Q4. (a) Survival times are available for four insureds, two from risk class A and two from risk class B. The two from risk class A passed away at times t = 1 and t = 9. The two from risk class B died at times t = 2 and t = 4. Using the Empirical Credibility Model I, estimate the credibility factor Z. [Marks 8] (b) An investigative journalist comes across information about two policy groups administered by an insurance company. The data however has missing values for some years in total losses and numbers in policy groups as shown in the following table. The missing values are represented by the symbol * Policy group Year 1 Year 2 Year 3 Year 4 Total Losses 750 600 Number in group 3 2 Total Losses 975 1200 900 Number in group 5 6 4 5 Using the Empirical Credibility Model II, determine the premium for each policyholder in Year 4. [Marks 8]Suppose a consumer has utility function u(x1, x2) = x} a) Find the demand functions x1 (p1, pz, m) and x2 (p1, p2, m). Show your work. b) Find the consumer's indirect utility function v (P1, pz, m). Roy's identity ( named for famous French economist Rene Roy) states that the demand for good i E [1,2) can be written in terms of the indirect utility function as av (P1, Pz, m) x (P1, P2, m) = - api av(P1, Pz, m) am c) Using your answers to a) - b), verify that Roy's identity holds for good 1.9. Which of the following statements is CORRECT? The term "IPO" stands for Introductory Price Offered, and it is the price at which shares of a new company are offered to the public. b. IPO prices are generally established by the market, and buyers of the new stock must pay the price that prevails at the close of trading on the day the stock is offered to the public. C. In a "Dutch auction," investors who want to buy shares in an IPO submit bids indicating how many shares they want to buy and the price they are willing to pay. The company determines how many shares it wants to sell. The highest price that enables the company to sell the desired number of shares is the price that all buyers must pay. d. It is possible that the price set in an IPO is so high that investors will refuse to buy the number of shares that the company wants to sell. In that case, the company is said to have "left money on the table." It is possible that the price set in an IPO is so low that investors will want to buy more shares than the company wants to sell. In that case, the company will have to issue more shares than it wants to sell. 10. Bauer Software's current balance sheet shows total common equity of $5.125,000. The company has 490,000 shares of stock outstanding, and they sell at a price of $27.50 per share. By how much do the firm's market and book values per share differ? a. $18.57 b. $19.09 C. $20.28 d. $17.04 e. $18.23 1 1. Emery Mining Inc. recently reported $167,500 of sales, $75.500 of operating costs other than depreciation, and $10,200 of depreciation. The company had $16,500 of outstanding bonds that carry a 7.25% interest rate, and its federal-plus-state income tax rate was 35%. How much was the firm's net income? The firm uses the same depreciation expense for tax and stockholder reporting purposes. a. $44,533.57 b. $50,296.74 C. $64,442.70 d. $57,107.76 e. $52,392.44 12. During 2008, Bascom Bakery paid out $33.525 of common dividends. It ended the year with $155,000 of retained earnings versus the prior year's retained earnings of $159.600. How much net income did the firm carn during the year? a. $23.719 b. $28.057 C. $24,008 d. $28.925 e. $27.768Exercise 1 Horizontal differentiation There are only two shops selling sweet-and-sour soup in this area. For sim- plicity, we set their marginal cost of production to zero. As it happens, one shop (named "Won-Ton" and indexed by 1) is located at point 0, while the other shop (named "Too-Chow" and indexed by 2) is located at point 1. Everyday, each inhabitant of the street may consume at most one bowl of sweet-and-sour soup, bought either from Won-Ton or from Too-Chow. The price per bowl of the two shops are respectively denoted by p, and p2. The net utility for a consumer located at r on the interva I[0, 1] is given by r - n(J) - PI if consumer buys at Won-Ton r - 72(1 - x) - p2 if consumer buys at Too-Chow if consumer does not buy. where it is assumed that r is large enough so that every consumer buys one bowl of soup. 1. Before 1993 and the installation of the Mid-Levels escalators, walking up the street was much more painful than walking down. This is translated by the following assumptions: 7(x) = tr and 72(1 - x) = ( + r)(1 -r) with t, 7 > 0. 1.1 Derive the identity of the consumer who is indifferent between the two shops. 1.2 Compute the equilibrium prices and profits of the two shops. 1.3 Show that Too-Chow's profits increase if walking up the street be- comes more costly for consumers, that is if 7 increases (e.g., because the temperature has risen). Explain the intuition behind this result. 2 After 1993, the Mid-Levels escalators made going up and down equally painful for consumers. However, consumers had to pay a fixed fee f (in- dependent of distance) to use the escalators. This is translated by the following assumptions: n(x) = tr and 72(1-x) = t(1-x) + f with f >0. 2.1 Derive the identity of the consumer who is indifferent between the two shops.11. Assume quantities must be integers. The following table gives your demand for slices of pizza. $10 $7 $5 $3 $1 1 2 w 4 The only pizzeria in town charges a per-person admission fee of $20, and then allows you to purchase as many slices as you want at $2 each. How many slices do you eat? a) 5. b) 4. 3. d) 2. e) None of the above. 12. Rahul's demand for coffee is given in the following table. $2.75 $1.75 $1.25 $0.75 $0.25 2 3 4 5 If he purchases coffee, he pays $3 for the first cup, and $1 for each additional cup. What is Rahul's consumer surplus from coffee? a) $0.00. b) $0.75. c) $1.00. d) $2.75. e) $3.75. 13. Refer to the table below, where MWTP is Marginal Willingness To Pay. Q 1 2 3 4 5 6 7 MWTP (Demand) $18 $14 $12 $10 $8 $6 $4 MC $1 $3 $5 $7 $9 $11 $13 If the government implements an $1 1 price floor, what is the largest possible producer surplus? a) $11. b) $24. c) $30. d) $35. e) None of the above
