Question 

DrugCo buys an input that costs $p from the market for its drug production. DrugCo knows that 4/5 of suppliers will provide a good input that the firm can use to produce $100 value of output and 1/5 of suppliers will provide a low quantity input that produces $60 value for the firm. The firm is matched with a potential input supplier in the market, but cannot tell whether it will supply a good or low quality product.

a. If DrugCo does not buy the input from the market, no production will occur. What is the maximum price p that DrugCo is willing to pay for the input? Show your working. (2 marks)

b. Assume now that DrugCo can also buy the same input from its long-term trading partner - Compound Corp at a price c. Compound Corp is supplying a good input for sure. What is the most the firm is willing to pay to Compound Corp for the input if the input costs $20 from the market? Show your working. (2 marks)

Now assume that Compound Corp can choose to supply a good input or a low-quality input. The cost of producing a good input is $10 and that of producing a low-quality input is $5. DrugCo will pay $25 to buy the input from Compound Corp.

c. If there are two years in which trade can occur, will Compound Corp supply a good input or a low-quality input in the first period? In the second period? Explain your answer. (2 marks)

d. Will DrugCo sign a 2-year contract with Compound Corp or buy from the market? Explain your answer. (2 marks)

e. Now trade can occur potentially an infinite number of times. DrugCo adopts a trigger- strategy if Compound Corp ever supplies low-quality inputs. Both parties have a discount factor of δ. For what value of δ will Compound Corp always supply good inputs? (2 marks)