Psychology and Economics - Problem Set Arya - Assessment Answer

Psychology and Economics Problem Set Arya Assessment 

Assessment Task:

1. A consumer lives for T + 1 periods, t = 1 through t = T + 1, where T ≥4. She decides in each of the periods 2 through T whether to hit. Hitting in a period t gives an instantaneous pleasure of 4 in period t, and generates an instantaneous cost of 3 in period t + 1. The price of a hit in the market is 2, which has to be paid immediately in any period in which the consumer hits. (Note that in the model considered in class, we did not have such a price for hitting.) The consumer is a hyperbolic discounter with β =1/2 and δ = 1.

  (a) (12p) Show that both if the consumer is sophisticated and if she is naive, she hits in every period 2 through T. Show that all selves would be better o? with a lifetime of no hitting.

  (b) (12p) Now consider a system of advance orders. In each period                    t = 1, ... , T −1, the consumer can submit an order for a hit in period t + 1. If she submits an order in period t, a hit is delivered to her in period t + 1, and she must pay for the hit on delivery. If she does not submit an order in period t, she cannot hit in period t + 1.   What does a naive consumer do? What does a sophisticated consumer do? Is the system of advance orders e?ective in preventing harmful overconsumption? If not, can you think of an improvement to the system? Explain the intuition for your answers.

 (c) (10p) Suppose that in period 1, the consumer has to decide (e.g. through voting) whether to set up a system of advance orders as in part (b) or have a spot market as in part (a). The cost of setting up the system of advance orders is 1. Does a naive consumer choose to set up advance orders? How about a sophisticated consumer? Explain the intuition.  

(d) (8p) Now suppose that the pleasure from hitting is uncertain. In each period 2 through T, the pleasure is 3 with probability one-half and 8 with probability one-half, and the pleasures in di?erent periods are independent of each other. The consumer learns the pleasure from hitting in period t at the beginning of period t, and knows only the above two possibilities and their probabilities beforehand. The price of a hit is still 2, and the utility cost in the next period is still 3. Without a system of advance orders, what does each type of consumer do?

 (e) (10p) Now consider advance orders in the setting in part (d) with uncertainty in the pleasure of hitting. What does each type of consumer do with advance orders? Do advance orders prevent harmful overconsumption? If not, can you think of an improvement to the system? Explain the intuition for your answers.  
 
 
2. As mentioned in the lecture, many companies nowadays run so-called de?ned-contribution plans for retirement savings. In a de?nedcontribution plan, employees decide how much of their income to save for retirement (with a match in many companies), and their savings grow tax-free until withdrawn in retirement. In any company, employees can always enrol or opt-out of the program, as well as set or change their contribution rates, through a simple phone call or web-based or paper-based form. Nevertheless, any company running a de?ned-contribution program has to decide the default option for new employees: will a new employee by default participate in the program or not participate in it? Researchers have examined the e?ect of such defaults on participation and savings rates. They found that in companies where the default is for new employees to participate, many more employees are saving for retirement, and employees have much higher savings rates on average. Similarly, when a company switches from the default of no participation to the default of participation, savings rates in the company increase drastically.

 (a) (5p) Argue that these facts cannot reasonably be explained by a model in which all employees are rational and time-consistent.

  (b) (5p) Argue that the facts are consistent with a model in which some employees are hyperbolic discounters.

 (c) (5p) Based on the above ?ndings, some policymakers (including Barack Obama) have suggested that employers should be required by law to default all employees into participation. Carefully explain to what extent this policy would be an example of libertarian paternalism.  

(d) (5p) Give a counterargument to the above policy proposal. [You can base your counterargument on concepts you have learned in this course, or on ideas from other courses.] 
   
 
  2. (8p) Examine the following table carefully. You do not need to worry about the medical details, just focus your attention on the number of doctors communicating prognostic optimism/pessimism to the patient and to the colleague. The number in each cell is the percentage of doctors giving that combination of answers. For example, 36.5% of doctors told both their colleague and the patient that the prognosis is pessimistic

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