Question

The following set up applies to the next four questions Consider the following relationship between firm A and firm B. Firm A wishes to buy an input I from B. Firm A wants an input that is specialised to its production processes; a specialised input I costs B $10 to make. Alternatively, B can deliver a low-quality product that costs $0 to produce, but is of no benefit to A. The timing is as follows:if A decides to trade, A agrees to pay firm B a price of p = $30 for a high-quality input I; payment p = $30 is then made from A to B; B delivers the input that can either be of high or low quality; finally, A discovers the quality of the input that has been delivered. 15. Assume that there are two types of producers of the input I honest and dishonest. With probability 0.8 firm B is honest; if B is honest she will always produce the high-quality input if that is the contract that has been agreed upon. If B is dishonest she will always cheat on the agreement and produce and sell a low-quality input to A.

Answer 1

From, the given set of information, we see, Price of Input, I = $30

We can compute the following table regarding input delivered by B to A:

Product	Specialized	Low Quality
Probability	0.8 (Honest)	0.2 (Dishonest)
Cost of Production ($)	10	0

Now, Firm A can underwrite a contract for $5.

15) Maximum Benefit that accrues to A from not underwriting a contract:
      (Value of the high quality input to A) – (Underwriting Costs) = $(30 – 5) = $25

16) Now, Net Payoff of Firm B from selling the high quality input to Firm A: (Price of Input) - (Cost of Input) = $(30 – 10) = $20

Firm B’s pay off from selling the high quality input to A under a trigger strategy for infinite periods:

20 + 20∂ + 20∂² + …….. (up-to infinite rounds) = 20(1 + ∂ + ∂² + ……..) = 20/(1 - ∂)