max y1 p (y 1 + f 2 (y 1 )) y 1 – c 1 ( y 1 ) determines y 1 .
Example: p ( y 1 + y 2 ) = a – b ( y 1 + y 2 ) , c = 0. Figures 26.1 and 26.2.
Price leadership : The leader sets p first, then max y2 py 2 – c 2 (y 2 ) gives S 2 (p). Now, the leader goes as a monopolist facing the residual demand R(p) = D (p) - S 2 (p). Fig.
Example: D(p) = a – bp, c 2 (y 2 ) = y 2 2 / 2, c 1 ( y 1 ) = c y 1 .
Simultaneous games . Bertrand price competition leads to p = MC even only two firms.
Only quantity setting consideration.
Cournot model of quantity competition: max yi p( y i + y j e ) y i – c i ( y i ), or MR i = p (y i +y j e ) + y i dp / dy i = MC i , where y j e is the output of Firm j expected by Firm i, gives reactions y i = f i (y j e ), then the consistence determines the equilibrium.
Adjustment to an equilibrium. Several firms in Cournot equilibrium: y = y 1 + … + y n , p ( y ) [1 – s i / | ε ( Y )| ] = MC i (y i ) where s i = y i / Y.
Chapter 28 Game Theory
Players , (pure) strategies or actions , and payoffs . Finite games .
Simultaneous(-move) games.
Two-person games, payoff matrices . Dominant and dominated strategies.
Method of iterated elimination of strictly dominated strategies.
A pair of strategies is a Nash equilibrium if A's choice is optimal given B's, and vice versa. A situation, or a strategy combination of no incentive to deviate unilaterally.
The Prisoner's Dilemma , which shows also that a Nash equilibrium does not necessarily lead to a Pareto efficient outcome.
Method of underlining relatively advantageous strategies. Battle of sexes.
There can be no, one, and multiple (pure) Nash equilibria.
Chapter 29 Exchange
Partial equilibrium and general equilibrium.
Edgeworth box : a pure exchange model of two goods, two consumers with fixed endowments. Region of mutual advantages . Pareto set and the contract curve .
From disequilibrium to the competitive equilibrium. Offer curve approach . Fig.
The first theorems of welfare economics: competitive equilibria are all Pareto efficient.
The second theorems of welfare economics: under certain conditions, every Pareto efficient allocation can be achieved as a competitive equilibrium.
Prices play two roles in market syste
m: an allocative role and a distributive role.
Two kinds of monopolies in the Edgeworth box. Figs.
Chapter 30 Production
Two outputs case: production possibilities . Exchange and production.
Trade leads to Separation of production and consumption, to Production specialization, and to Wealth improvement . Fig.
Heckscher-Ohlin theory on international trade. Fig.
Chapter 32 Externalities
Consumption externality and production externality. The lack of markets for externalities causes problems. With externalities, the market will not necessarily result in a Pareto efficient provision of resources. However, some other social institutions can "mimic" the market mechanism.
The model of smokers and nonsmokers (showing excellent analysis techniques). Fig.
The practical problems with externalities generally arise because of poorly defined property rights. The Caose Theorem . Social cost and private cost.
The tragedy of the commons: with falling AP, AP ( c ) = a vs MP ( c ) = a .
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 .