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The simplest market
• Two people, or agents– Agent A and Agent B
• Two goods– Good x and Good y
• Agents interact by exchanging or trading goods• There is no production of either good
Questions we’re interested in
• Will unregulated exchange lead to “good” outcomes?– Under what conditions?
• How does trade occur?– Bargaining?– Using prices?
• Can an outsider (e.g., government) intervene to improve things?
Endowments
Person A
x
y
Ay
Endowment
• Endowments
A has (Ax, A
y)
B has (Bx, B
y)
Ax (A
x+Bx)
(Ay+B
y)• Any possiblebundle ofgoods for A isin this space
The simplest market
• Allocation: A pair of consumption bundles– (xA, yA), (xB, yB)
• Feasible allocation: pair of consumption bundles that add up to total endowment– (xA, yA)+(xB, yB)=(A
x, Ay)+(B
x, By)
The Edgeworth Box: endowments
Person A x
y
Person BBx
Ay
Endowment
By
• Endowments
A has (Ax, A
y)
B has (Bx, B
y)
Ax
• Any feasibleallocation ofgoods amongthe agents isa point in thisbox
The Edgeworth Box: preferences
Person A x
y
Person BBx
Ay
Endowment
By
A’s indifferencecurves
B’s indifferencecurves
Ax
Trade in the Edgeworth Box
Person A x
y
Person BBx
Ay
Endowment
By
A’s indifferencecurves
B’s indifferencecurves
Ax
Points to whichA would be willingto trade
Trade in the Edgeworth Box
Person A x
y
Person BBx
Ay
Endowment
By
A’s indifferencecurves
B’s indifferencecurves
Ax
Points to whichB would be willingto trade
Mutually beneficial trade
Person A x
y
Person BBx
Ay
Endowment
By
A’s indifferencecurves
B’s indifferencecurves
Ax
If trade is voluntarythey should end upsomewhere in here
What does the result look like?
Person A x
y
Person BBx
Ay
Endowment
By
Ax
At thereare no moregains fromtrade
Describing potential outcomes
• Pareto set, or contract curve: The set of all points that could be the outcome of a bargain – Depends on – Can only make one individual better off by
making the other worse off
The Pareto Set
Person A x
y
Person BBx
Ay
Endowment
By
Ax
Allocation if A hasall the bargainingpower
Allocation if B hasall the bargainingpower
Pareto set
Potential bargaining outcomesfrom endowment
Example: Pareto set
• Consumer A:– (A
x, Ay)=(5,10)
– u(xA, yA)=1/3 ln(xA) + 2/3 ln(yA)
• Consumer B:– (B
x, By)=(10,5)
– u(xB, yB)=1/2 ln(xB) + 1/2 ln(yB)
• Find the contract curve
Can we narrow down outcomes?
• So far we’ve said nothing about the mechanism or process by which people trade
• We’ve found that agents should get to the contract curve…..
• …..but we’re not sure what point they’ll reach on that curve
• If trading is via prices, this indeterminacy can be resolved
What about prices?
• A price-based process– Set py=1– Try a value of px=p– Gives slope of budget line for both consumers– Find gross demands of both consumers– Vary p until demand is a feasible allocation
• Excess supply of x– Lower p
• Excess demand of x– Raise p
Market equilibrium
Person A x
y
Person BBx
Ay
Endowment
By
Ax
At these prices, excessdemand and excesssupply are both zero
Prices and excess supply
Person A x
y
Person BBx
Ay
Endowment
By
Ax
Budget constraint
Amount of x thatB wants to buy
Amount of x thatA wants to sell
Excess supply of x
Prices and excess demand
Person A x
y
Person BBx
Ay
Endowment
By
Ax
Budget constraint
Amount of y thatB wants to sell
Amount ofy that A wants tobuy
Excessdemand for y
Using price offer curves to find the market equilibrium
Person A x
y
Person BBx
Ay
Endowment
By
Ax
Agent B’s priceoffer curve
Agent A’s priceoffer curve
Example: Price offer curves
• Consumer A:– (A
x, Ay)=(5,10)
– u(xA, yA)=1/3 ln(xA) + 2/3 ln(yA)
• Consumer B:– (B
x, By)=(10,5)
– u(xB, yB)=1/2 ln(xB) + 1/2 ln(yB)
• Find the IOCs and the equilibrium allocation and price.
The Pareto Set
Person Ax
yPerson B
Bx
Ay B
y
Ax
Pareto set
155
15
10 5
10
EndowmentPOC A
POC B
6.43
8.57
9 6
The First Fundamental Theorem of Welfare Economics
• The First Fundamental Theorem of Welfare Economics– All equilibria resulting from a competitive
market are Pareto efficient– There are no gains from trade available from
the result of a price-based exchange
• There may be other undesirable properties of a market outcome
The First Fundamental Theorem of Welfare Economics
Person A x
y
Person BBx
Ay
Endowment
By
Ax
The market equilibriumallocation is on the contractcurve, so is Pareto efficient
Contract curve
The Second Fundamental Theorem of Welfare Economics• The Second Fundamental Theorem of
Welfare Economics– If preferences are convex, any Pareto efficient
allocation can be reached by a competitive market, with the correct redistribution of the endowments
– Using redistribution then allowing price-based trade, a planner can choose any PE allocation
The Second Fundamental Theorem of Welfare Economics
Person A x
y
Person BBx
Ay
Endowment
By
Ax
Can the market get usto any Pareto efficientallocation we want?
Pareto efficientallocations
Redistribute goodx from B to A
Answer: Yes, withconvex preferencesand redistribution
Trade