王则柯
MICROECONOMICS ( 4 credits, as of 2002 )
Classroom Lecture Notes ( Draft, to be improved )
By
Wang Zeke
Lnswzk@zsu.edu
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.
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;
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, …, p n )T, the value of the commodity bundle x = ( x1, x2, …, x n )T is p T x = Σi p i x i.
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 singl
e one, for example u (x1, x2) = v (x1) + x2 . Fig.
Cobb-Douglas preferences: u (x1, x2) = x1c x2d , or u (x1, x2) = x1a x21-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 / MU2by 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
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