Problem 2 : Alyosha's utility function is given by u(1) = (/)05, where I represents annual income in thousands of dollars. a. Let's assume that he has $10,000 and is offered a gamble of a $1,000 gain with 50 percent probability and a $1,000 loss with 50 percent probability. Is Alyosha risk loving, risk neutral, or risk averse? Explain. b. What is the certainty equivalent of the lottery? c. Suppose that Alyosha is currently earning an income of $10,000 (1 = 10) and can earn that income next year with certainty. He is offered a chance to take a new job that offers a .5 probability of earning $16,000, and a .5 probability of earning $5,000. Should he take the new job? d. Assume that Alyosha takes the risky job in part b. Would he be willing to buy insurance to protect against the variable income associated with the new job? If so, how much would he be willing to pay for that insurance? (Hint: What is the risk premium?) Problem 3: Joanna is offered a choice between two gambles. In gamble one, she wins 200 if a coin comes up heads and loses 100 if the coin comes up tails. In gamble 2 she wins 20,000 if a coin comes up heads and loses 10,000 if the coin comes up tails. Assume Joanna's initial wealth, W, is 10,000. a. Would Joanna accept either, both, or neither of the gambles if she is risk neutral? b. Would Joanna accept either, both or neither of the gambles if her utility function is given by U(x)=x1/2? Problem 4: David has an investment opportunity that pays 33 with probability 50% and loses 30 with probability 50%. a. If his current wealth is 111 and his utility function is U(x)= x05, will he make the investment? b. Will he make the investment if he can take a partner who will share equally in the net return (positive or negative) from the investment? Problem 5: Suppose Chris can invest in shares of the Alpha Heater Company and the Beta Air Conditioner Company. If she invests only in Alpha shares, her wealth, W, is 16 if the weather is cold and 9 if the weather is hot. If she invests only in Beta shares, her wealth is 9 when the weather is cold and 16 when the weather is hot. The probability that the weather is hot is 50% and the probability that the weather is cold is 50%. Chris' utility function is U(x)= x05. Will Chris invest all her funds in either of the companies or will she invest in both? Explain your answer.17 MC 16 - 12- ATC Suppose that a firm in a competitive market faces the following revenues and costs: Quantity Total Revenue Total Cost 0 $0 $5 $8 $9 2 $16 $14 $24 $20 4 $32 $27 5 $40 $35 6 $48 $44 7 $56 $54 8 $64 $65 9 $72 $72 If the firm's marginal cost is $5, it should4. You are the chief financial officer for a firm that sells digital music players. Your firm has the following average-total-cost schedule: Quantity Average Total Cost 600 players $300 601 players $301 Your current level of production is 600 devices, all of which have been sold. Someone calls, desperate to buy one of your music players. The caller offers you $550 for it. Should you accept the offer? Why or why not? 5. Consider the following total cost and total revenue: Quantity 0 1 2 3 4 5 6 7 Total Cost $8 $9 $10 $11 $13 $19 $27 $37 Total Revenue $0 $8 $16 $24 $32 $40 $48 $56 Calculate profit for each quantity. How much should the firm produce to maximize profit? 6. From the previous question, calculate marginal revenue and marginal cost for each quantity. At what quantity are they equal? 7. From questions 5 & 6, is this firm in a competitive industry? If so, is the industry in long-run equilibrium?Quantity Price Total Cost Marginal Cost Total revenue Marginal Revenue |Average Total Cost 12 11 10 3.666666667 16 4 Profit = $16 100 10 Cost and revenue 20 marginal cost 18 16 14 12 10 average cost (p) 00 PROFIT -demand curve (A) 1 2 9 10 11 output -4 -6 marginal revenue jaj -10 Short run equilibrium condition is MR=MC Here the equilibrium Price will be $8 and the equilibrium quantity will be 4 units. Profit earned is $16 Profit = TR - TC TR = Quantity * Price per unit = 4 58 = $32 TC = Quantity * ATC = 4 * $4 = $16 Profit = $16Welcome to the Quiz Admin Program. The program welcomes the user, then shows a ist of options to choose from. Choose [aldd, [llist, [search, [view, [delete or [qluit. >1 The user chooses I" to list the current There are no questions saved. questions but there are none saved yet. Choose [aldd, [Ilist, [search, [vliew, [delete or [qluit. >a Enter the question: In which year was Halley's Comet last visible. 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