# Lernkarten

Karten 40 Karten 0 Lernende English Universität 31.05.2019 / 06.06.2019 Namensnennung - Nicht-kommerziell - Keine Bearbeitung (CC BY-NC-ND)     (Unversité de Genève, cours de Pr. Monika Mrazova)
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Pareto-improving allocation

An allocation of the endowment that improves the welfare of a consumer without reducing the welfare of another

All points in the box, including the boundary, represent

feasible allocations of the combined endowment

Edgeworth-Bowley Box: Endowment

Feasible allocation

xA1 + xB1 < wA1 + wB1 and xA2 + xB2 < wA2 + wB2

general equilibrium analysis

Prices of other goods may/will affect people’s demands and supplies for a particular good (e.g. substitutes, complements ...)

In exchange, we relax some assumptions

Identical consumers
Exogenous prices

Differents payoffs

Oligopoly: Comparing the outcomes

Monopoly / Collusion VS Cournot VS Stackelberg

Collusion

The Stackelberg equilibrium

Leader’s profit-maximizing output, Follower's profit-maximizing output, Individuals output, Industry output

The follower's problem

Stackelberg Competition: Example
Consider an industry which is characterised as follows:
Two firms producing an identical good
(Inverse) demand is given by: p(y) = a - by = a - b(y1 + y2)
Each firm has a zero marginal cost
Firm 1 has a first-mover advantage
Find the Stackelberg equilibrium (y1;y2) for this industry.

Solve the follower’s problem to obtain the reaction function.

Stackelberg Competition: Main Assumptions

Sequential quantity setting
Two firms producing identical product
Assume firm 1 chooses its quantity first. Firm 2 observes q1 and then chooses q2.
! Backward solution: Solve firm 2’s problem first as firm 1 (the leader) needs to anticipate the follower’s reactions.

STWE: Can a Pareto efficient allocation be achieved as a competitive equilibrium?

Yes, if preferences are convex

FTWE does not hold in

the presence of externalities

FTWE focuses on efficiency, not fairness

Allocation where one person owns everything is Pareto efficient

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

Implicit assumptions of the FTWE: Each consumer knows only

his own tastes, endowment and the market prices

FTWE

any competitive equilibrium is Pareto efficient

Using Walras’ Law we can show that

if demand equals supply in one market, the same must be true in the other market.

Walras’ law states that

the value of aggregate excess demands is always 0 (at any prices), i.e

In equilibrium the aggregate excess demand for each good

Aggregate excess demand for good 1

Net/Excess demand of consumer A for good 1

The Algebra of Equilibrium

Equilibrium is a set of prices (p1*;p2*) such that

total demand for each good equals total supply

Competitive Equilibrium: we must have