Title: CHAPTER 30 EXCHANGE
1CHAPTER 30EXCHANGE
2- Partial equilibrium analysis The equilibrium
conditions of ONE particular market, leaving
other markets untreated. - General equilibrium analysis The equilibrium
conditions of ALL markets, allowing interactions
between different markets.
330.1 The Edgeworth Box
- Two consumers A and B.
- Two goods 1 and 2.
- Initial endowment
- Allocation
- Feasible allocation total consumption does not
exceed total endowment for both goods.
430.1 The Edgeworth Box
530.1 The Edgeworth Box
- Each point in the Edgeworth box represents a
feasible allocation. - From W to M
- Person A trades units of good 1
for units of good 2 - Person B trades units of good 2
for units of good 1.
630.2 Trade
730.2 Trade
- Trade happens whenever both consumers are better
off. - Starting from W, M is a possible outcome of the
exchange economy because - Person A is strictly better off with
than with - Person B is strictly better off with
than with .
830.3 Pareto Efficient Allocations
- An allocation is Pareto efficient whenever
- There is no way to make everyone strictly better
off - There is no way to make some strictly better off
without making someone else worse off - All of the gains from trade have been exhausted
- There are no (further) mutually advantageous
trades to be made.
930.3 Pareto Efficient Allocations
1030.3 Pareto Efficient Allocations
- Pareto efficiency is given by the tangency of the
indifference curves. - Contract curve the locus of all Pareto efficient
allocations. - Any allocation off the contract curve is Pareto
inefficient.
1130.4 Market Trade
- Gross demand Quantity demanded for a good by a
particular consumer at the market price. - Excess demand The difference between the gross
demand and the initial endowment of a good by a
particular consumer. - Disequilibrium Excess demands by both consumers
do not sum up to zero.
1230.4 Market Trade
1330.4 Market Trade
- Competitive equilibrium A relative price
and an allocation ,
such that - The allocation matches the gross demands by both
consumers, given the relative price and initial
endowments - The allocation is feasible.
1430.4 Market Trade
1530.5 The Algebra of Equilibrium
- Consumer As demands
- Consumer Bs demands
- The equilibrium condition
1630.5 The Algebra of Equilibrium
1730.6 Walras Law
1830.6 Walras Law
- Walras Law The value of aggregate excess demand
is always zero. - Applications of the Walras law
- implies
- Market clearing for one good implies that of the
other good - With k goods, we only need to find a set of
prices where k-1 of the markets are cleared.
1930.7 Relative Prices
- Walras law implies k-1 independent equations for
k unknown prices. - Only k-1 independent prices.
- Numeraire prices the price which can be used to
measure all other prices. - If we choose p1 as the numeraire price, then it
is just like multiplying all prices by the
constant t1/p1.
20EXAMPLE An Algebraic Example of Equilibrium
- The Cobb-Douglas utility function
21EXAMPLE An Algebraic Example of Equilibrium
- Aggregate excess demand for good 1
22EXAMPLE An Algebraic Example of Equilibrium
2330.8 The Existence of Equilibrium
- The existence of a competitive equilibrium can be
proved rigorously. - A formal proof is quite complicated and far
beyond the scope of this course.
2430.9 Equilibrium and Efficiency
- Both indifference curves are tangent to the
budget line at the equilibrium allocation. - The equilibrium allocation lies upon the contract
curve. - The First Theorem of Welfare Economics Any
competitive equilibrium is Pareto efficient.
25EXAMPLE Monopoly in the Edgeworth Box
26EXAMPLE Monopoly in the Edgeworth Box
- First degree price discrimination
2730.11 Efficiency and Equilibrium
- Reverse engineering
- Starting from any Pareto efficient allocation
- Use the common tangent line as the budget line
- Use any allocation on the budget line as the
initial endowment. - The Second Theorem of Welfare Economics For
convex preferences, any Pareto efficient
allocation is a competitive equilibrium for some
set of prices and some initial endowments.
2830.11 Efficiency and Equilibrium
- The Second Theorem of Welfare Economics
2930.11 Efficiency and Equilibrium
- A Pareto efficient allocation that is not a
competitive equilibrium.