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Question 4 Webster Ltd has the following partial statement of nancial position as at 31 December 2010. EQUITYAND LIABILITIES $ 500,000 ordinary shares 2,500,000 25,000 convertible preference shares, 10% cumulative 2,500,000 Rammedeaminss 9.099.020 14m Non-current liabilities Notes payable. 14% 1,000,000 Convertible bonds payable [issueA) 2,500,000 Convertible bonds payable (issue B) 2,500,511.10 W 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. 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 bend (issue 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. The average income tax rate is 40%. The 500,000 ordinary shares were outstanding during the entire year. Question 3. Answer the following questions about social insurance. a) Consider one of the social insurance programs we have studied. Present an argument as to why there are incomplete private insurance markets in this case. What is the likely (insurance) outcome in the absence of government intervention? b) The optimal social insurance problem is a balance between protection and distortion. Discuss each of these in the context of the unemployment compensation literature. What are we concerned about distorting? What are we protecting? What are the key elasticities that we need to measure to determine optimal UI benefits? How does each qualitatively affect the optimal UI benefit? Two of the key social insurance benefit programs in the US are disability insurance (DI) and social security (SS). Both programs are federal; therefore all persons face the same eligibility and benefit structure (e.g. no variation across states). Further, benefits are a function of prior earnings. c) Discuss the challenges for causal identification of the impact of social insurance (DI/SS) on labor supply given the program characteristics listed above. d) Suppose we estimate the impact of the social insurance program by regressing labor supply (4) on the DI or SS benefit (B) using cross sectional data (for example, I, = a + BX, + >B, + 8, ). Discuss the validity of this estimator and the sign of the possible bias for the parameter of interest (7 ). e) Describe an identification strategy used in the literature on DI or SS that you think provides the best alternative approach for estimating the impact of B on L. Focus your discussion on the identification strategy.2. Consider a real business cycle model in which the representative agent chooses capital and and labor to maximize the utility of consumption (c) and leisure ((1 -()), where the time endowment is unity and labor is f. u(c, 1 - () subject to stochastic productivity shocks (4). Output (y) is given by y = Ako (1 - (1- where the firm rents capital from the household at rental rate r. (a) Write the firm's profit maximization problem and solve for the values of the wage (w) and the rental rate (r) . (b) Write the expression for the agent's budget constraint using recursive notation (primes for one-period-ahead values) Let the rate of depreciation on capital be o. Why can't the representative agent in a closed economy use bonds to smooth consumption? (c) What are the state variables in the consumer's optimization problem? Write the value function for the consumer, using recursive notation and take first order conditions. Write the expression for the envelope condition and write an expression for the Euler equation and one for the labor supply decision. (d) Explain the permanent income theory of consumption. Use this theory to compare the effect of a transitory increase in A on consumption with a permanent increase. (e) Now, consider three different specifications of utility, each of which is used in macro models. u(c, 1 - () = Inc+ 1-q- 130,9>1 (BL) 1-7 u(c, 1 - f) = Inc - we (IDL) u(c, 1 - () = In c+1(1 -41-7 1 - 7 (GHH) where (BL) represents the baseline specification, (IDL) is the specification with indi- visible labor, and the (GHH) is due to Greenwood, Hercowitz and Huffman. Write the equations for the equilibrium relationship between consumption and leisure for each specification. (f) Define a balanced growth equilibrium. Which, if any, of the specifications have a labor- leisure choice which is consistent with balanced growth? Explain. (g) Compare the response of labor supply to a transitory increase in A which raises the wage using the baseline model and the GHH model