There are three little pigs, Luke, Kethan, and Arjun. Each of the three pigs lives for five
periods, 1, 2, 3, 4, and 5, and is a hyperbolic discounter as introduced in class. In period 1,
Luke and Kethan have to decide whether to build a house of bricks or of straw (the market
is out of sticks). Building a house of straw has no instantaneous utility cost (it takes no
effort), but building a house of bricks has an instantaneous utility cost of 3 (it requires some
Every day the three little pigs get utility from rolling around in the mud near the house
they live in. This includes the first period, in which they get to roll around in the mud after
houses have been built. But how much utility they get depends on whether they are safe
from the big bad wolf, and this in turn depends on what their house is made of. If a pig
lives in a brick house, he gets an instantaneous utility of 5 each period from rolling around
in the mud. But if a pig lives in a straw house, he knows that the big bad wolf could come
and huff and puff and blow his house down, and so he only gets instantaneous utility of 4
each period from rolling around in the mud.
1. Luke has a long-run discount factor d = 0.8 and a short-run discount factor ß = 0.7.
Write out his discounted utilities with each of the two possible houses. Which type of
house will he build in the first period?
2. Kethan instead has d = 0.8 and ß = 0.3. Which type of house will he build in the first
3. Arjun has a cold and Mama Pig lets him stay in her brick house for the first period
and roll around in the mud near her house. Hence, Arjun only needs to build his house
in the second period. Like Kethan, he has d = 0.8 and ß = 0.3. Write out Arjun’s
discounted utilities from the two types of houses from the perspective of period 1.
(Remember to write Arjun’s discounted utility beginning with the period in which
he is planning, the first period, which is before the period he will build.) From the
perspective of period 1, which type of house would he like to build in the second period?
4. Without commitment, which type of house will Arjun end up building in the second
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