A village has six residents, each of whom has accumulated savings of $100. Each villager can use this money either to buy a government bond that pays 14 percent interest per year or to buy a year-old llama, send it onto the commons to graze, and sell it after 1 year. The price the villager gets for the 2-year-old llama depends on the quality of the fleece it grows while grazing on the commons. That in turn depends on the animal’s access to grazing, which depends on the number of llamas sent to the commons, as shown in the following table: Number of llamas on the commons Price per 2-year-old llama ($) 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. a. If each villager decides individually how to invest, how many llamas will be sent onto the commons, and what will be the resulting village income?Number of llamas: Instructions: Enter your response as a whole number.Village income: $ b. What is the socially optimal number of llamas for this village?Socially optimal number of llamas: What would village income be if the socially optimal number of llamas were sent onto the commons?Instructions: Enter your response as a whole number. Village income: $ 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 14 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: $
A village has six residents, each of whom has accumulated savings of $100. Each villager can use this money either to buy a government bond that pays 14 percent interest per year or to buy a year-old llama, send it onto the commons to graze, and sell it after 1 year. The price the villager gets for the 2-year-old llama depends on the quality of the fleece it grows while grazing on the commons. That in turn depends on the animal’s access to grazing, which depends on the number of llamas sent to the commons, as shown in the following table:
| Number of llamas on the commons | Price per 2-year-old llama ($) |
| 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.
a. If each villager decides individually how to invest, how many llamas will be sent onto the commons, and what will be the resulting village income?
Number of llamas:
Instructions: Enter your response as a whole number.
Village income: $
b. What is the socially optimal number of llamas for this village?
Socially optimal number of llamas:
What would village income be if the socially optimal number of llamas were sent onto the commons?
Instructions: Enter your response as a whole number.
Village income: $
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 14 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: $
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