:Clearly solve the following problems.

QUESTION 4 Consider a market for a homogeneous good, which is produced at zero cost. Market inverse demand is given by P=1-20 (where ( is industry output). Let #, be monopoly profits and , be Cournot duopoly profits in this market. A firm, call it M, is currently a monopolist in this market but faces a potential entrant, call it PE. They play the following game. M chooses a level of investment, A, where & can be any nonnegative number. This decision is observed by PE. Next, PE decides whether or not to enter the market. If PE does not enter, M remains a monopolist and earns profits equal to (2* + 1), -*, while PE earns zero profits and the game ends. If PE enters, M observes PE's decision and decides whether or not to exit the market. If it exits, it earns 0-k, while PE earns profits equal to * -F, where Fis the cost of entry. If M does not exit, then we have a Cournot duopoly, with corresponding equilibrium profits of (2k +1)x -k for M and *-F for PE. Assume throughout that " > F> >, and that, if indifferent between exiting and staying, M chooses to stay and this is common knowledge between M and PE. (a) Calculate , and #2- (b) Assume that the value of @ is common knowledge. Show the structure of the game by sketching the extensive form. (c) Still assuming that the value of O is common knowledge, find the subgame-perfect equilibrium of the game (clearly, your answer should be conditional on the value of @). For the remaining questions, assume that there are only two possible values of k: 0 and &, that is, ke (0,A) . The value of & is private information to M. However, it is commonly known that there are only two possible values: , and @, , with @, > 0, >0. Let pe (0,1) be the probability that PE assigns to @, [and (1-p) the probability that PE assigns to 0, ]. PE's beliefs are common knowledge between Mand PE as is the fact that M knows the true value of d. Thus we have a situation of incomplete information. (d) Using the Harsanyi transformation sketch the extensive form of the corresponding imperfect-information game. Make sure that information sets are clearly drawn. [You can simplify the sketch by replacing the Cournot duopoly interactions with terminal nodes and associating with them the corresponding equilibrium profits.] (e) For the game of part (d) show that under the following parameter restrictions there is no pure-strategy separating weak sequential equilibrium (that is, there is no pure-strategy equilibrium where the two types of A make different investment choices): 15 (f) With the parameter values of part (e), and assuming that the players are risk neutral, for what values of p is there a pooling weak sequential equilibrium where both types of M choose k and, observing this, PE stays out?2. Caroline's productivity is always $200,000, per period. Hume's productivity, per period, is high ($300,000) with probability 0.5, and low ($100,000) with probability 0.5. All human capital for both is purely general, i.e. not firm specific. You do not know until after the first period if Hume is high or low productivity. There are no firing restrictions. There are two periods, no discounting, and firms are risk neutral. a. (5 points) What is the expected output from Caroline in any given period? b. (5 points) What is the expected output from Hume in any given period? Assume that the salary is $100,000 per period. c. (5 points) What is the expected profit from hiring Caroline? d. (5 points) What is the expected profit from hiring Hume? e. (5 points) Given your answers in a,c,d, who is a better hire? 3. (5 points) Marginal product of labor (MPL) of a worker who is employed in a price-taking profit- maximizing firm is equal to: i. Zero. ii. The value of her output plus the rental cost of capital used for her job. iii. Her wage. iv. Rental cost of capital that is used for her job. 4. (5 points) Consider a firm that makes zero profit on a marginal worker; i.e., the change in the firm's profit as a result of hiring an extra worker is zero. Most likely: i. The firm employs the optimal number of workers. ii. The firm should hire additional workers. iii. The firm's profit is equal to zero. iv. None of the above. 5. (5 points) A recent productivity study in your firm showed that, on any given day, the output produced by workers who graduated high school is the same as the output of the workers who are high school dropouts. The only difference between high school dropouts and high school graduates is in the turnover rate. High school graduates always stay with the firm for their entire career of 40 years. High school dropouts quit after a year with probability 50%; if they do not quit after a year, they always stay for the remaining 39 years of their work-life. Suppose that the interest rate is zero and that the market wage of a high school graduate is $ 28,000 per year, while a high school dropout commands a wage of $24,000. The cost of a quit to a firm is $15,000. What type of labor should this firm hire? i. Only high school graduates. ii. Only high school dropouts. iii. Both types. iv. More information is needed in order to answer this question.6. (5 points) Assume that a start-up is hiring. The firm does not know how many employees to hire. New hires lead to increased revenue, but also increased cost in terms of wages. The firm's sales depend on its employees according to the following equation: Sales = N x 100 - N3 where / is number of employees. The wage is fixed at $50 per employee. How many employees should the firm hire? Illustrate your answer with the help of a table of figure. 7. A firm is hiring and has 30 positions that it needs to fill. Each position is for 1 year only. The firm has received 1000 applications. Among the applicants are both high-skilled and low-skilled workers, but the firm does not know the individual applicant's type (high- or low-skill). The firm knows that 25% of the applicants are high-skilled and will produce a value of $100,000 per person per year, and that 75 are low- skilled and will produce a value of $50,000 per person and year. a. (5 points) What is the expected value if the firm hires 30 of the applicants randomly, without screening, and pay $40,000 per employee in wages? Calculate the total expected profit as well as the expected profit per employee. b. (5 points) Assume that the firm chooses to screen all of the 1000 applicants for a cost of $10,000 per person to get complete information about the applicant (i.e. the firm will know if the applicant is high- or low-skilled). Which type will the firm employ? Was this a good decision or should they have done random hire like in a? 8. Find the Syllabus for this course on eCourseware. a. (5 points) On what date is the final exam for this course? b. (5 points) On what date is the first midterm? c. (5 points) What percent of the final grade is dependent on homework?Chamberlain Co. wants to issue new 19-year bonds for some much-needed expansion 14 projects. The company currently has 9.4 percent coupon bonds on the market that sell for $1,114.56, make semiannual payments, and mature in 19 years. What coupon rate should the company set on its new bonds if it wants them to sell at par? Assume a par value of $1,000.Both Bond Sam and Bond Dave have 8 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 4 years to maturity, whereas Bond Dave has 14 years to maturity. If interest rates suddenly rise by 3 percent, what is the percentage change in the price of Bond Sam? O 9.71% O-9.48% O-9.50% O-10.50% If interest rates suddenly rise by 3 percent, what is the percentage change in the price of Bond Dave? O-21.18% O-21.16% O 23.05% O-26.87% If rates were to suddenly fall by 3 percent instead, what would the percentage change in the price of Bond Sam be then?15 -21.16% O 23.05% O-26.87% If rates were to suddenly fall by 3 percent instead, what would the percentage change in the price of Bond Sam be then? O 10.76% 10.74% 0 9.71% O-9.45% If rates were to suddenly fall by 3 percent instead, what would the percentage change In the price of Bond Dave be then? O-21.13% 23.05% O 29.95% O 29.93%