中级微观经济学教学大纲(王则柯).doc

四学分中级微观经济学教学大纲

王则柯

MICROECONOMICS ( 4 credits, as of 2002 )
Classroom Lecture Notes ( Draft, to be improved )
By
Wang Zeke
Lnswzk@

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:
Essential 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
Item with stars, such as * Nash Theorem, are optional

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 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;
and 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

Economics proceeds by developing Models of social phenomena. By a model we mean a simplified representation of reality. (Example: Market of apartments)
Exogenous variables, taken as determined by factors not discussed in a model, versus endogenous variables, determined by forces described in the model.
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.

Other ways to allocate apartments:
Monopoly: a market dominated by a single seller of a product.
The ordinary monopolist. (Single revenue-maximizing price)
The discriminating monopolist. (Image that the monopolist auctions off its apartments one by one to the highest bidders)
Rent control. (if effective, it leads usually to a situation of excess demand)

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

* Vector variables and vector functions. * The inner product of two vectors.
* With the price vector p = ( p1, p2, …, pn )T, the value of the commodity bundle x = ( x1, x2, …, xn )T is pTx = Σi pixi.
However, two goods are often enough to discuss.
The budget constraint: p1 x1 + p2 x2 ≤ m.
The budget line and the budget set (the market opportunity set). Fig.
The slope of the budget line: dx2 / dx1 = – p1 / p2 .
How the budget line changes when income increases, or when a price increases. Figs.
The numeraire price: you set it to 1 since only relative prices are essential.
Taxes: quantity taxes, value taxes (ad valorem taxes), and lump-sum taxes.
A subsidy is the opposite of a tax. Rationing. Point rationing.
Their effects on the budget set. Figs.

Chapter 3 Preferences

* Prerequisite: A binary relation R on X is said to be
Complete if xRy or yRx for any pair of x and y in X;
Reflexive if xRx for any x in X;
Transitive if xRy and yRz imply xRz.
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 = dx2 / dx1. It is the marginal willingness 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

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 ( x1, x2 ). Fig.
Utility functions are indifferent up to any strictly increasing transformation.
Constructing a utility function in the two-commodity case of well-behaved preferences: draw a diagonal line and label each indifference curve with how far it is from the origin.
* Mathematical economics has shown that a complete, reflexive, transitive and continuous preference can be always represented by a cardinal utility function.
* Continuity: both the sets {y: y is w.p. to x} and {y: x is w.p. to y} are closed for any x.

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– a) ln x2 . Fig.
Marginal utilities, and MRS along an indifference curve.
Derive MRS = – 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 = – 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 necessary goods (by income). Fig.
Normal and Giffen goods (by price). Fig.
The income expansion path or the income offer curves (x1 - x2 plane), and the Engel curve (m – x1 plane). Figs.
The price offer curve (x1 - x2 plane) and the demand curve (p1 – x1 plane). Figs.
Substitutes and complements. Codd-Douglas preferences. Quasilinear preferences.
Homothetic preferences: if (x1, x2) is preferred to (y1, y2), then (tx1, tx2) is preferred to (ty1, ty2) for any t > 0. Thus both the income offer curves and the Engel curves are all rays through the origin.
With homothetic preferences, the utility function u can be represented as the composition of a strictly monotone transformation g and a function h homogeneous of degree one: u ( x ) = g ( h ( x ) ).
Example: Quasilinear preferences lead to vertical (horizontal) income offer curves and vertical (horizontal) Engel curves.

Chapter 7 Revealed Preference

From (observable) behavior to (perhaps hidden) preference.
Direct revealed preference and indirect revealed preference. Recovering preference.
Weak axiom of revealed preference: If x is directly revealed preferred to y≠x, then it cannot happen that y is directly revealed preferred to x. Checking WARP.
Strong axiom of revealed preference: If x is revealed preferred to y≠x (either directly or indirectly), then y cannot be directly or indirectly revealed preferred to x. Checking SARP.

Quantity Indices: I q = (w 1 x 1 t + w 2 x 2 t ) / (w 1 x 1b + w 2 x 2b )
Paasche quantity index: P q = (p 1 t x 1 t + p 2 t x 2 t ) / (p 1 t x 1b + p 2 t x 2b )
Laspeyres quantity index: L q = (p 1 b x 1 t + p 2 b x 2 t ) / (p 1 b x 1b + p 2 b x 2b )
Price Indices: I p = (p 1 t w 1 + p 2 t w 2 ) / (p 1 b w 1 + p 2 b w 2 )
Paasche price index: P p = (p 1 t x 1 t + p 2 t x 2 t ) / (p 1 b x 1t + p 2 b x 2 t )
Laspeyres price index: L p = (p 1 t x 1 b + p 2 t x 2 b ) / (p 1 b x 1b + p 2 b x 2b )
Indexing Social Security Payments

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)
The standard, the Slutsky, and the Hicks (the compensated) demand curves, according to holding income, purchasing power, or utility fixed.
Slutsky identity: Δx1 =Δx1s +Δx1m with Δx1s negative while Δx1m and Δx1 either, or x1 (p1’, m) - x1 (p1, m) = [x1 (p1’, m’) - x1 (p1, m)] + [x1 (p1’, m) - x1 (p1’, m’)].
* The Slutsky equation: x1s (p1, p2 , x1*, x2 *) ≡ x1 (p1, p 2 , p1x1*+ p2x2*), thus x1 (p1, p2 , m*) / p1 = x1s (p1, p2 , x1*, x2*) / p1 - x1*x1 (p1, p2 , m*) / m
Rebating a small tax: p x + y = m , p’= p + t , R = t x’, and (p + t) x’+ y’ = m + t x’. Thus p x’ + y’ = m , showing worse off by the rebating tax. Or using calculus,
d x = (x /p) d p + (x /m) d m = (x /p) t + (x /m) t x = (x s /p) t .

Chapter 9 Buying and Selling for a consumer with an endowment ω

Net and gross demands, net supply. Offer curve and demand curve. A figure review.
Slutsky revisited: Ordinary vs endowment income effects,
Δx1 / Δp1 = Δx1s / Δp1 + (ω1 - x1)Δx1m / Δm.
Labor supply. A graphical discussion.

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 Asset Markets

Assets are goods that provide a flow of services over time.
Assets that provide a monetary flow are called financial assets.
The no arbitrage condition: in equilibrium, there should be no opportunities to realize a sure return by buying some of one asset and selling some of another.
Assets with consumption returns: The housing example.
Taxation of asset 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 = Σi 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 Assets

Mean-variance utility: if a random variable w takes values ws for s = 1,…, S with probability πs , then the mean of the probability distribution is μw = Σπs ws and the variance is σw2 = Σπs ( ws –μw ) 2 while its square root σw is the standard deviation. The associated utility is then u (μw , σw2 ) or u (μw , σw ).
A simple portfolio problem: if 1-x :Þ ( r f ), and x :Þ (m s , p s ; r m , s m ), then we have r x = Σs ( x m s + (1-x ) r f )πs = x Σs m s πs + (1-x ) r f Σsπs = x r m + (1-x ) r f and σx2 = x 2 σm 2. Thus, between risk and return, MRS = ( r m - r f ) / s m , the price of risk. As for Figure 13.3, think of y as a new mutual fund.
Measuring risk: the beta b i = how risky asset i is / how risky the stock market is. The risk adjustment = b i ( r m - r f ), and thus r i = r f + b i ( r m - r f ), the Capital Asset Pricing Model.
r i = r f + b i ( r m - r 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 losses. 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:
ε= (Δq / q ) / (Δp / p)= ( p / q ) / (Δp /Δq), or
ε= (dq / q ) / (dp / p)= ( p / q ) / (dp /dq).
It is normally negative. So, very often peop