little pigs, Luke, Kethan

Assignment 6: Behavioral Economics: Economics 4374

• Solve

There are three little pigs, Luke, Kethan, and Arjun. Each of the three pigs lives for ve 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 e ort), but building a house of bricks has an instantaneous utility cost of 3 (it requires some e ort).

Every day the three little pigs get utility from rolling around in the mud near the house they live in. This includes the rst 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 hu and pu 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 = 0:8 and a short-run discount factor = 0:7. Write out his discounted utilities with each of the two possible houses. Which type of house will he build in the rst period?

2. Kethan instead has = 0:8 and = 0:3. Which type of house will he build in the rst period?

3. Arjun has a cold and Mama Pig lets him stay in her brick house for the rst 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 = 0:8 and = 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 rst 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 period?

5. Give a verbal example of a commitment device that Mama Pig could o er that will help Arjun stick to his period-1 plan.

6. Show how your commitment device could work in terms of utilities. Speci cally, give an example of how the commitment device might modify Arjun’s instantaneous utilities in the di erent periods, and show that this is su cient for him to stick with his period-1 plan for which house to build. Use numbers to illustrate this.

• Think

1. Aaron must do an activity on one of Monday, Tuesday, Wednesday, or Thursday. Aaron is a hyperbolic discounter. Depending on the perspective, he ranks the alternatives as follows: On Sunday (and at earlier times) Aaron ranks the alternatives as follows: (T hursday)   (W ednesday)   (M onday)   (T uesday)

Note: The symbol ” means is preferred to.” So A B” can be read as A is preferred to B”

On Monday, Aaron ranks the alternatives as follows:

(T hursday) (W ednesday) (M onday) (T uesday) On Tuesday, Aaron ranks the alternatives as follows: (T uesday) (T hursday) (W ednesday)

On Wednesday, Aaron ranks the alternatives as follows: (W ednesday) (T hursday)

• Is this activity a burdensome activity or a pleasurable activity? Brie y explain.

• If Aaron is naive, when will he do the activity? Brie y explain.

• If Aaron is sophisticated, when will he do the activity? Brie y explain.

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