Question 4 Webster Ltd has the following partial statement of financial position as at 31 December 2010. EQUITY AND LIABILITIES $ 500,000 ordinary shares 2,500,000 25,000 convertible preference shares, 10% cumulative 2,500,000 Retained earnings 9,000,000 Non-current liabilities Notes payable, 14% Convertible bonds payable (issue A) Convertible bonds payable (issue B) 14.000.000 1,000,000 2,500,000 2,500,000 6.000.000 Additional information during the year ended 31 December 2010: 1. 50,000 options were granted in July 2008 to purchase 50,000 ordinary shares at $20 per share. The average market price of Webster's ordinary shares during 2010 was $30 per share. All options are still outstanding at the end of 2010. 2. Both convertible bonds were issued in 2009. Each convertible bond is convertible into 40 shares of ordinary shares with a face value of $1,000. In 2010, interest expense of $200,000 on the liability component of convertible bonds (issue A) is recorded, and interest expense of $250,000 is recorded on the liability component of convertible bond (issue B). 3. The 10% cumulative, convertible preference shares were issued at the beginning of 2010 at $100 each. Each preference share is convertible into four ordinary shares. 4. The average income tax rate is 40%. 5. The 500,000 ordinary shares were outstanding during the entire year. 1. A firm produces output with two factors of production, capital (K) and labor (L), according to the following production function KL Y(K, L) = 10 Suppose that the rental rate of capital is $100 and the wage rate is $10. a. Derive the conditional factor demand equations for K and L. b. Derive the long run total cost function. c. Derive the firm's average cost function. d. Derive the firm's marginal cost function. e. Graph both the average cost and marginal cost functions. f. If the firm wants to produce 2 units of output, how many units of K and L should it use? How much will it cost? 11. Consider an economy with 2 firms and 2 consumers. Firm i is owned by consumer i(= 1, 2). Firm 1 produces virtual reality machines (VRMs) using oil via the production function v = 2x. Firm 2 produces bread via the production function b=3x. Consumer 1 has utility function U (v) = 100+4v0.4 and has an endowment of 10 units oil. Consumer 1 has utility function U2 (12) = 100 and has an endowment of 10 units of oil too. a. Determine the input demand and output supply functions for the two firms. Problem 1 Suppose that a person has a utility function of U(W) = W04, where Wis that person's level of wealth. Answer the following questions, and write your answers in the Answer Sheet. > What is the general nature of the person's risk attitude: risk-averse, risk-neutral, or risk-loving? What is the Arrow-Pratt measure of absolute risk aversion (ARA) for this person? What is the Arrow-Pratt measure of relative risk aversion (RRA) for this person? Suppose that this person starts with wealth of W= $100. He is offered a gamble. He has a 50% chance of winning, in which case he ends up with $400 (his original $100, plus a $300 prize). If he loses (50% chance), then he ends up with nothing (W=$0), having lost all of his money. Based on expected utility theory and this person's utility function, will the person take the gamble: yes or no? Problem 3. Let u(.) be a utility function defined over the values of wealth, w. Then, the coefficient of absolute risk aversion at wealth w is defined as A(w)=- u"(w) u'(w) while the coefficient of relative risk aversion at wealth w is defined as R(w)= wu" (w) u'(w) (a) Consider the exponential utility function u(w) = -exp(-pw). Show that it is increas- ing (i.e., u' > 0) and concave (i.e., u" < 0) for all w as long as p > 0, that is, as long as the agent is risk-averse. Calculate its absolute and relative risk aversion coefficients. (b) Consider the utility function u(w) = u > 0) and concave (i.e., " < 0) for all relative risk aversion coefficients. for p 1. Show that it is increasing (i.e., as long as p > 0. Calculate its absolute and