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
3 models of why sharecropping exists
- Insurance
- Double sided incentives
- Limited liability
Risk aversion?
An individual is risk-averse if he/she prefers an amount X for sure, to a lottery with expected value X
Example of risk aversion?
- 500 for sure?
- Or 800 with probability 1/2, 200 with probability 1/2
- Expected value of lottery
E(lottery)= 1/2800+1/2200=500
Variables in math function of risk aversion?
U: utility function
H: high payoff with probability p, L low payoff with probability (1-p)
When is an individual risk-averse?
U [pH+(1-p)L] > pU (H) + (1-p)U (L)
OR
U(50o) > weighted AVERAGE of utilities of H and L payoffs (on a graph)
What’s better in terms of insurance for cultivator…?
FIXED WAGE
But sharecropping might be a good compromise between:
- fixed rent (that provides the most incentives to exert effort)
- and fixed wage (that provides the most insurance in case of natural disasters)
… For landlord?
Fixed rent!
Model 2: Double-sided incentves
Incentives for the landlord too! What if landlord can contribute to the success of the harvest? (Advice, seeds, fertilisers…)
NO incentives for landlord’s effort if fixed rent
MAXIMUM incentives for landlords’ effort if fixed wage
AGAIN: sharecropping a good compromise between incentives for cultivator and incentives for landlord
What’s better in terms of insurance for each party…?
- Cultivator: fixed wage
- Landlord: fixed rent
Again: sharecropping a good compromise (If landlord is actually important in production)
