1. Bargaining, Institutions, and Allocations
Develop a model that will help us understand how different institutions/rules of the game affect allocations in a simple economy.
Two agents: Angela the farmer and Bruno the exploiter/landlord.
Two goods: Grain and Angela’s Leisure.
Note: Could be about any productive activity.
Different Institutions:
Isolated Individual,
Coercion,
Private Property and Freedom of Contract,
PP and FC plus Democratic Politics.
Special ingredients:
Quasilinear preferences
Survival constraint

2. Quasi-Linear Preferences
Bushels of Grain
per Day
The MRS of quasi-linear indifference
curves change only with L, not with G.
Same MRS
𝐸.g.: 𝑈 𝑔,ℓ =𝑔+ ℓ
IC3
IC2
IC1
Hours of Leisure
per Day

3. Technically Feasible Bundles12
Angela’s FF for farming
Technically
infeasible
Technically
feasible set
Bushels of grain
Biologically
infeasible
Biological survival constraint 24
Angela’s hours of free time

4. First Institution: Isolated Individual12
If an individual is isolated, there is no one else to constrain her. Nobody has power over her.
Angela chooses her optimal combination of free time and grain according to her production capabilities, preferences, and survival constraint.
She produces 9 bushels, 5.5 more than needed to ensure her survival.
With the illustrated preferences, survival constraint does not constrain Angela, but there are bundles on the FF that never would get chosen. 9
Bushels of grain
MRS=MRT
3.5 16 24
Angela’s hours of free time

5. Second Institution: Coercion I12
A second person, Bruno, arrives on Angela’s farm. He has a gun.
Bruno can force Angela to produce any technically feasible combination of goods and free time.
Bruno can force Angela to give him all grain in excess of her survival constraint (he plans to be around a while).
Does this kind of coercion happen in the real world?
Point A represents the allocation where Bruno forces Angela to work 16 hours.
Angela produces 11 bushels of grain.
Point A shows 7 bushels are allocated to Angela and 4 bushels are allocated to Bruno.
ALERT: We are assigning points inside the FF a new meaning! They are allocations of output determined by hours of free time and the FF.
How much will Bruno tell Angela to produce?
Bruno wants the quantity between the feasible frontier and survival constraint to be as large as possible. 11 8
Bruno 7
Bushels of grain A
Does coercion of this kind ever happen in the real world.
Slavery
Soviet agriculture in the 1920s.
Angela 24
Angela’s hours of free time

6. Second Institution: Coercion II12
MRT of FF
The maximum Bruno can extract from Angela and have her still survive is at the level of work where MRT of the FF is the same as the MRS of the survival constraint (SC).
We represent the allocation with point A.
Angela works 11 hours and produces 10 bushels.
Bruno takes 6 and leaves Angela 4.
Angela is far below the indifference curve she reached in isolation.
Note Bruno’s role here is purely exploitative.
He isn’t maintaining the land or purchasing inputs such as seeds or fertilizers. 10
Bruno
MRS of SC
Bushels of grain 4 A
Angela 13 24
Angela’s hours of free time

7. Second Institution: Coercion III12
Why is the maximum where MRT of the FF is the same as the MRS of the survival constraint?
Suppose Bruno tells Angela to work 14 hours and take 10 of free time.
MRT < MRS
This means if Angela worked one hour less, the reduction in the amount of grain she needs to survive is greater than the reduction in output from less work. More for Bruno!
Suppose Bruno tells Angela to work 4 hours and take 20 of free time.
MRT > MRS
This means if Angela worked one hour more, the increase in the amount of grain she would produce is greater than the additional amount she would need to survive. More for Bruno!
Bushels of grain 10 20 24
Angela’s hours of free time

8. Third Institution: Private Property & Freedom of Contract I
There is now a government that enforces two laws.
There is private property in land.
A landowner can do with the land what they like. They can exclude someone from the land or allow them to use it.
There is freedom of contract for all.
Economic relations must be freely entered into with the consent of all parties.
Contracts specify the obligations of each party and payments to be made.
Coercion is illegal.
Bruno is now the landlord. He owns the land. Angela does not have any land.
Bruno and Angela may enter into a contract in which Angela works the land in exchange for a payment to Bruno in bushels of grain.

9. Third Institution: Private Property & Freedom of Contract II
RIC 12
Angela has an outside option or reservation option Z.
She can get 2.5 bushels of grain per day from family without having to work.
This is her opportunity cost of working for Bruno.
Z is on Angela’s reservation indifference curve (RIC). She won’t work for Bruno for bundles below the curve.
The feasible set is now bounded below by the RIC.
All allocations in pink Pareto dominate Z.
Both Bruno and Angela would like an allocation in the pink set better than having Angela not farm and take Z.
This suggests they will contract on an outcome in the pink set.
Bushels of grain
2.5 Z 24
Angela’s hours of free time

10. Third Institution: Private Property & Freedom of Contract III
RIC 12
The joint surplus is the gains relative to opportunity cost of a contract where Angela works Bruno’s land. Also called gains from exchange.
This is maximized where the MRS of the RIC equals the MRT of the FF. About 5.25 bushels.
Bruno and Angela bargain to point on line between C and D. This line is called the Pareto efficiency curve or contract curve.
Because Angela’s preferences are quasi-linear, MRT=MRS at all the indifference curves between the two shown along the contract curve.
Allocations on the line between C and D Pareto dominate other allocations in the feasible set because joint surplus is maximized. C 9
Joint
Surplus
Bushels of grain
3.75 D 2 Z 16 24
Angela’s hours of free time

11. Third Institution: Private Property & Freedom of Contract IV
RIC 12
If they bargain to:
Point C, Angela gets all of the joint surplus.
Point D, Bruno gets all the joint surplus.
The model predicts they will be on the contract curve, but not where.
Additional information on bargaining power can help.
Compare the following:
Bruno has many potential workers and can always farm himself if he fails to hire.
Bruno is disabled and Angela is the only workers available.
Since the RIC is above the survival constraint, the joint surplus is lower when Angela and Bruno bargain than when Bruno can coerce Angela. C 9
Bushels of grain
3.75 D Z 16 24
Angela’s hours of free time

12. Fourth Institution: PP, FC, & Democratic Politics I
Suppose the government is democratically elected by universal suffrage (i.e. every adult can vote)
If there are more Angelas than Brunos, what Angelas want will tend to be passed.
The Angelas can use their political power to increase their economic bargaining power relative to the Brunos.
Does anyone know of ways in which workers can increase bargaining power?
Unions, minimum wages, maximum hours, child labor laws, unemployment insurance…

13. Fourth Institution: PP, FC, and Democratic Politics II
RIC 12
Suppose the legislature passes a law mandating a maximum working day of four hours and a minimum pay of five bushels.
The allocation is D’. Bruno gets about 2.5, Angela gets 5.
Angela is on a higher indifference curve than her RIC, so she is happier. Bruno gets less grain than at D so he is not happier.
MRT>MRS, so raising the hours maximum would lead to an expansion of joint surplus if it were allowed.
D’ is NOT Pareto efficient.
Do you think D’ is fairer than D? C 9
7.5
Bushels of grain D’ 5
3.75 D Z 16 20 24
Angela’s hours of free time

14. Fourth Institution: PP, FC, and Democratic Politics III
RIC 12
Bruno may now feel some regrets. He could have made Angela as well off as the legislation by giving up some surplus and bargaining to point E. He gets more there.
Bruno might ask Angela to collude with him.
He offers her point F if she will not report to the government that she is working longer hours.
Is this an offer she would accept?
Alternatively, would both would agree to a modification of the law that allows workers and landlords to bargain over compensation for hours worked over the maximum? C 9 F E
Bushels of grain D’ 5
3.75 D Z 16 20 24
Angela’s hours of free time

15. Fourth Institution: PP, FC, and Democratic Politics IV
RIC 12
An alternative legislative proposal is that workers get paid a minimum of 0.75 bushels per hour worked.
This restricts the set of feasible allocations.
The set of Pareto efficient allocations are still where MRS=MRT, and the contract curve is as shown.
Allocation D’’ gives Angela the same utility as D’, but has more for Bruno than the hours restricting legislation.
An increase in the minimum wage would find Angela and Bruno still on the contract curve, with more grain for Angela. C 6
D’’
Bushels of grain D’ D Z
Minimum wage 16 24
Angela’s hours of free time

16. Angela and Bruno: Lessons learned
Technology and biology determine which allocations are technically feasible.
Institutions and policies help determine which allocations are economically feasible.
The allocation chosen depends further on parties’ preferences (what they want) and their bargaining power (their ability to get it).