Question: a suppose that when tomorrow time t 1 arrives...
(a) Suppose that when tomorrow (time t + 1) arrives, an individual will order food to be eaten tomorrow as if he is maximizing a utility function U(ft+1I ht+1) = −(ft+1 − ht+1)2
where ft+1 stands for food at time t + 1 and ht+1 stands for how hungry she is at time t + 1. Solve for the amount of food that he will order tomorrow, for tomorrow.
(b) Now suppose that when ordering food today to be eaten tomorrow, the same individual behaves as if she has the following utility function:
U(ft+1| ht+1, ht) = −(1 − α)(ft+1 − ht+1) 2 − α(ft+1 − ht) 2
where α ∈ [0, 1]. Thus, the amount she orders for tomorrow depends on how hungry she is today, and how hungry she will be tomorrow (which you can assume she forecasts with perfect accuracy). Solve for the optimal amount of food that she will order today, for tomorrow.
(c) How might we interpret the parameter α in terms of projection bias?
(d) If α = 1, how much food does the individual order today, for tomorrow?
(e) Suppose the individual orders food today for tomorrow. Under what conditions would she prefer, once tomorrow arrives, to throw all of the food away rather than eat everything she ordered?
(f) Describe a real-life example of where such projection bias may lead to economic inefficiency or misallocated resources. This example can be from a paper we discussed in lecture, or you may think of another application.