ECMC02 – Week 9
General Equilibrium Analysis
- What is it?
- What is an Edgeworth Exchange Box
(EEB) and what do you put in it?
- How is efficiency defined in an EEB?
- Who trades what, with whom, and why?
- Does a competitive price system
encourage trading efficiency?
1
Price
$60
$50
Supply
$30
$25
$15
$10
0
Demand
100
200
300
350
450 475
Boxes of tomatoes
per month
This is partial equilibrium analysis - an equilibrium in
one market.
2
Price
What is the effect of a tax of $10 per box on
tomatoes? As economists, we can analyze the
problem graphically using partial equilibrium
analysis.
$60
$50
Supply
+ Tax
$32
Supply
$25
$20
Tax
$10
0
Demand
100
200
275
3
350
450 475
Boxes of tomatoes
per month
There is only one problem. The answer is
wrong. Because there is a potentially
important factor that we have ignored.
What?
4
Market for tomatoes
5
Market for lettuce
Partial equilibrium analysis:
- one good (or service)
- one market
- assume no other markets affected
General equilibrium analysis
- when a butterfly flaps its wings in
Mexico…
- all markets, all goods
- simultaneous equilibrium in all markets
(for us, two)
- takes into account feedback effects
- good for trade, efficiency, general
taxation, etc.
6
What does GE analysis look like?
Graphically:
- Edgeworth Exchange Box
- Edgeworth Production Box
- Indifference curves, isoquants
- Production Possibility Frontiers
- Utility Possibility Frontiers
Algebraically:
- Lagrangeans, constrained optimization
7
- 3 levels of discussion
- exchange economy (lots of time)
- production economy
- product mix
- put them all together in discussion of how
parts of economy interact in any
reallocation of resources
8
What is an Edgeworth Exchange Box?
Who was Francis Ysidro Edgeworth?
9
Mike’s
Clothing
0 for Mike
Pat’s
Food
Mike’s
Food
0 for
Pat
Pat’s
Clothing
An Edgeworth Exchange Box shows the allocation of (a
fixed amount of) two goods to two consumers. Every
point in the box represents a different allocation of the
goods.
We can draw indifference curves in the box, and discuss
issues of consumer preference, efficiency and trade
10
Called an “exchange” box because there is no
production, only exchange.
Start from an initial “endowment” of goods
Assume two consumers (Pat and Mike), two
goods (Guinness and Lamb). Consumers have
preferences over any possible allocation of
the two goods
UP = U(XP, YP) and UM = U(XM, YM)
For algebra, we typically assume consumers
have well-behaved indifference curves
- convex to origin
- smooth, differentiable
- both goods essential (interior solutions)
- nothing else affects utility
Graphs:
- linear, rectangular, corner solutions
11
12
Let X be Guinness
Let Y be lamb
Draw Pat’s indifference curves over all
possible allocations of Guinness and lamb
Mike’s
Guinness
0 for
Mike
Pat’s
lamb
Mike’s
lamb
0 for Pat
Pat’s
Guinness
13
Now draw on Mike’s indifference curves
Mike’s
Guinness
0 for Mike
Pat’s
lamb
Mike’s
lamb
0 for
Pat
Pat’s
Guinness
14
Mike’s
Guinness
60
80
40
0 for Mike
20
Pat’s
lamb
10
A
40
20
E
D
30
C
20
B
F
10
40
Mike’s
lamb
0 for
Pat
10
30
50
80
100
Pat’s
Guinness
15
Rank these allocations in order for Pat
Rank these allocations in order for Mike
Now adopt society’s perspective. This social
view does not favour either Pat or Mike.
Can you rank these allocations from society’s
perspective. What might the social
perspective take into account?
16
Consider “pareto efficiency”
Comparing two allocations, allocation I is
pareto-preferred (or pareto-superior) to
allocation J if no one is worse off in allocation
I, and at least one person is better off.
Allocation I is pareto-inferior to allocation J
if no one is better off in allocation I, and at
least one person is worse off.
An allocation is pareto-optimal (or paretoefficient) if no other attainable allocation is
pareto-preferred to it.
Consider all possible allocations on the next
page. Which are pareto-superior to others?
Which are pareto-inferior to others? Which
are pareto-optimal?
17
Mike’s
Guinness
60
80
40
0 for Mike
20
Pat’s
lamb
10
A
40
20
E
D
30
C
20
B
F
10
40
Mike’s
lamb
0 for
Pat
10
30
50
80
100
Pat’s
Guinness
18
How does this differ from maximizing
consumer surplus as a concept of efficiency?
Consider this matrix of utilities. The possible
allocations are labeled A, B, C, D and E.
Which are pareto-preferred to others?
Which is/are pareto-optimal?
A
Tom
2
Dick
4
Harry 6
B
3
5
7
C
2
5
6
19
D
40
4
7
E
35
160
6
Consider the Edgeworth Exchange Box again.
Do you remember what a marginal rate of
substitution (MRS) is?
What is it graphically?
What is it conceptually?
20
What is it algebraically, if U = U(X, Y)?
21
If the initial endowment is at point A, what is
Pat’s MRS?
What is Mike’s MRS?
Who will be willing to trade what?
What would they be willing to accept in
return?
What about at point F?
What about at point D?
22
Mike’s
Guinness
40
60
80
0 for Mike
20
Pat’s
lamb
10
A
40
20
E
D
30
C
20
B
F
10
40
Mike’s
lamb
0 for
Pat
10
30
50
80
100
Pat’s
Guinness
23
Sample Problems:
Problem #1
Bill has 6 glasses of scotch and 3 glasses of
water. Ann has 3 glasses of scotch and 6
glasses of water. Bill regards scotch and
water as perfect 1-for-1 complements while
Ann regards them as perfect 1-for-1
substitutes.
(a) Is this initial endowment paretoefficient?
(b) If not, what is the feasible set of
pareto-efficient allocations? Give an
example of a feasible trade that could
be made to reach a pareto-optimal
outcome.
24
Problem #2
Charlie has an initial endowment of 3 apples
and 12 bananas while Doris has 6 apples and 6
bananas. Charlie’s utility function is U = ACBC
where AC is the amount of apples Charlie
consumes and BC is the amount of bananas he
consumes and ACBC is the product of these
two numbers. Doris’ utility function is U = AD
BD ,where AD is the amount of apples Doris
consumes and BD is the amount of bananas she
consumes.
Given their initial allocation, at every Pareto
optimal allocation in the interior of the
Edgeworth Exchange Box, does Doris consume
the same number of apples as she does
bananas?
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