Question

A village has six residents, each of whom has accumulated savings of $100. Each villager can use this money either to buy a government bond that pays 18 percent interest per year or to buy a year-old llama, send it onto the commons to graze, and sell it after 1 year. The price the villager gets for the 2-year-old llama depends on the quality of the fleece it grows while grazing on the commons. That in turn depends on the animal’s access to grazing, which depends on the number of llamas sent to the commons, as shown in the following table: Number of llamas on the commons Price per 2-year-old llama ($) 1 125 2 119 3 116 4 113 5 111 6 109 The villagers make their investment decisions one after another, and their decisions are public.

c. The village committee votes to auction the right to graze llamas on the commons to the highest bidder. Assuming villagers can both borrow and lend at 18 percent annual interest, how much will the right sell for at auction?

Instructions: Enter your response rounded to two decimal places.

$

What will be the resulting village income?

Instructions: Enter your response as a whole number.

Village income: $

Answer 1

Ans:-

Given:- Each of the six residents of village has accumulated savings of $100.

Each villager can use this money to buy a government bond that pays 18% interest per year.

The table looks like->

No.of llamas commons	Price per 2 year old llamas($)	Income per llama ($/year)	Total village income ($/year)	Marginal income ($/year)
1	125	25	25	25
2	119	19	38	13
3	116	16	48	10
4	113	13	52	4
5	111	11	55	3
6	109	09	54	-1

• If a single villager could control access to commons, the most profitable way to use this land is to send only a single llama and earn $25 per year.
• The opportunity cost of $100 spend on llama is the interst could have earned from buying government bond, $18.
• If the land were free, the owner would thus earn $25 per year by raising one llama per year on it, or $7 more than she would have earned had she used her $100 to buy a bond.
• The price of the land will be bid up until it owning the land is no better than putting the same amount in the bank at 18% interest.
• That price is the amount of money that would yield $7 per year if deposited at 18% interest, that is,

          0.18x=7

         x=38.89

Therefore, the new owner will graze one llama.

Instructions: Enter your response rounded to two decimal places.

The resulting village income will be ->    $ 38.89 (+/-) .02

The village income will be   $115 ;   $25 + 5($18)