Microeconomics I
Fiches de réveisions
Fiches de réveisions
Trade and Pareto Efficiency: The Core
Economic Problem
Given initial endowments, what is the allocation that ensures that
consumers maximise their utility
demand equals supply in all markets
Edgeworth Box: Disequilibrium
Edgeworth Box: adjustment to equilibrium
A competitive equilibrium is
an allocation E* and a set of prices, p1* and p2*, such that, given these prices (and given the initial endowments), each consumer is maximising his/her utility at that allocation
Competitive Equilibrium: we must have
Equilibrium is a set of prices (p1*;p2*) such that
total demand for each good equals total supply
The Algebra of Equilibrium
Net/Excess demand of consumer A for good 1
Aggregate excess demand for good 1
In equilibrium the aggregate excess demand for each good
Walras’ law states that
the value of aggregate excess demands is always 0 (at any prices), i.e
Using Walras’ Law we can show that
if demand equals supply in one market, the same must be true in the other market.
FTWE
any competitive equilibrium is Pareto efficient
Implicit assumptions of the FTWE: Each consumer knows only
his own tastes, endowment and the market prices
The FTWE tells us that
the resulting equilibrium from these independent, self-interested and decentralised actions is efficient
This is the nature of the “Invisible Hand” of Adam Smith
FTWE focuses on efficiency, not fairness
Allocation where one person owns everything is Pareto efficient
FTWE does not hold in
the presence of externalities
STWE: Can a Pareto efficient allocation be achieved as a competitive equilibrium?
Yes, if preferences are convex
Questions about how appartments rents are determined
- Who will rent close appartments?
- At what price?
- Will the allocation of appartments be desirables at any sense?
Two basic postulates
Rational choice and equilibrium
Rational choice
Each person tries to choose de best alternative available to him or her
Equilibrium
Market price adjust untill quantity demanded equals quantity supplied
Market demande curve
The quantity demanded vs price graph
Supply for appartments
Quantity fixed
Low rental price
quantity demanded of close apartments exceeds quantity available ) price will rise
High rental price
quantity demanded less than quantity available ) price will fall
Competitive equilibrium
Quantity demanded = quantity available ) price will neither rise nor fall
Competitive market allocation
by willingness to pay
Endogenous in the model of appartments
I price of close apartments
I exchanged quantity of close apartments
Exogenous in the model of appartments
I price of distant apartments
I quantity of close apartments
I incomes of potential renters
Suppose de price of distant appartments rises
Demand for close apartments increases (rightward shift), causing
a higher price for close apartments
Comparative statics: price of distant appartment rises graph
Comparative statics: more close appartments
Supply is greater, so the price for close apartments falls
More close appartments graph
Imperfectly competitive market
a monopolistic landlord
a perfectly discriminatory monopolistic landlord
a competitive market subject to rent control
Monopolistic market equilibrium
If renters buy some houses
Supply (<-) because less appartments to rent
Demand (<-) because they don't ask for appartment anymore
Price doesn't change
Q diminishes
If government ask for a tax (appartments)
landlords suport burden of tax
zéro passthrough: rare because supply is fixed
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Lernkarten
Consumers' demand: perfect complements
Concave preferences
corner solution
Quasi-linear preferences
Establish the maximum utility
Express x2 from de budget constraint
Inject it into the utility function
Derive to get the FOC
Equalize the partial utility function according to the prices
Cobb-Douglas optimal choices
Solve with the lagrangian for good2
Application to tax choice
If the government wants to raise R of revenue, should it use a quantity tax or an income tax?
Income tax better than quantity tax.
Change in m: m'' < m <m'
Normal goods
(delta X, / delta m) > 0
Inferior goods
(delta x1 / delta m) < 0, use of public transports, low quality food
Income offer curve
Income expansion path
Engel curve
Perfect substitutes: One-to-one: with p < p : x1 = m/p1: income offer curve
Perfect substitutes: One-to-one: with p < p : x1 = m/p1: Engel curve
Perfect complements: income offer curve
x1= m/ (p1+p2)
Perfect complements: Engel curve
Cobb-Douglas utility function: income offer curve and Engel curve
Quasi-linear preferences: income demand curve and Engel curve
Change in prices
Ordinary goods VS Giffen goods
Price offer curve and demand curve with change of price
Perfect substitutes: price offer curve and demand curve
Perfect complements: price offer curve and demand curve
Discrete goods
Price effect and income effect with change in price: normal good
Price effect and income effect with change in price: giffen good
Slutsky decomposition: perfect complements
Subsitution effect = 0
Perfect substitutes: 3 scenari for change in demand
Quasilinear preferences
only substitution effect
Slutsky equation
Change with endowment income effect
Slutsky equation: an example
Assume the demand function is: x1(p1;p2;m) = 10 + 1m/10p1
Initially m = 120 and p1 = 3
Initial demand?
14
Slutsky equation, an example: Now suppose p1 diminishes to 2. New demand?
16
Slutsky equation: an example: substitution and income effect
Hicks substitution effect
change in demand when prices
change but a consumer’s utility is held constant (consumer is indifferent between the original bundle and the one he can now afford) ! roll the budget line around the indifference curve
Slutsky equation with calculus 1/2
Slutsky equation with calculus 2/2
With endowment: budget constraint, gross demand, net demand
Assumptions/notation:
I Nonlabour income
I Amount of consumption, price of consumption
I Amount of labour supplied, wage rate
Budget constraint
Further notation:
I Maximum amount of labour time
I Maximum consumption without work
I Leisure time
Budget constraint becomes
Labour supply starting with an endowment
Assume that leisure is a normal good. How does labour supply change when w augments?
