Land Flashcards
Principal Agent Theory
- Only landlord can choose the type of contract
- Perfect monitoring is not possible (too costly and other things to do)
- Therefore imperfect monitoring: cannot contract on cultivator’s effort
Cultivator’s revenue?
αf(e)+w
- where e is effort
- f(e) is harvest (function of effort)
(decreasing returns to effort, so f’>0 (growth of harvest is greater than 0) - Now, harvest depends solely on effort e
- α: share of the harvest kept by the cultivator
w: wage obtained by the cultivator
Application of formula: examples of fixed wage, sharecropping and fixed rent
If fixed wage:
- α=0, w>0 (share kept by the cultivator is 0, wage is greater than 0)
If sharecropping:
- 0<0
Cultivator keeps all the harvest, but pays landlord a fixed rent (wage is less than 0, but share kept is 100%)
Cultivators profit with cost of effort?
c(e)=cost of effort:
- c’>0 (cost increases with more than 0)
- and c’‘>0: rate of increase in cost is more than 0
Conclusion of C’s profit?
C’s profit is: αf(e)+w-c(e)
maxe [αf(e)+w-c(e)] ?
first derivatives must be equal to zero
αf’(e)=c’(e)
α=c’(e)/f’(e)
- (share kept by the cultivator = growth in cost of effort and growth in harvest)
Math: how to maximize profit?
What happens if (e) effort goes up?
If e (effort) goes up:
c’(e) ↑
f’(e) ↓ , so 1/ f’(e) ↑
So c’(e)/f’(e) ↑
So α ↑
- increase in cost (goes up)
- decrease in harvest, so 1/growth in harvest goes up?
- so c’(e)/f’(e) goes up
- so share of harvest kept by the cultivator goes up
Therefore: α ↑ means e ↑
Effort increases if α increases
Landlord should increase α to increase e
Effort increases if ….
What should the landlord do?
Effort increases if α (share kept by the cultivator) increases
Landlord should increase α (share kept by the cultivator) to increase e (effort)
Marginal benefit
Marginal cost
MB: α * increase in production due to increase in effort
MC: increase in cost due to increase in effort
Contracts and incentives: intuition?
- Marginal benefit decreases after a while (decreasing returns to effort)
- Marginal cost increases
- At some point, marginal benefit < marginal cost
- I stop where marginal benefit = marginal cost
- If α ↑, marginal benefit ↑
(It becomes more interesting to exert effort)
THUS: c has more incentive to provide maximum effort if he keeps more of the harvest (because MB is higher)
- If he only keeps 50% of the fruits of his effort (Harvest), then he should keep his effort lower
Graphic: owner??
Where to maximise economic surplus?
Cultivator wants to maximize economic surplus?
= Difference between harvest and cost (e* efficient level of effort)
Graphic: sharecropping?
Because efficient level of effort (e*) when sharecropping is lower (because economic surplus is lower)
Landlord’s profit in sharecropping?
Distance between αf(e) and f(e) is:
(1- α)f(e) = landlord’s profit
Which one is better?
Fixed rent is clearly better then sharecropping because:
- it maximises economic surplus
- the landlord can charge a high rent
- it gives good incentives to cultivator to exert effort
Studies on sharecropping and omitted variable bias in empirical test in sharecropping?
- Where studies find a negative correlation between harvest and sharecropping. (bs quality