What are the characteristics of an adverse selection problem?
• Principal (P) wants an agent (A) to perform a task
- P=firm, A=supplier of an intermediate good
- P=firm, A= production worker
- P=government, A=monopolist
- only A knows their production cost (or ability, intrinsic productivity)
- A observes their costs before the contract is signed -> precontractual private information/adverse selection
Which elements does an asymmetric information problem contain?
- q – units of the good A should produce
- S(q) – P’s valuation for the good; S’>0, S’’<0, S(0)=0
- C(q, θ) A’s production costs, unobservable by P
- C(q, θ)= θq
- Cost can be high or low, which is reflected by θ ∈ {θᴸ, θᴴ} with 0 < θᴸ < θᴴ
- A observes θ before P offers the contract
- P only knows that Pr (θ = θᴸ ) = v
- t(q) – transfer payment from P to A
- A’s reservation utility is normalized to zero
Which elements in an asymmetric information problem are observable?
Verifiable variables: quantity q and transfer t(q)
( -> can be part of a contract)
What is the timing of an asymmetric information (adverse selection) problem?
- A observes his type θ
- P offers contract (or a menu of contracts with different price‐output combinations)
- A accepts or refuses the contract
- The contract is executed
What is the revelation principle?
the revelation principle holds that there is a payoff-equivalent revelation mechanism that possesses an equilibrium in which players truthfully report their types to any Bayesian game.
What is the difference in outcomes of asymmetric information problems when there is “Ex Ante Contracting” (i.e. contract is signed before agent learns their type)?
- P can induce the Pareto‐efficient (first‐best) allocation without leaving an expected rent to A. >> Such a contract is optimal for P. It maximizes P’s profit because he obtains all gains from trade.
- When A is risk neutral and contracting takes place ex ante, the optimal incentive contract implements the first‐best outcome.
- It is important when the information asymmetry arises! In this setting, post‐contractual private information does not lead to an efficiency loss (assuming that contracting is costless).
What problems could hinder/change the contract offered in an asymmetric -ex ante- situation?
- Contract imposes risk on A, which is only costless if A is risk neutral.
- No first‐best if A is risk averse or if U < 0 is not feasible (e.g., because A can quit).
What is a selling-the-firm-contract?
- Special type of an optimal contract (there are infinitely many possibilities in this setting)
- A makes an up‐front payment T* to P, which is equal to the expected surplus from the relationship. A receives in return the gross value S(q) if he delivers output q.
- Ex post, A has efficient incentives to produce because he will receive all the gains from production.
- However, P still obtains the entire (expected) value from trade because he extracts A’s (expected) surplus via T*.
In summary, what are the different implications of pre- or post-contractual information asymmetries?
Precontractual asymmetric information can lower the surplus from the relationship.
- The party with the private information has an incentive to use its information strategically.
- Favorable private information leads to an information rent.
Postcontractual asymmetric information is not necessarily a problem.
- E.g., a so‐called selling‐the‐firm contract may provide efficient incentives.
How can you calculate the first-best solution an adverse selection problem?
For the principal, the first best solution is an optimization problem:
profit/utility - production/effort costs
Through taking the FOC and solving for e.g. the first-best quantity and then inserting this into the production function of both types, you get the first-best solution
Would self-selection work for the first best solution in an adverse selection problem with two different types?
usually not - check whether the low-cost type has a positive payoff by pretending to be the high-cost type?
Usually, the low-cost type will receive an information rent!
Which constraints do you have to take into account in an adverse selection problem with two types of agents?
2x incentive constraints
2x participation constraints
-> then check which ones are included in the other ones (usually, IC for low cost type and PC for high cost type remain) - but DO CHECK AT THE END WHETHER THE OTHER CONSTRAINTS ARE SATISFIED (esp. the incentive constraints)
Why can a selling-the-firm contract implement the first-best solution in asymmetric information (adverse selection)?
It is also a situation where the agent does not know their type at the signing of the contract. When the worker makes the up front payment, they internalize the firm’s objective of profit maximization
How does a problem change when the agent in an adverse selection problem does not know their type at the signing of the contract?
The first-best solution can be implemented and the agent does not get an information rent. In terms of solving the problem, there is only one (probabilistic) participation constraint which determines the wages and two incentive constraints that give further conditions for the problem solution.
What should you include in a graph of an asymmetric information problem solution (offering menus for different types)?
- x-axis: quantity
- y-axis: transfer
- two contract lines for the two types
- iso profit curves
- first-best solutions: where iso-profit-curve is tangent to the contract line
Why is the first-best solution usually not implementable in an adverse selection problem?
Because the more efficient/better/sophisticated agent can get information rent from pretending to be the other type, therefore the first-best menu is not incentive compatible.
How is the offered menu in the second-best solution of an adverse selection problem different and why?
The required quantity for the better type is the same (but transfer payment higher), the required quantity for the worse type is lower.
This is to keep the information rent (which comes from the offering to the worse type and is not affected by the better type’s quantity) as low as possible.
