0:04

Now consider the sharecropping contract.

The agent is paid a given share (say alpha) of the total revenues.

Formally the compensation C is equal to the product of pbar times Q

(i.e., prices times yield, that is the revenue) and the share alpha.

This compensation scheme has a property.

If effort increases, yield increases, revenues increase, and therefore, C increases.

How does this property affect efficiency?

Consider the agent utility function and substitute the compensation for C,

then substitute the yield formula for Q.

This is what we obtain.

Now consider the first order condition of utility maximization with respect to effort.

Compared with the fixed wage case, here, there is an important difference:

the marginal benefit of effort is positive.

The more the agent works, the more he gains.

This means that zero effort is not appealing anymore.

True, for zero effort there is no cost.

But, also there is no gain.

Maybe, the agent is willing to put in some effort in order to get some compensation.

Actually, the agent optimal effort is this: the alpha share times prices divided by two.

Unless alpha or price are equal to zero, this is strictly positive.

Meaning that the farmer will choose an effort level that is increasing with the market price for the crops,

and the share of revenues he will get as compensation.

The higher is the share, the more incentives the farmer has to apply effort for.

Note that the principal can elicit a desired level of effort simply by playing with the share alpha.

Let’s store this result here for the moment and let’s move to the principal’s point of view.

2:09

Consider the principal’s utility function, substitute the compensation for C, and simplify.

Now substitute the yield formula for Q and the formula on top of the screen,

for estar because the agent will apply the optimal effort, and the principal knows that.

Consider the effects of a change in alpha on the principal’s utility.

On one hand, an increase in alpha reduces the principal’s share of revenues.

More revenues for the agent, less revenue left for the principal.

This has a negative impact on utility.

On the other hand, an increase in alpha elicits more effort, therefore, more yield,

and the total value of farming increases.

In this case, a higher share for the agent means a larger coordination surplus.

Here you see the problem of choosing between surplus maximization and surplus appropriation.

By increasing alpha, the principal creates a bigger pie (the farmer works harder),

but she/he gets a smaller slice (left yield is left for her/him).

The optimal solution depends on the trade-off between these two effects.

We do not need to walk through the algebra, but if you take the first order condition

of the principal’s utility maximization with respect to alpha, you will obtain

the result alpha star equals one half.

Substituting the optimal alpha in the agent’s optimal effort equation

(the equation on the top of the screen), you obtain that the optimal effort given that the principal offers

the optimal share as estar equals pbar divided by 2.

These numbers do not mean much per se, but they give an idea

of the type of equilibrium we are talking about.

The question is “Is this equilibrium self-enforcing?”

Let’s store the results up here.

Consider our usual representation of farming revenues,

the optimal share is 50% and lies approximately here.

Note that sharecropping agreements leave more surplus to the farmer than fixed wage.

Is this contract incentive compatible?

The key point is that for alpha equals 0.5 the farmer maximizes the utility setting

e = pbar divided by 4.

He maximizes utility by fulfilling the contract.

There is no need for enforcing or monitoring.

The effort level is a free decision of the farmer.

He wants to work that amount of time, because it is in his own interest.

An important point is that sharecropping is more costly than fixed wage

(the farmer gets an higher share of the coordination surplus).

You can consider this is the price that the landowner must pay for not being able to monitor and enforce e.

Yet, sharecropping has information requirements, too.

The landowner must be able to observe Q. Otherwise the farmer can cheat and hide part of the yield

(taking it all for himself, instead of sharing).

Now let’s consider the rent contract.

Here the farmer pays a fixed lease (say 1000€ per hectare)

to the landowner and takes the entire production.

The farmer is free to use any amount of effort he sees fit.

Formally, the compensation equation is Revenues minus Lease.

The key point is that the lease is independent of effort.

The farmer always pays the same amount.

An increase of effort always increases compensation because it increases yield and revenues.

However, a low value of effort might result in negative compensation.

If you consider it carefully, land rental is like a sharecropping agreement

with alpha=1 and a fixed cost (the lease).

Because the lease is a fixed cost, it does not change the farmer’s production decision,

and the optimal effort level is obtained by the formula of sharecropping, setting alpha = 1.

That is pbar divided by 2.

This is higher than the sharecropping outcome (remember, it was pbar divided by 4),

meaning that land rental increases the total value of farming.

In a land rental agreement, the optimal rent splits the coordination surplus between

the farmer and the landowner.

As per the Coase Theorem, the distribution of the surplus, that is, the share of value

the landowner can appropriate, depends on the relative bargaining power.

Is land rental incentive compatible?

Once the rent is paid, the farmer has no incentive to shirk.

He will get the entire yield, therefore, refraining from effort does not harm the principal.

Most importantly, land rental has almost no information requirement.

In our example, we compared three alternative contracts: fixed wage, sharecropping and Land Rental.

Let’s compare the principal’s appropriation share and the information requirements.

In a fixed wage contract, the principal can appropriate almost all the coordination surplus,

so the appropriation share is high.

Yet, the information requirements are strict: the agent effort must be observable and

sanction must be immediate, effective and costless/free.

In a sharecropping contract, the coordination surplus is shared between the principal and the agents.

The appropriation share is usually lower than a fixed wage.

At the same time, the information requirement is less strict than a fixed wage.

The principal does not need to observe e, observing the yield is sufficient.

Finally, in the land rental case, the appropriation rent depends on the relative bargaining power of the parties.

If the landowner has high bargaining power (for example, land is scarce),

she/he can appropriate a large share.

If her/his bargaining power is low (for example, land is abundant), then the appropriation share is small.

The contract, however, has little information requirements.

The main conclusion is that there is no contract that is always preferable.

The optimal contract design depends on the specific circumstances we are working within.

In this example, the contract choice depends on the information such as the monitor capability.

Other factors, such as other types of transaction costs can affect our choice.

Well, this is all for Lesson 3 and Module 11.

I hope you enjoyed this topic and my videos.

We will meet again in Module 12, when we will talk about modern retail, coordination and quality.

In the meantime, have a good day and good luck with this MOOC.