General Equilibrium Theory

Question 1

What is General Equilibrium Theory

Answer 1

The aim of general equilibrium theory is to look at the economy as a whole: brings
together consumers and producers who interact through markets.

Question 2

Pure-Exchange Economy

Answer 2

Two commodities: x1 and x2 non-produced consumption goods

Two consumers: A and B who consume x1 and x2

Utility functions UA(x1A, x2A), UB(x1B, x2B)

Endowments: there is a fixed supply of the consumption goods as represented
by the consumers’ endowments w1A, w2A, w1B, w2B

Question 3

Feasible Allocation

Answer 3

An allocation is said to be feasible if demand equals supply for both commodities:
x1A + x1B = w1A, w1B
x2A + x2B = w2A, w2B

Question 4

Pareto Optimality

Answer 4

A feasible allocation is said to be Pareto optimal if there does not exist another
feasible allocation that makes one of the consumers better-off without making the
other consumer worse-off

Question 5

Contract curve

Answer 5

shows the locus of Pareto optimal

allocations

Question 6

Mathematical Derivation of Pareto optimality

Answer 6

Choose an allocation to maximise: UB(x1B, x2B)
Subject to:
UA(x1A, x2A) = UA
x1A + x1B = w1A, w1B
x2A + x2B = w2A, w2B

Question 7

The Core of the Economy

Answer 7

The core is the set of Pareto optimal allocations that give both consumers at least as much utility as they obtain from their endowment bundles

Question 8

General competitive equilibrium

Answer 8

An allocation and prices for the two commodities such that two conditions are satisfied:
i) both consumers are maximising utility subject to their budget constraints:
maxUA(x1A, x2A) s.t. p1x1A + p2x2A = mA = p1w1A + p2w2A
maxUB(x1B, x2B) s.t. p1x1B + p2x2B = mB = p1w1B + p2w2B
ii) markets clear (demand = supply)
x1A + x1B = w1A, w1B
x2A + x2B = w2A, w2B

Question 9

First Theorem of Welfare Economics

Answer 9

The general competitive equilibrium allocation is Pareto optimal.

Modern statement of Adam Smith’s invisible hand metaphor.
The general competitive equilibrium allocation lies in the core.

Question 10

Second Theorem of Welfare Economics

Answer 10

Any Pareto optimal allocation can be achieved via a general competitive equilibrium, provided the government can implement lump-sum transfers

An allocation can be Pareto efficient but also unfair

Question 11

The Robinson Crusoe Economy

Answer 11

in which one person (Robinson) is both a consumer and a producer

Two commodities: c is the consumption good and L is the production input labour.
One consumer who consumes c and supplies L. Utility function is U(c, L)
One producer who produces c using L. Production function is c = f(L)

Question 12

GCE for Robinson Crusoe Economy

Answer 12

an allocation and prices for consumption, p, and for labour, w, which satisfy the following
three conditions:
(i)The consumer is maximising utility subject to his budget constraint: max U(c, L) subject to pc = wL + π where π denotes the consumer’s profit income.
(ii) The producer is maximising profit subject to his technology constraint:
max π= pc - wL subject to c(f, L)
(iii) Demand equals supply for the consumption good and for labour