This post is aming to provide a intuitive explanation on the Institutional Economics course, taught by Prof. Dr. Eva Hoppe, University of Bonn, Summer Term 2022.
Case 1 : basic case, hidden action
Setting:
Date 1: Principal offers contract
Date 2: Agent accepts or rejects
Date 3: Agent chooses effort level e
Date 4: Principal's return v is realized, realization of v depends on effort e
Date 5: Contractually specified payment t is made
Principal's payoff : v - t
Agent's payoff: t - c(e) (c(e) is the cost function with e)
Agent's effort e is hidden action, Principal does not know how much effort Agent has made.
Here Principal can be seem as employer, and Agent is the employee. Employer hires employee to produce some good, and the employee pays personal effort e, and creates corresponding cost c, then employer gets return v, and he or she has to pay his or her employee salary t.
The solution suggests that employer uses "sell the shop" contract, which gives employee all return v minus expected total surplus at the first best production volume. Such contract gives employees incentives to choose first best effort level.
Here "first best" means that as if there is no hiring or contracting actions, and only one person in such production process, and what action he or she will choose to balance return and maximize his or her total surplus.
This is the case when employer has the dominant bargaining power, and he or she decides the distribution of surplus products (which is the return v minus cost c). Meanwhile, employees under such contract only could gain 0 expected surplus payoff, and he or she earns more or less than the cost by chance, since total return v is a random variable which its distribution usually depends on effort e.
Such contract can be understood as "franchising" in real world, for example, in China, "franchising" some popular brands' milk tea street shop required a lot membership fee and recipe fee, after substracting such fee, shop owner's (Agent's) monthly payoff keeps as a middle class white collar's monthly income, here this only compensates shop owner's living cost and "human capital" cost.
Case 2 : Hidden action and limited liability
In most hiring relationships, employees do not have much money for franchising or money paid to employer as deposit. In other words, they are under limited liability.
Here is our setting:
Assumption: Agent has no wealth
Agent's unobservable effort:
e could be el or eh with 0 < el < eh <= 1, el is low effort, eh is high effort
Effort costs (non-monetary disutility of effort):
c(eh) = c
c(el ) = 0
Principal's verifiable return:
v could be vl or vh (value low or value high) with 0 <= vl < vh
Technology:
Probability of vh equals to effort level e
Here we are facing a trade-off of choosing which effort level in the first best solution, according to the comparison of expected total surplus. Then we can set payment tl and th according to realization of vl or vh to the Agent. If Principal want Agent implement high effort, then the incentive scheme should be: tl = 0, and th = c/(eh - el). Employer has to pay an positive incentive to encourage employee inputs high effort. If employer only wants low effort input, then he or she could just make tl = th = 0, no wage no effort. Which effort level that employer prefers depends on the expected value of surplus he or she could gain. But because of such transmission process, employers have to pay more when he or she wants to have high effort level, and this will lead to a inefficiency in employers' decision boundary.
In addition, if employee has full bargaining power, he or she could act as in first best case, and the employer here plays only some sort of redundant role.
Case 3 : Hidden information (one-sided)
Here we assume Agent has his or her hidden information, that is cost c, and then Agent decides production or trading quantity x. But there is no wealth limitation on Agent.
For the sake of simplicity, we assume the investment or effort level e ( or denoted as x in some settings) does not influence distribution of cost or value, cost level is private information by the Agent.
Date 1: Principal offers contract
Date 2: Agent accepts or rejects (reserv. utility 0)
Date 3: Agent learns his type c >= 0
Date 4: Agent chooses quantity x >= 0
Date 5: Contractually specified payment t is made
Principal's payoff: v (x) - t
Agent's payoff: t - cx
c is a random variable
Distribution F (c) is common knowledge
Only agent learns realization of c (private information)
Quantity x is verifiable
Here implement the "sell the shop" contract works, and the franchising fee or deposit is the expected total surplus on cost, correspond with first best quantity x determined by cost.
Interpretation at here is similiar with Case 1.
Case 4 : Hidden information (two-sided)
Here imagine Principal is a Buyer who orders some goods from Seller (Agent).
Timing:
Date 1: Principal offers contract
Date 2: Agent accepts or rejects (reserv. utility 0)
Date 3: Principal learns his type v >= 0, Agent learns his type c >= 0
Date 4: Contractually specified trade decision x =0 or 1 and payment t
Principal's payoff: vx - t
Agent's payoff: t - cx
v is a random variable, cumulative distribution function G(v )
c is a random variable, cumulative distribution function F (c)
stochastically independent
Only principal learns realization of v
Only agent learns realization of c
Trade decision x is verifiable
We could implement a contract that at date 3.5 Buyer announces his or her value v_hat.
And use some sort of "sell the shop" contract, then Buyer has incentive to announce his or her real value v_hat = v, and Seller will tend to trade x as in first best case. Here is franchising fee or deposit for Seller is the expected surplus on cost c conditional on reported value v_hat and trade decision based on c and v_hat.
Here we can imagine Buyer is a supermarket, and Seller is some supplier of some particular good. And now Buyer has the market power, and v is retail price. Then Seller should decide whether to deliver produced goods under cost c, if v_hat is smaller than c, then Seller prefers to not trade, and keep these as inventroy.
Note that in such moral hazard setting, the bargaining power only influences the reallocation of total surplus, but not the amount of total surplus under proper contracts.
Comments