BARGAINING, INSTITUTIONS AND ALLOCATIONS – LESSON 2
LEARNING OUTCOMES
After completing this module, you will be able to:
1. explain, in detail, the stable equilibrium in the case where Angela is free to
farm the land as she sees fit.
2. explain, in detail, the stable equilibrium in the case where Bruno owns the
land and can force Angela to work as he sees fit.
3. explain how bargaining power influences the outcome in a case where there is
free exchange
4. show how different government policies that change the institutional
arrangement governing exchange affect outcomes between Angela and Bruno
5. be able to calculate optimal allocations between Angela and Bruno given
different functional forms for production and utility
5.6 Allocations imposed by force
With the help of his gun, Bruno can choose any point in the lens-
shaped technically feasible set of allocations.
But which will he choose?
He reasons like this:
Bruno:
For any number of hours that I order Angela to
work, she will produce the amount of grain
shown by the feasible frontier. But I’ll have to
give her at least the amount shown by the
biological survival constraint for that much
, work, so that I can continue to exploit her. I get
to keep the difference between what she
produces and what I give her. Therefore I should
find the hours of Angela’s work for which the
vertical distance between the feasible frontier
and the biological survival constraint (Figure
5.5) is the greatest.
The amount that Bruno will get if he implements this strategy is
his economic rent, meaning the amount he gets over what
he would get if Angela were not his slave (which, in this model,
we set at zero).
Bruno first considers letting Angela continue to work 8 hours a
day, producing 9 bushels, as she did when she had free access to
the land. For 8 hours of work she needs 3.5 bushels of grain to
survive. So Bruno could take 5.5 bushels without jeopardizing his
future opportunities to benefit from Angela’s labour.
Bruno is studying Figure 5.5 and asks for your help. You have
noticed that the MRS on the survival constraint is less than the
MRT at 8 hours of work:
- Bruno’s plan cannot be right.
- If he forced her to work a little more, she’d only
need a little more grain to have the energy to
work longer, because the biological survival
constraint is relatively flat at 8 hours of work.
But the feasible frontier is steep, so she would
produce a lot more if you imposed longer hours.
, You demonstrate the argument to him using the analysis in Figure
5.5, which indicates that the vertical distance between the feasible
frontier and the biological survival constraint is the greatest when
Angela works for 11 hours.
If Bruno commands Angela to work for 11 hours, then she will
produce 10 bushels and Bruno will get to keep 6 bushels for
himself. We can use Figure 5.5 to find out how many bushels of
grain Bruno will get for any technically feasible allocation.
Figure 5.5 Coercion: The maximum technically feasible transfer from
Angela to Bruno.
Bruno can command Angela to work
Bruno can choose any allocation in the technically feasible set. He considers letting Angela continue
working 8 hours a day, producing 9 bushels.
LEARNING OUTCOMES
After completing this module, you will be able to:
1. explain, in detail, the stable equilibrium in the case where Angela is free to
farm the land as she sees fit.
2. explain, in detail, the stable equilibrium in the case where Bruno owns the
land and can force Angela to work as he sees fit.
3. explain how bargaining power influences the outcome in a case where there is
free exchange
4. show how different government policies that change the institutional
arrangement governing exchange affect outcomes between Angela and Bruno
5. be able to calculate optimal allocations between Angela and Bruno given
different functional forms for production and utility
5.6 Allocations imposed by force
With the help of his gun, Bruno can choose any point in the lens-
shaped technically feasible set of allocations.
But which will he choose?
He reasons like this:
Bruno:
For any number of hours that I order Angela to
work, she will produce the amount of grain
shown by the feasible frontier. But I’ll have to
give her at least the amount shown by the
biological survival constraint for that much
, work, so that I can continue to exploit her. I get
to keep the difference between what she
produces and what I give her. Therefore I should
find the hours of Angela’s work for which the
vertical distance between the feasible frontier
and the biological survival constraint (Figure
5.5) is the greatest.
The amount that Bruno will get if he implements this strategy is
his economic rent, meaning the amount he gets over what
he would get if Angela were not his slave (which, in this model,
we set at zero).
Bruno first considers letting Angela continue to work 8 hours a
day, producing 9 bushels, as she did when she had free access to
the land. For 8 hours of work she needs 3.5 bushels of grain to
survive. So Bruno could take 5.5 bushels without jeopardizing his
future opportunities to benefit from Angela’s labour.
Bruno is studying Figure 5.5 and asks for your help. You have
noticed that the MRS on the survival constraint is less than the
MRT at 8 hours of work:
- Bruno’s plan cannot be right.
- If he forced her to work a little more, she’d only
need a little more grain to have the energy to
work longer, because the biological survival
constraint is relatively flat at 8 hours of work.
But the feasible frontier is steep, so she would
produce a lot more if you imposed longer hours.
, You demonstrate the argument to him using the analysis in Figure
5.5, which indicates that the vertical distance between the feasible
frontier and the biological survival constraint is the greatest when
Angela works for 11 hours.
If Bruno commands Angela to work for 11 hours, then she will
produce 10 bushels and Bruno will get to keep 6 bushels for
himself. We can use Figure 5.5 to find out how many bushels of
grain Bruno will get for any technically feasible allocation.
Figure 5.5 Coercion: The maximum technically feasible transfer from
Angela to Bruno.
Bruno can command Angela to work
Bruno can choose any allocation in the technically feasible set. He considers letting Angela continue
working 8 hours a day, producing 9 bushels.
