3. A village has six residents, each of whom has accumulatedsavings of $100. Each villager can use this money either tobuy a government bond that pays 15% per year. Or theycan buy a llama, send it onto the commons to graze andthen sell it after one year. The price the villager gets forselling the llama depends on quality of fleece it grows. Thequality of fleece depends on how many llamas are grazing.At the end of the year the villager will have $115 if theybuy the bond or $109-$122 if they buy the llama dependingon how many llamas are purchasedNumber ofLlamas123456Price perLlama122118116114112109a. If each villager decides individually how to invest, howmany llamas will be sent onto the commons and whatwill be the net village income?b. What is the socially optimal number of llamas for thisvillage?c. The village committee votes to auction the right to grazethe llamas to the highest bidder. How much will thegrazing right sell for? What will be the net villageincome afterwards?

The terms "Auction Revenue" and "Socially Optimal Income" refer to two different concepts in the context of the village's decision-making regarding whether to graze llamas on the commons or invest in government bonds.Auction Revenue:Auction revenue is the amount of money the village can earn by auctioning off the right to graze llamas on the communal grazing land (the commons) to the highest bidder. In this scenario, the villagers collectively decide to auction the grazing rights to an individual or entity willing to pay the most for that privilege.In the provided context, the auction revenue is calculated as the difference between the income generated by grazing llamas on the commons (in this case, with 1 llama) and the income from investing in government bonds. The highest bidder is willing to pay this difference for the right to graze llamas on the commons.Socially Optimal Income:Socially optimal income represents the income that would be best for the entire village as a whole. It's the income level that maximizes the overall well-being or wealth of the community.In the context of the village's decision on the number of llamas to graze on the commons, the socially optimal income is calculated by determining the number of llamas that, when collectively grazed on the commons, maximizes the total income earned by all villagers. This is the number of llamas that benefits the village as a whole, rather than just individual villagers.The socially optimal income considers the common interest of the village and aims to achieve the highest total income or overall benefit for the entire community.In summary, auction revenue is the income generated by selling the rights to graze llamas, and socially optimal income is the income level that maximizes the overall well-being of the village by determining the optimal number of llamas to graze on the commons. These concepts are used to analyze how the village should collectively make decisions to benefit the entire community.a. If each villager decides individually how to invest, they will compare the return from buying a government bond to the return from buying llamas and selling them after one year, taking into account the quality of fleece based on the number of llamas purchased. Each villager wants to maximize their individual income.To determine how many llamas each villager will send onto the commons, they will choose the option that provides them with higher income.For each villager, the choice depends on the number of llamas already in the commons and the potential income from selling llamas:With 0 llamas on the commons, each villager can earn $115 by buying a government bond ($15 interest).With 1 llama in common, you can earn $122 by selling a llama.With 2 llamas in common, you can earn $118 by selling a llama.With 3 llamas in common, you can earn $116 by selling a llama.With 4 llamas on the commons, you can earn $114 by selling a llama.With 5 llamas on the commons, you can earn $112 by selling a llama.With 6 llamas on the commons, you can earn $109 by selling a llama.Since each villager wants to maximize their income, they will send llamas onto the commons as long as the income from selling a llama is higher than the income from the government bond. Based on the provided prices per llama and income values, here's how many llamas each villager will send to the commons:Villager 1: 0 llamas (bond)Villager 2: 0 llamas (bond)Villager 3: 1 llamaVillager 4: 1 llamaVillager 5: 1 llamaVillager 6: 1 llamaThe total number of llamas sent onto the commons is 4, and the net village income will be the sum of the income from selling these llamas.The socially optimal number of llamas for the village should maximize the total village income. To find this, we can calculate the income for each possible number of llamas and choose the number that maximizes the total income:Formula Table:Calculation Table:The socially optimal number of llamas is 1 because it maximizes the total village income of $718.If the village committee votes to auction the right to graze the llamas to the highest bidder, the grazing right will sell for an amount equal to the value it provides to the highest bidder. In this case, the highest bidder will be willing to pay up to the difference between the income from selling llamas with 1 on the commons and the income from the government bond.The grazing right will sell for $603, and the net village income afterward will be the sum of the income from selling llamas and the revenue from the auction.a) The number of llamas sent to the commons is 4 and net village income is $2,328.b) The socially optimal number of Ilamas for this village is 1 because it maximizes the total village income of $718.c) The highest bidder's value was $603 and net village income was $1,335.

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a. If each villager decides individually how to invest, how many llamas will be sent onto the commons and what will be the net village income? b. What is the socially optimal number of llamas for this village? c. The village committee votes to auction the right to graze the llamas to the highest bidder. How much will the grazing right sell for? What will be the net village income afterwards?

a. If each villager decides individually how to invest, how many llamas will be sent onto the commons and what will be the net village income? b. What is the socially optimal number of llamas for this village? c. The village committee votes to auction the right to graze the llamas to the highest bidder. How much will the grazing right sell for? What will be the net village income afterwards?

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Concept explainers

Real Estate

Real estate means ownership of land along with the assets and natural resources that exist on the land. These properties are in real/physical form which is tangible. Real estate simply means land or addition made to land permanently like constructing a residence or different buildings. People invest in real estate to either reside or for wealth creation. Many people investing in real estate further lend the place for occupation or businesses in return for a monthly payment.

Question

3. 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 15% per year. Or they
can buy a llama, send it onto the commons to graze and
then sell it after one year. The price the villager gets for
selling the llama depends on quality of fleece it grows. The
quality of fleece depends on how many llamas are grazing.
At the end of the year the villager will have $115 if they
buy the bond or $109-$122 if they buy the llama depending
on how many llamas are purchased
Number of
Llamas
1
2
3
4
5
6
Price per
Llama
122
118
116
114
112
109
a. If each villager decides individually how to invest, how
many llamas will be sent onto the commons and what
will be the net village income?
b. What is the socially optimal number of llamas for this
village?
c. The village committee votes to auction the right to graze
the llamas to the highest bidder. How much will the
grazing right sell for? What will be the net village
income afterwards?

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Step 1: Introduction to Auction Revenue and Socially Optimal Income

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Step 3: Socially Number of Optimal Ilamas for Village

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