Outline for Wednesday, August 13

� Final Friday 8am-9:50 in 105, across the hallway

& Review session Thursday 6pm here

� Review

� Edgeworth box� Edgeworth box

Two-part tariff

� A type of 2nd-degree price discrimination

� Charge a flat per-unit price

� Then charge an access fee to get the rest of the

consumer’s utilityconsumer’s utility

Two-part tariff example

� A type of 2nd-degree price discrimination

� Charge a flat per-unit price

� Then charge an access fee to get the rest of the

consumer’s utilityconsumer’s utility

� Each consumer will demand QD = 300 – 3P and we

are charging them a flat rate of P = MC = 20.

What access fee should we charge? You don’t need

to simplify your answer.

General equilibrium

� Calculate prices and quantities in all markets

together

� Takes care of the positive feedback effects we have

in partial equilibrium analysisin partial equilibrium analysis

General equilibrium example

�QD1 = 10-3P1+P2

�QD2 = 6-4P2+P1

�QS1 = -3+4P1

�QS2 = -2+5P2QS2 = -2+5P2

� To solve

� Set quantities supplied and demanded equal

� Find prices

� Substitute back into quantities

Outline for Wednesday, August 13

� Final Friday 8am-9:50 in 105, across the hallway

& Review session Thursday 6pm here

� Review

� Edgeworth box� Edgeworth box

Edgeworth Box

� A distribution of the two goods is called an

allocation

� When curves are smooth, the two consumers MRS

match at every Pareto optimal (PO, means efficient) match at every Pareto optimal (PO, means efficient)

allocation

� The Pareto set or contract curve consists of all PO

allocations

� The core is the set of efficient allocations that are

Pareto improvements over the endowment

Edgeworth Box

� The initial endowments are

� Ann starts with ωA = (ωAX,ωAX) = (6, 4)

� Bob has ωB = (ωBX, ωBY) = (2, 2)

� So the total endowments are� So the total endowments are

� There are 6+2 = 8 Xs

� There are 4+2 = 6 Ys

� This is the size of the box

Starting an Edgeworth Box

Most slides seem to be

From Huangkai on SlideShare

Starting an Edgeworth Box

Width = 826 =+=+BXAX

ωω

Starting an Edgeworth Box

Height =

24+=

+BYAY

ωω

Width = 826 =+=+BXAX

ωω

6

24

=

+=

Starting an Edgeworth Box

Height =

The dimensions of

the box are the

quantities available24+=

+BYAY

ωω

Width =

quantities available

of the goods.

826 =+=+BXAX

ωω

6

24

=

+=

OB

6

The Endowment Allocation

)4,6(=A

ωOA

8)2,2(=

Bω

OB

6

The Endowment Allocation

OA

8

4

6

)4,6(=A

ω

)2,2(=B

ω

OB

6

2

2

The Endowment Allocation

OA

8

4

6

)4,6(=A

ω

)2,2(=B

ω

OB

6

2

2

The

The Endowment Allocation

OA

8

4

6

The

endowment

allocation

)4,6(=A

ω

)2,2(=B

ω

Adding Preferences to the Boxx

A2

For consumer A.

ωωωω 2A

ωωωω1A

xA1

OA

Adding Preferences to the Boxx

A2

For consumer A.

ωωωω 2A

ωωωω1A

xA1

OA

Adding Preferences to the Box

ωωωω 2B

xB2

For consumer B.

ωωωω 2

ωωωω1B

xB1

OB

Adding Preferences to the Boxx

B2

For consumer B.

ωωωω 2B

xB1

OB

ωωωω 2

ωωωω1B

Adding Preferences to the Box

ωωωωB

ωωωω1B

xB1

For consumer B.OB

ωωωω 2B

xB2

Adding Preferences to the Boxx

A2

For consumer A.

ωωωω 2A

ωωωω1A

xA1

OA

Edgeworth’s Boxx

A2

ωωωω1B

xB1

OB

ωωωω 2A

ωωωω1A

xA1

OA

ωωωω 2B

xB2

xA2

ωωωω1B

xB1

OB

Pareto-Improvements

ωωωω 2A

ωωωω1A

xA1

OA

ωωωω 2B

xB2

The set of Pareto-

improving allocations

Pareto-Improvements

Pareto-Improvements

Pareto-Improvements

Trade

improves both

A’s and B’s welfares.

This is a Pareto-improvement

over the endowment allocation.

Pareto-ImprovementsNew mutual gains-to-trade region

is the set of all further Pareto-

improving

reallocations.

Trade

improves both

A’s and B’s welfares.

This is a Pareto-improvement

over the endowment allocation.

Further trade cannot improve

both A and B’s

welfares.

Pareto-Improvements

Pareto-Optimality

Better for

consumer A

Better for

consumer B

Pareto-OptimalityA is strictly better off

but B is strictly worse

off

Pareto-OptimalityA is strictly better off

but B is strictly worse

off

B is strictly better

off but A is strictly

worse off

Pareto-OptimalityA is strictly better off

but B is strictly worse

off

Both A and

B are worse

off

B is strictly better

off but A is strictly

worse off

Pareto-OptimalityA is strictly better off

but B is strictly worse

off

Both A and

B are worse

off

B is strictly better

off but A is strictly

worse off

Both A

and B are

worse

off

Pareto-Optimality

The allocation is

Pareto-optimal since the

only way one consumer’s

welfare can be increased is to

decrease the welfare of the other

consumer.

Pareto-Optimalityx

A2

ωωωω1B

xB1

OB

ωωωω 2A

ωωωω1A

xA1

OA

ωωωω 2B

xB2

Pareto-Optimalityx

A2

ωωωω1B

xB1

OB

All the allocations marked by

a are Pareto-optimal.

ωωωω 2A

ωωωω1A

xA1

OA

ωωωω 2B

xB2

Pareto-Optimalityx

A2

ωωωω1B

xB1

OB

All the allocations marked by

a are Pareto-optimal.

ωωωω 2A

ωωωω1A

xA1

OA

ωωωω 2B

xB2

The contract curve

The Corex

A2

ωωωω1B

xB1

OB

ωωωω 2A

ωωωω1A

xA1

OA

ωωωω 2B

xB2

The Corex

A2

ωωωω1B

xB1

OB

Pareto-optimal trades blocked

by B

ωωωω 2A

ωωωω1A

xA1

OA

ωωωω 2B

xB2

Pareto-optimal trades blocked

by A

The Corex

A2

ωωωω1B

xB1

OB

Pareto-optimal trades not blocked

by A or B

ωωωω 2A

ωωωω1A

xA1

OA

ωωωω 2B

xB2

The Corex

A2

ωωωω1B

xB1

OB

Pareto-optimal trades not blocked

by A or B are the core.

ωωωω 2A

ωωωω1A

xA1

OA

ωωωω 2B

xB2

Edgeworth Box

� A distribution of the two goods is called an

allocation

� When curves are smooth, the two consumers MRS

match at every Pareto optimal (PO, means efficient) match at every Pareto optimal (PO, means efficient)

allocation

� The Pareto set or contract curve consists of all PO

allocations

� The core is the set of efficient allocations that are

Pareto improvements over the endowment

Edgeworth Box

� To find how the two consumers will trade

� Find demand functions

� How do their choices change with prices?

� Four total: one for each consumer and each good

�Quantities demanded as functions of prices

� Find where they are compatible

� They must add up to the total amount of resources

Edgeworth Box

� To find how the two consumers will trade

� Find demand functions

� How do their choices change with prices?

� Four total: one for each consumer and each good

�Quantities demanded as functions of prices

� Find where they are compatible

� They must add up to the total amount of resources

�Only the ratio of prices matters

� It’s the slope through the endowment

� So suppose PY = 1; rename PX = P

Edgeworth Box

� To find how the two consumers will trade

� Find demand functions

� Four total: one for each consumer and each good

�Quantities demanded as functions of prices

� Let PY = 1; rename PX = P

� Find where they are compatible

� Add up to the total amount of resources

� uA = X2Y ωA = (90, 12)

� uB = XY ωB = (60, 8)

Edgeworth Box

� To find how the two consumers will trade

� Find demand functions

� Four total: one for each consumer and each good

�Quantities demanded as functions of prices

� Let PY = 1; rename PX = P

� Find where they are compatible

� Add up to the total amount of resources

� uA = X3Y ωA = (2, 2)

� uB = XY ωB = (3, 1)

Edgeworth Box

� So, given UA, UB, ωA ,ωB, solve using

� PY = 1 as given in the problem

� PX = P for simpler notation

� IA = PXA+YA and IB = PXB +YB as income

Solve each consumers problem for� Solve each consumers problem for

� XA(P), YA(P), XB(P) and YB(P)

� Demand for each good as a function of the price of X

�Make sure the demands add up to the “supply”, which is the total endowment� XA+XB = ωXA + ωXB and YA+YB = ωYA + ωYB

� Solve either of these for P, the answer should be the same

� Substitute P into the four demand functions to find the allocation

Edgeworth Box

� We’ll only consider Cobb-Douglas preferences