Open Word and answer the following questions. Save the document and print it when you are done.
1. Use analytical methods to derive a general reduced-form solution for K∗. Show your work.
Although you can use the Lagrangean method, it is easier to maximize the utility directly, substituting in the values for each state of nature.
The key is that consumption in the good and bad states of nature depends on K:
We can simply substitute these equations into the utility function and maximize.
2. Compare the analytical versus numerical approaches by evaluating your answer to question 1 at the initial parameter values in the OptimalChoice sheet. (Click the Reset button if needed.) Do you find that K∗ = $10,000?
3. Use your reduced form for K∗ to find the probability of loss elasticity of insurance demand at π = 1%. Show your work. If you cannot find the reduced form, use
4. Use the Comparative Statics Wizard to find the probability of loss elasticity of insurance demand from π = 1% to 1.1%. Take a picture of your results, including the elasticity calculation.
5. Compare your answers in question 3 and 4. Do these elasticities differ? Why or why not?