Suppose that the head of the household is deciding whether or not to invest in a...

 

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Suppose that the head of the household is deciding whether or not to invest in a health product. If she chooses to invest, she will buy an insecticide-treated bed net to prevent malaria infection; if she chooses not to invest, she will not purchase a bed net. There are two periods: period 0 (today/present) and period 1 (1 year from period 0). The head of household earns an income of Y= $100 in each period. If the head of household chooses to invest, then she will pay an upfront cost of C = 36 for the bed net in period 0 and receive a return of R = 96 in period 1 when she does not get sick. She has a (time-consistent) discount factor of = 0.4. = (a) Suppose that the head of the household has a utility function of u(x) = px (therefore she is risk averse; this is equivalent to the utility function u(x) = x+ where = 0.5). Determine whether the head of household will decide to invest or not. You should compute the expected utility if she chooses to invest and if she chooses not to invest. (b) Suppose that the head of the household has a utility function of u(x) = x2 (therefore she is risk-loving; this is equivalent to the utility function u(x) = x+ where -- Determine whether the head of household will decide to invest or not. You should compute the expected utility if she chooses to invest and if she chooses not to invest. (c) Based on the difference between your answer in (b) and in (a), what can you conclude about the effect of risk tolerance on the likelihood that the head of household will choose to invest in the health product or not? You may want to consider the differences in utility between investing and not investing. (d) Suppose the head of the household has a utility function of u(x) = px, but instead has a discount factor of 0.9. Determine whether the head of household will decide to invest or not. You should compute the expected utility if she chooses to invest and if she chooses not to invest. (e) Based on the difference between your answer in (d) and in (a), what can you conclude about the effect of the discount factor on the likelihood that the head of household will choose to invest in the health product or not? (Hint: think about the interpretation of the discount factor.) You may want to consider the differences in utility from investing and not investing. (f) Suppose that the head of the household has inaccurate beliefs about the return to chlo- rinating her water and believes instead that the return is lower than the actual return. How would this affect her decision to invest? Describe how her behavior will change compared to the scenario in which she has accurate beliefs. -2). Suppose that the head of the household is deciding whether or not to invest in a health product. If she chooses to invest, she will buy an insecticide-treated bed net to prevent malaria infection; if she chooses not to invest, she will not purchase a bed net. There are two periods: period 0 (today/present) and period 1 (1 year from period 0). The head of household earns an income of Y= $100 in each period. If the head of household chooses to invest, then she will pay an upfront cost of C = 36 for the bed net in period 0 and receive a return of R = 96 in period 1 when she does not get sick. She has a (time-consistent) discount factor of = 0.4. = (a) Suppose that the head of the household has a utility function of u(x) = px (therefore she is risk averse; this is equivalent to the utility function u(x) = x+ where = 0.5). Determine whether the head of household will decide to invest or not. You should compute the expected utility if she chooses to invest and if she chooses not to invest. (b) Suppose that the head of the household has a utility function of u(x) = x2 (therefore she is risk-loving; this is equivalent to the utility function u(x) = x+ where -- Determine whether the head of household will decide to invest or not. You should compute the expected utility if she chooses to invest and if she chooses not to invest. (c) Based on the difference between your answer in (b) and in (a), what can you conclude about the effect of risk tolerance on the likelihood that the head of household will choose to invest in the health product or not? You may want to consider the differences in utility between investing and not investing. (d) Suppose the head of the household has a utility function of u(x) = px, but instead has a discount factor of 0.9. Determine whether the head of household will decide to invest or not. You should compute the expected utility if she chooses to invest and if she chooses not to invest. (e) Based on the difference between your answer in (d) and in (a), what can you conclude about the effect of the discount factor on the likelihood that the head of household will choose to invest in the health product or not? (Hint: think about the interpretation of the discount factor.) You may want to consider the differences in utility from investing and not investing. (f) Suppose that the head of the household has inaccurate beliefs about the return to chlo- rinating her water and believes instead that the return is lower than the actual return. How would this affect her decision to invest? Describe how her behavior will change compared to the scenario in which she has accurate beliefs. -2).

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a If the head of the household has a utility function of ux px therefore she is risk averse this is equivalent to the utility function uxx where 05 then the expected utility of investing in the bed ne... View the full answer