Please see attached problem regarding firm interactions

Incentives for Research You are the CEO of firralsis Biotech; your rm is a small startup that is researching a drug to increase. mental awareness and reduce dementia in the elderly. You must choose how much effort to devote to the research; in order for your chance of success to be I), you must invest p2. After the success of your research has been determined, you will need to sell the results of your research to Atreides Corporation, if your research is successful, you expect it to have a value of V to Atreides; if your research fails, it is worth U. You expect that in your bargain with Atreides, you will be able negotiate for half of the value of the dmg to Atreides. (Note that your answers will he terms of V, W, and I. Else, to simplify the problem, you may assume that V is small enough mat Arralris and Atreides will never wish to invest enough to be certain of success, i_e., the optimal I! will be strictly less than 1.) a) What price do you expect to obtain for your drug if you are successful? How much research will you choose to do, i.e_, what Probability of success p will you choose? You decide you may wish to try and sell the rm to Atreides before you undertake your research. However, there will be additional transaction costs of t for Atreides if you sell to Atreides before undertaking your research. If Atreides buys the rm before I? is chosen, then Atreides will choose the level ofp but incur all of the research costs. b) At what Prices would both you be willing to sell and Atreides be willing to buy? 1Why might you malse a deal early, even though it involves additional transaction costs? You become aware of another rm, Harhonnen Pharmaceuticals, which values the drug (if your research is successful) at W, where E i: W S V. Hence, if you have not sold the rm to Atreides and your research is successful, you plan to run a secondprice auction for your research. c] Suppose that you are unable to strike a deal with Atreides to sell your rm to them before engaging in research. What price do you expect to sell the drug for in the auction? How much research will you choose to do, i_e., what probability of success y will you choose? How has the possibility of competition affected the holdup problem? d) Suppose Atreides is still interested in buying the rm before research is begun. At what prices {if any) would both you be willing to sell andtreides be willing to buy?r