Notesale: Turn your study into money

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Model of a principle and an agent
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The problem is that of moral hazard - the actions of the agent and the state of nature are not observable
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It is high if and only if effort is high and the state of nature is good
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There is a cost for agent to exert high effort
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This is a constraint on the principle (the state must
allow the agent to retain this amount of food to survive
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In equilibrium, the contract takes this into account
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The principle
cannot reduce the payments such that the agent barely survives, because the agent could just shirk and receive y
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Need multiple period because we’re interested in the contract: the incentive scheme which has a
carrot (bonus) and a stick
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V = value of employment
delta = time discount factor
0 = value of unemployment
At the end of the first period the agent could be punished and obtain 0, or stay and retain the job and obtain a level of
welfare of V
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There are two types of contracts: using dismissal, or not using dismissal (only relevant in the first period)
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punishment incentives the agent on account of the bonus payment
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If b2=y the value of employment in the second period for the agent = the cost of effort (V=y)
The principle pays the agent full compensation for the cost of effort (y) + a bonus (b) which is equal to y
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agent obtains is income above subsistence of the cost of effort
principle must compensate agent for effort with additional bonus payment of size of compensation

(9:40)
Now we go the first period optimisation, and the objective function of the principle is to minimise the cost of
incentivising the agent, subject to the incentive constraint compatibilities holding
This is expected utility of agent if they exert high effort: (LHS)

This is expected utility of agent if they exert low effort: (RHS)

LHS > RHS otherwise agent will not exert effort

Agent know states of nature, so this is only relevant when the state of nature is good
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But if the state of nature is good, the agent knows that if he works he receives
the bonus + (minimum wage - cost of effort) + value next period being employed * discount factor
If d=0, pure carrot contract means that the agent retains the job, for sure -> just receives w
But the agent knows he could avoid working: benefit from shirking is receiving
the minimum wage (without paying the cost of effort) + income next period if not dismissed (d<1) + income next
period if signal on state of nature is misleading
§ Agent takes into account the probability that the state of nature is misleading: q= accuracy of the signal
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If q is close to 1, and agent is shirking, very high chance they will be dismissed
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The threat of dismissal by the principal (if output is low, when signal on state of nature is good) reduces the bonus
as the agent doesn’t want to be dismissed
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Principle compares using the stick and carrot, to pure carrot
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If the IC holds this means that the agent is working hard in every period
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The other cost, in addition to the bonus, is the probability that the agent is dismissed
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The agent is dismissed
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When is this cost high/low?
We are interested in transparency/ accuracy of the signal
If the signal is accurate (q=1)

Then this (the cost of wrongly dismissing the agent in a stick and carrot contract) is very low, and therefore the principle
is justified in using a stick and carrot contract
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g, Ancient Egypt) because cost associated with
stick and carrot contract (falsely dismissing the agent) is very low
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If q < q^ then we will use pure carrot contract
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In terms of why q matters:
(1-p)(1-q) is expected probability of dismissal [bad state of nature and incorrect signal]
Expected cost of dismissal:
(1-p)(1-q)x

Calculating the expected income of the principle

Agents prefers for q to be low (q=0
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He wants a bad signal so that’s he’s more likely to get away with shirking

Figure is taken from the paper, so is for the more general case
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Threshold level of accuracy of signal, above which principle chooses the stick and carrot
Total income falls once the stick enters the contract: because there are wasted resources in the economy due to the
cost x of replacing agents - an inefficiency arises (1-p)(1-q)x
As q increases there is less and less wasted resources as the signal becomes perfect
Once the stick is in the contract, the more accurate the signal, the less the stick is used, because punishment rarely
happens
Punishment is effective when it is correlated with the behaviour of the person you want to incentive
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Standard reason in the literature for granting property rights:
The explanation for granting property rights (protecting property - public goods), from a non-benevolent govt because it
creates incentives for farmers to exert high effort
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Over output the standard explanation is correct: govt provides property rights to grant incentives
For factors of production, it is not clear why ex-post the government would like to suddenly take the land
away (as the king will not become a farmer & will have to find a new tennant)
But there may be a benefit in not granting property rights over land by telling the farmers “we give you this
land to use, but it’s not really yours
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This generates incentives, despite going in the opposite way to the standard argument
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The standard argument of granting property rights to create incentives is relevant for output, but not factors, like land
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By not using this threat (granting property rights) incentives to work hard are actually reduced - because
the farmer’s land will not be taken away regardless of effort
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In reality, there isn’t a contract between the elite and each farmer
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There were heads of regions etc
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But if there is low transparency, village heads would be autonomous

State Concentration
We can think of two main cases:
Ancient Egypt
1
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Local farming is transparent to local officials but not to the state
So there would be a stick & carrot farming contract, but a pure carrot contract between officials and the state
Implies: Peripheral Centres are strong
City states

Part 4
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The rivers of Mesopotamia are fed by rain and melting snows - risk of flooding - mismatch between when water was
needed and when it was received
Therefore, canal system instigated

Unlike, Egypt: there was perfect matching
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A simple geographical difference: the timing of the flow of the river and its matching to the farming season
created different irrigation systems - which created the big difference in transparency
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The local elite of Lower Mesopotamia had full control of the supply of water and therefore a lot information
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Tennant-farmers do not own land & have no property rights, so no disputes

In Mesopotamia, information didn’t go straight to centre, which is why local elite was autonomous and had power
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Strong central state with high state capacity in Egypt rose faster -> pyramids

I expect you to know models we went over in detail
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