Download ECMC02 – Week 10

ECMC02 – Week 10
General Equilibrium Analysis – continued
Objectives this week:
- review contract curve, pareto efficient
points, pareto efficient trades (barter)
- a competitive market in an Edgeworth
Exchange Box, the role of the auctioneer
- the first and second welfare theorems
about competitive markets
- production box and efficiency in
production
- competitive market in inputs and
efficiency
- production possibilities frontier from the
contract curve in the production box
- Robinson Crusoe and the grand optimum
1
Allocation J and allocation K are the only two
possible allocations of goods amongst a group of
potential consumers. We are told that allocation K
is Pareto-preferred to allocation J. We may
therefore conclude that:
A) every consumer must be better off with K than
with J
B) a majority of consumers are better off with K
than J
C) a move from K to J will make some consumers
better off and none worse off
D) a move from J to K will not make any consumers
better off
E) K is pareto optimal
F) none of the above
Allocation K is pareto-preferred to allocation J.
This means that this allocation is better for at
least one person and is no worse for all others.
This implies that K is pareto optimal. The correct
answer is (E).
2
Initial endowment, pareto-preferred
allocations, pareto-efficient trades (barter)
Mike’s
Guinness
80
40
60
0 for Mike
20
Pat’s
lamb
10
40
20
30
20
10
40
Mike’s
lamb
0 for
Pat
10
30
50
80
100
Pat’s
Guinness
3
The contract curve of all possible paretoefficient allocations
Mike’s
Guinness
80
60
40
0 for Mike
20
Pat’s
lamb
10
40
20
30
20
10
40
Mike’s
lamb
0 for
Pat
10
30
50
80
100
Pat’s
Guinness
4
Will consumers have incentives to trade
towards pareto-efficient allocations? Is
trade welfare-improving?
5
What is a competitive market in an EEB? In
barter, the outcome of trade can depend on
the bargaining power of the two parties.
Competitive markets have many buyers and
sellers, so no one has power (individually) to
change price.
Excess demand for a product will make its
price rise. Excess supply of a product will
make its price fall. A competitive
equilibrium will be one where the quantity
demanded of each product is equal to the
quantity supplied of each product. (a
general equilibrium). (Remember there is no
production, so consumers supply from
endowment).
How does the price respond to excess
demand or excess supply? To ensure there
are no disequilibrium trades, economists
invent auctioneer to call out bids. Bids will
only be accepted if demand = supply.
6
What if PX/PY is too shallow? Too steep?
Mike’s
Guinness
80
60
40
0 for Mike
20
Pat’s
lamb
10
40
20
30
20
10
40
Mike’s
lamb
0 for
Pat
10
30
50
80
100
Pat’s
Guinness
7
Competitive equilibrium will exist, will be
unique, and will be pareto-optimal.
Mike’s
Guinness
80
40
60
0 for Mike
20
Pat’s
lamb
10
40
20
30
20
10
40
Mike’s
lamb
0 for
Pat
10
30
50
80
100
Pat’s
Guinness
8
In competitive equilibrium, the ratio of the
prices (PX/PY will equal the ratio of the
marginal utilities = MRS.
Invisible Hand leads to pareto-efficient
equilibrium
First Theorem of Welfare Economics
Every competitive equilibrium allocation is
pareto-efficient
Second Theorem of Welfare Economics
Any allocation on the contract curve can be
sustained as a competitive equilibrium
Separability of efficiency and equity
9
Two consumers, Bill and Fred, each consume only
two goods, X and Y. At the initial endowment point
in the Edgeworth Box, Fred's MRS is 1/2 while
Bill's MRS is 1 (in both cases, the MRS is defined
as -dY/dX holding U constant). Then:
A) both benefit if Fred trades 3 units of X to Bill
in exchange for 1 unit of Y
B) both benefit if Bill trades 3 units of X to Fred
in exchange for 1 unit of Y
C) both benefit if Fred trades 3 units of Y to Bill
in exchange for 1 unit of X
D) both benefit if Bill trades 3 units of Y to Fred
in exchange for 1 unit of X
E) neither benefits from a trade because they are
on the contract curve
F) to make a definitive statement about a trade,
we would need more information
G) none of the above
10
MRSXY (= -dy/dx) means the rate at which
the individual is willing to substitute X for Y.
Fred’s MRS is ½, so he is willing to trade ½
unit of Y for one unit of X. Bill’s MRS is 1, so
he is willing to trade 1 unit of Y for 1 unit of
X. Relatively speaking, Fred regards Y as
valuable, while Bill regards X as valuable. So,
Fred will seek to get Y from Bill and Bill will
seek to get X from Fred. However, the deal
must be a good one. Fred will want to get Y
at a rate that is better than his MRS (more
than 1 unit of Y for every 2 units of X). And
Bill feels the same way. He will want to get X
at a rate that is better than his MRS (more
than 1 unit of X for every 1 unit of Y). Any
deal that satisfies both Fred and Bill’s
demands will result in a trade.
11
The options with Bill giving up X or Fred giving
up Y are not welfare-improving, so options B
and C are not possible. Option A would make
Bill happy, but Fred would be worse off.
Option D would make Fred happy, but Bill
would be worse off. A possible trade would
be something like Bill gives up 1 unit of Y for
1½ units of X. In this case, both Bill and Fred
are better off.
12
Consider a simple economy with two goods - food
and clothing - and two consumers (Bert and Ernie).
There is an initial endowment in this simple
“exchange” economy, and the initial price ratio is
price of food/price of clothing = 3/1. At this
initial price ratio, Bert wants to buy 6 units of
clothing while Ernie wants to sell 2 units of food.
We can conclude that this initial price ratio is:
(A) an equilibrium price ratio
(B) too low (in other words, the ratio of the price
of food to the price of clothing will have to rise to
give us equilibrium
(C) too high (in other words, the ratio of the price
of food to the price of clothing will have to fall to
create an equilibrium
(D) none of the above
13
Both Bert and Ernie want to buy clothing and to
sell food. The price of clothing must be too low
and the price of food must be too high. In other
words, the ratio of the price of food to the price
of clothing is too high. The correct answer is (C).
14
Conclusions from Edgeworth Exchange Box
Competitive markets can lead to a general
equilibrium across all markets that exhausts all
potential gains from trade (i.e., is efficient).
We do not need to give up efficiency in order to
get equity.
15
To be done in class:
Efficiency in an Edgeworth Production Box
Competitive market in inputs
The contract curve in the production box and
the Production Possibilities Frontier
Looking for the optimum product mix along the
PPF.
16