I. Two Definitions
Asymmetric Information: Is a situation where one party to an economic activity has more information the other parties in the economic activity.
Moral Hazard: Is a situation where a person modifies their behavior due to a rule change that was not intended to affect their behavior.
II. Principle-Agent problem with full information
A franchisor (principle) contracts with a franchisee (agent) to produce and/or sell a product in a local market.
Local demand depends on two things:
a) the state of demand: either high or low.
b) the level of quality or service the agent provides. This will be denoted as X
The state dependent revenue functions are:
State 1 (Low): R1 = 10 + 4*X1
State 2 (High): R2 = 12 + 6*X2
The cost of producing x in each state is C1 = (X1)2 and C2 = (X2)2
Therefore profits in each state are
p1 = R1 - C1 = 10 + 4*X1 - (X1)2 and p2 = 12 + 6*X2 - (X2)2
Using calculus to maximize profits in each state, we get: X1 = 2 and X2 = 3.
The profits to be shared between principle and agent in each state are:
p1 = 18 - 4 = 14 and p2 = 30 - 9 = 21
Suppose the income the franchisee can earn in his next best alternative is 2. The franchisor can then charge the franchisee a fee in each state that extracts all the economic profit, or
State one fee: F1 =12 State two fee: F2 = 19
profits for the franchisee (agent): p1A = 14 - F1 = 2 and p2A = 21 - F2 = 2.
The model and equilibrium are shown in Figure 1.
Figure 1 shows the equilibrium service, costs, and sales in each state.
In state one, X1 = 2, Profits to be shared equals C to D.
In state two, X2 = 3, Profits to be shared equals A to B.
III. Principle-Agent problem with Asymmetric information
Now suppose the franchisee has better information about local demand than the franchisor. Specifically, the franchisee knows what state exists at any point in time, but the franchisor does not. Furtheremore, the franchisor cannot observe directly X, the level of service or quality.
However the franchisor can measure revenues, R, and knows that in a good state R = 30 and in the bad state R = 18. Therefore he infers the state from observed sales. Any sales other than 30 or 18 means that the franchisee is not supplying the correct amount of X.
The franchisee knows that if sales are 18 in the good state, the franchisor will think it is a bad state and only charge him the bad-state franchise fee (F1).
By setting X = 1 in the good state, R2 = 18 and C = X2 = 1.
The franchisee's profits are: R2 - C -F1 = 18 - 1 -12 = 5. Thus it pays the franchisee to
cheat.
Game Tree
PROBLEM: How can the franchisor (principle) ensure that the franchisee (Agent) does not cheat?