Time inconsistency and chocolate. The latest craze sweeping Pcoria is a new kind of exotic chocolate imported from the faraway alpine nation of Chplandia. Chplandian chocolate is delicious and cheap: each bar produces $2 worth of utility and only costs $1. But unfortunately, it is not very healthy: if a Pcorian eats x bars on any given day, she suffers negative health effects the next day that amount to  −$1 /4x2 . But she does not suffer any ill effects on the day she eats the chocolate.
a)     Assume Pcorians are beta-delta discounters with β = 1 and δ = 1, and that each day is a period. Interpret these assumptions about β and δ. Are Pcorians patient? Are they time-consistent?
b)     What is the optimal number of Chplandian chocolate bars x∗ for each Pcorian to eat each day under these assumptions? [Hint: Balance the marginal benefit and marginal cost.]
c)      Now assume δ = 2 /3 instead. How does this affect optimal chocolate intake x∗? Explain intuitively why x∗ changes the way it does when δ falls.
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