You would like to be holding a protective put position on the stock of xyz co. to lock in a guaranteed minimum value of $100 at year-end. xyz currently sells for $100. over the next year, the stock price will either increase by 10% or decrease by 10%. the t-bill rate is 5%. unfortunately, no put options are traded on xyz co. a. suppose the desired put option were traded. how much would it cost to purchase? b. what would have been the cost of the protective put portfolio? c. what portfolio position in stock and t-bills will ensure you a payoff equal to the payoff that would be provided by a protective put with x = $100? show that the payoff to this portfolio and the cost of establishing the portfolio match those of the desired protective put.

5. profit maximization and shutting down in the short run suppose that the market for polos is a competitive market. the following graph shows the daily cost curves of a firm operating in this market. 0 2 4 6 8 10 12 14 16 18 20 50 45 40 35 30 25 20 15 10 5 0 price (dollars per polo) quantity (thousands of polos) mc atc avc for each price in the following table, calculate the firm's optimal quantity of units to produce, and determine the profit or loss if it produces at that quantity, using the data from the previous graph to identify its total variable cost. assume that if the firm is indifferent between producing and shutting down, it will produce. (hint: you can select the purple points [diamond symbols] on the previous graph to see precise information on average variable cost.) price quantity total revenue fixed cost variable cost profit (dollars per polo) (polos) (dollars) (dollars) (dollars) (dollars) 12.50 135,000 27.50 135,000 45.00 135,000 if the firm shuts down, it must incur its fixed costs (fc) in the short run. in this case, the firm's fixed cost is $135,000 per day. in other words, if it shuts down, the firm would suffer losses of $135,000 per day until its fixed costs end (such as the expiration of a building lease). this firm's shutdown price—that is, the price below which it is optimal for the firm to shut down—is per polo.

An employer who is considering hiring eva has asked donna, eva’s former supervisor, for a report on eva. in truth, eva’s work for donna has been only average. however, eva is donna’s friend, and donna knows that eva probably will not get the job if she says anything negative about eva, and donna knows that eva desperately needs the job. further, donna knows that if the situation were reversed, she would not want eva to mention her deficiencies. nevertheless, it has been donna’s policy to reveal the deficiencies of employees when she has been asked for references by employers, and she knows that some of eva’s faults may be bothersome to this particular employer. finally, this employer has leveled with donna in the past when donna has asked for a report on people who have worked for him. should donna reveal deficiencies in eva’s past performance? (remember to use one of the three moral theories acceptable for this test to solve this dilemma. any discussion of any personal opinion, religious perspective, or theory other than the moral theories acceptable for this test will result in a score of "0" for this question.)

Penelope summers received certain income benefits in 2018. she received $1,400 of state unemployment insurance benefits, $2,000 from a federal unemployment trust fund and $3,700 workers’ compensation received for an occupational injury. what amount of the compensation must penelope include in her income