refer to the questions below

4 Testing for Insurance Suppose Barack Obama has asked you for your opinion on whether or not the government should raise the amount of benefits provided to individuals with a disability (aka DI). He asks you a series of questions. For each question, discuss a potential empirical method that would allow you to answer his question. Most importantly, discuss the potential limitations of your proposed approach. Assume you have access to any reasonable amount of data that would be required. 1. Obama asks: "I'm not sure if people are sufficiently insured against the onset of disability, since they potentially have access to informal sources of insurance and can also buy some insurance in the private insurance market. Can you tell me, given where we're at today, to what extent are people currently insured against the onset of a disability? 2. Obama asks: "All of these Republicans keep telling me that if we raise the amount of disability benefits then we'll see more people stop working and claim to be disabled. I see this could be a potential problem, but how large is this effect?4. Again consider the same setting, but now assume that the tree is also risky. This new assumption will be in force for the rest of the problem. Specifically, assume that there are now two states. In the good state, the tree pays (1 + a)c and the firm pays 1 (assume a > 0). In the bad state the tree pays c and the firm pays nothing. As before, the good state occurs with probability a and the bad state occurs with probability 1 - p. 5. Use a perturbation argument to explain why the following (slightly different) Euler Equation characterizes the equilibrium price, p. (1 - p)au'((1 +a)c+1) -p(1 -4) u'(c) =0 6. Show that lim P= 1ta(1 - 4) 1. 7. Explain the results in part 6 using economic intuition. Specifically, explain why the equilbrium price of the firm is less than the expected value of the firm (whether or not c is large). Why does risk aversion now play a role? Contrast this case with the earlier case (when the tree was not risky). 6 8. Using the equations in part 6, one can generate a high required return on the firm by setting o = 0.12 and # = 1/2. This calibration has the desirable property that it explains the historical equity premium of 0.06. What is wrong with such a calibration? In other words, why is such a calibration inconsistent with other empirical facts? 9. Why is the equity premium negative if we instead made a 0). In the bad state the tree pays c and the firm pays nothing. As before, the good state occurs with probability a and the bad state occurs with probability 1 - p. 5. Use a perturbation argument to explain why the following (slightly different) Euler Equation characterizes the equilibrium price, p. (1 - p)au'((1 +a)c+1) -p(1 -4) u'(c) =0 6. Show that lim P= 1ta(1 - 4) 1. 7. Explain the results in part 6 using economic intuition. Specifically, explain why the equilbrium price of the firm is less than the expected value of the firm (whether or not c is large). Why does risk aversion now play a role? Contrast this case with the earlier case (when the tree was not risky). 6 8. Using the equations in part 6, one can generate a high required return on the firm by setting o = 0.12 and # = 1/2. This calibration has the desirable property that it explains the historical equity premium of 0.06. What is wrong with such a calibration? In other words, why is such a calibration inconsistent with other empirical facts? 9. Why is the equity premium negative if we instead made a 0. Let q(f) represent the NPV of the stream of profits from a marginal unit of installed capital. o(t ) = = (45-* (k' (s)ds a. Interpret off). How and why does this definition of q() differ from the definition we used in class? Using the Envelope Theorem, show that With = 4. where V[k, A) is the value function of a firm. b. Derive the firm's Bellman Equation, and the first-order condition: q() =1+C(0) c. Derive the Bellman Equation associated with q(f): (r+ 7)(() = =(K(0) + () d. Analyze the phase diagram associated with this inchestry. Plot the K = 0 and q = 0 boxi. Graph the saddle path. How does this diagram differ from the one we derived in class? How does a rise in the depreciation rate affect the steady state level of capital? Explain. e. Now suppose the industry is in steady state. At time period to the government announces a temporary investment tax credit which will last until time period - The investment tax credit provides a # (-#) subsidy per unit of positive (negative) investment (0