Information Economics

Question 1

What is adverse selection?

Answer 1

Market situation in which one of the parties is informed while the other is not and, for the uninformed party, the fact that the other party wants to contract is bad news

Question 2

What happens in signalling?

Answer 2

In the first stage, high-ability workers decide the education signal as a function of ability, s(a)
In the second stage, firms can condition wages on education level, w (s)

Question 3

What happens with a separating equilibrium? And under what circumstances can this happen?

Answer 3

High-ability students choose s = 1 while low-ability students choose s = 0
Firms offer w (1) = aH and w (0) = aL

• Firms are acting rationally, given the education pattern, with a salary w (1) (respectively, w (0)) to educated (respectively, uneducated) students. Above this, they make losses. Below this, they fail to hire them because of competition
• High-able islanders wish to educate given firms’ reaction:
  aH − c(1; aH ) ≥ aL − 0
• Low-able islanders wish not to educate given firms’ reaction
  aL − 0 ≥ aH − c(1; aL)

Question 4

What is a pooling equilibrium? And under what circumstances can it occur?

Answer 4

An equilibrium in which firms offer the same salaries to all workers
All students choose s = 0
Firms offer an intermediate salary w = λaH + (1 − λ)aL but the market does not unravel

Firms are acting rationally given the education levels with an intermediate salary w = λaH + (1 − λ)aL. Above this, they make expected losses. Below this, they fail to hire them
- High-able islanders decide not to educate, despite they can migrate
λaH + (1 − λ)aL ≥ aH − c(1; aH )
- Notice that low-able islanders will also decide not to educate, as they have a higher cost. No check needed

Question 5

How can a monopolist screening through products?

Answer 5

• A monopolist can sell a product in different qualities/dimensions and at different prices. We write (d, p) for the contract offered, that has dimension d, and price p
• There are two types of consumers:
  High-type (H) in proportion λ
  Low-type (L) in proportion 1 − λ
• High-type buyers value more the quality of the product. Let vH > vL and utility of buying is:
  uH (d, p) = vH d − p
  uL(d, p) = vLd − p
• Profits of the monopolist for a sale are p − c(d), for a convex cost function

Solution for high type market
- Find (dH , pH ) to maximise pH − c(dH ), constrained by willingness to buy vH dH ≥ pH (IR)
- Extract all rents from them vH dH = pH
- Find the optimal product for this type, maximising vH dH − c(dH )
- FOC: vH = c′(dH )

Solution for low-type market:
- Find (dL, pL) to maximise pL − c(dL), constrained by
willingness to buy vLdL ≥ pL (IR)
- Extract all rents vLdL = pL
- Find optimal product for this type, maximise vLdL − c(dL)
- vL = c′(dL)

Question 6

What should an uniformed monopolist do?

Answer 6

Design some (sub-optimal) contracts allowing to screen for free:
- Offer (dH , pH ), (dL, pL)
- Buyers want to buy (IR)
- Each type prefers their product (IC)
- Largest possible profits

Question 6

What are the conditions for the uninformed monopolist separating solution?

Answer 6

max λ(pH − c(dH )) + (1 − λ)(pL − c(dL)) subject to

vH dH − pH ≥ 0 IRH
vLdL − pL ≥ 0 IRL
vH dH − pH ≥ vH dL − pL ICH
vLdL − pL ≥ vLdH − pH ICL

IRH is an inequality, IRL must be an equality otherwise raise both prices.

ICH is an equality or just raise the price. ICL is an inequality

maximise profits to find solution

Question 7

What is moral hazard?

Answer 7

Market situations in which:
- the outcome of a contract depends upon specific actions of one of the parties contracting but
- the other part cannot verify/monitor such actions, remaining uninformed

Question 8

How should a firm figure out the minimum wage to pay to guarantee high effort (in principal-agent)?

Answer 8

First, we need the agent to like the contract (IR). Second, we need the agent to do what has been hired to do (IC), and not to act differently.

min (1 − pH )w1 + pH w2 subject to
(1 − pH )u(w1) + pH u(w2) − cH ≥ ̄U
(1 − pH )u(w1) + pH u(w2) − cH ≥ (1 − pL)u(w1) + pLu(w2) − cL

usually will be equalities as if IC is not an equality transferring too much risk, and if IR fails to be equality are paying too much

Question 9

What is the agency cost?

Answer 9

The difference between the profits of the firm in the full-information case and in the moral-hazard case are usually known as the agency cost

Question 10

How is the optimal decision different in the full information vs moral hazard case?

Answer 10

Notice that eH is less desirable in the presence of moral hazard than in the full information case
- eL requires the same compensation
- eH requires more compensation because we can only achieve it by transferring some risk

If the optimal decision with full information was eL, it will remain the same, and the firm has no extra cost (pays cheap and expects nothing)

If the optimal decision with full information was eH , two things may happen:
- The optimal decision is yet eH with moral hazard; the firm has an additional cost to compensate for the risk transferred
- The optimal decision is now eL with moral hazard; the firm prefers not to pay the huge additional cost and cuts loses somewhere in the middle (there is a loss, obviously)