This question applies to parts 1-10. It contains drop-down multiple choice and numerical questions. Consider a world in which there are only two dates: 0 and 1. At date 1 there are three possible states of nature: a good weather state (G), a fair weather state (F), and a bad weather state (B). The state at date zero is known. There is one non-storable consumption good, apples. There is one representative consumer in the economy. The endowment of apples at time 0, is 2. At time 1 the endowment of apples is state-dependent. The physical probabilities, π, and state-dependent endowments, e, of the states at time 1 are given in the table: State Probability Endowment G 0.5 3 F 0.2 2 B 0.3 1 The expected utility is given by u(co) + B[TG · U(CG) + TF · U(CF) + TB · U(CB)], where the instantaneous utility function is: u (c) = ln(c) (natural logarithm). The consumer's time discount factor, ẞ, is 0.95. In this economy, only atomic (Arrow-Debreu) securities can be traded. Note: round your answers to 2 decimal places if necessary. 1) How many different atomic (Arrow-Debreu) securities is required for this market to be complete? 2) Compute the equilibrium fair weather state price: 3) Compute the equilibrium traded quantity of the fair weather atomic (Arrow-Debreu) security: 4) Compute the equilibrium quantity consumed in the fair weather state: 5) In this Arrow-Debreu economy, market-clearing conditions imply that 6) The Lagrangian in this setting is used to: 7) The agent in this economy is 8) The risk-neutral probability of the good weather state is 9) Assume now that the instantaneous utility is u (c) = 10c and all other parameters remain the same. Compute the discount factor: 10) Assume again that the instantaneous utility is u (c) fair weather atomic (Arrow-Debreu) security: = 10c and all other parameters remain the same. Compute the risk premium of the
This question applies to parts 1-10. It contains drop-down multiple choice and numerical questions. Consider a world in which there are only two dates: 0 and 1. At date 1 there are three possible states of nature: a good weather state (G), a fair weather state (F), and a bad weather state (B). The state at date zero is known. There is one non-storable consumption good, apples. There is one representative consumer in the economy. The endowment of apples at time 0, is 2. At time 1 the endowment of apples is state-dependent. The physical probabilities, π, and state-dependent endowments, e, of the states at time 1 are given in the table: State Probability Endowment G 0.5 3 F 0.2 2 B 0.3 1 The expected utility is given by u(co) + B[TG · U(CG) + TF · U(CF) + TB · U(CB)], where the instantaneous utility function is: u (c) = ln(c) (natural logarithm). The consumer's time discount factor, ẞ, is 0.95. In this economy, only atomic (Arrow-Debreu) securities can be traded. Note: round your answers to 2 decimal places if necessary. 1) How many different atomic (Arrow-Debreu) securities is required for this market to be complete? 2) Compute the equilibrium fair weather state price: 3) Compute the equilibrium traded quantity of the fair weather atomic (Arrow-Debreu) security: 4) Compute the equilibrium quantity consumed in the fair weather state: 5) In this Arrow-Debreu economy, market-clearing conditions imply that 6) The Lagrangian in this setting is used to: 7) The agent in this economy is 8) The risk-neutral probability of the good weather state is 9) Assume now that the instantaneous utility is u (c) = 10c and all other parameters remain the same. Compute the discount factor: 10) Assume again that the instantaneous utility is u (c) fair weather atomic (Arrow-Debreu) security: = 10c and all other parameters remain the same. Compute the risk premium of the
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![This question applies to parts 1-10. It contains drop-down multiple choice and numerical questions.
Consider a world in which there are only two dates: 0 and 1. At date 1 there are three possible states of nature: a good weather state (G), a fair
weather state (F), and a bad weather state (B). The state at date zero is known. There is one non-storable consumption good, apples. There is
one representative consumer in the economy. The endowment of apples at time 0, is 2. At time 1 the endowment of apples is state-dependent.
The physical probabilities, π, and state-dependent endowments, e, of the states at time 1 are given in the table:
State Probability Endowment
G
0.5
3
F
0.2
2
B
0.3
1
The expected utility is given by u(co) + B[TG · U(CG) + TF · U(CF) + TB · U(CB)], where the instantaneous utility function is:
u (c) = ln(c) (natural logarithm). The consumer's time discount factor, ẞ, is 0.95.
In this economy, only atomic (Arrow-Debreu) securities can be traded.
Note: round your answers to 2 decimal places if necessary.
1) How many different atomic (Arrow-Debreu) securities is required for this market to be complete?
2) Compute the equilibrium fair weather state price:
3) Compute the equilibrium traded quantity of the fair weather atomic (Arrow-Debreu) security:
4) Compute the equilibrium quantity consumed in the fair weather state:
5) In this Arrow-Debreu economy, market-clearing conditions imply that
6) The Lagrangian in this setting is used to:
7) The agent in this economy is
8) The risk-neutral probability of the good weather state is
9) Assume now that the instantaneous utility is u (c) = 10c and all other parameters remain the same. Compute the discount factor:
10) Assume again that the instantaneous utility is u (c)
fair weather atomic (Arrow-Debreu) security:
= 10c and all other parameters remain the same. Compute the risk premium of the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67d2beea-2f31-4ba6-8acf-b2fdf62c17dd%2Fc6575d77-c3d6-4df7-8a41-d62d48c61f39%2Fbfhgq53_processed.png&w=3840&q=75)
Transcribed Image Text:This question applies to parts 1-10. It contains drop-down multiple choice and numerical questions.
Consider a world in which there are only two dates: 0 and 1. At date 1 there are three possible states of nature: a good weather state (G), a fair
weather state (F), and a bad weather state (B). The state at date zero is known. There is one non-storable consumption good, apples. There is
one representative consumer in the economy. The endowment of apples at time 0, is 2. At time 1 the endowment of apples is state-dependent.
The physical probabilities, π, and state-dependent endowments, e, of the states at time 1 are given in the table:
State Probability Endowment
G
0.5
3
F
0.2
2
B
0.3
1
The expected utility is given by u(co) + B[TG · U(CG) + TF · U(CF) + TB · U(CB)], where the instantaneous utility function is:
u (c) = ln(c) (natural logarithm). The consumer's time discount factor, ẞ, is 0.95.
In this economy, only atomic (Arrow-Debreu) securities can be traded.
Note: round your answers to 2 decimal places if necessary.
1) How many different atomic (Arrow-Debreu) securities is required for this market to be complete?
2) Compute the equilibrium fair weather state price:
3) Compute the equilibrium traded quantity of the fair weather atomic (Arrow-Debreu) security:
4) Compute the equilibrium quantity consumed in the fair weather state:
5) In this Arrow-Debreu economy, market-clearing conditions imply that
6) The Lagrangian in this setting is used to:
7) The agent in this economy is
8) The risk-neutral probability of the good weather state is
9) Assume now that the instantaneous utility is u (c) = 10c and all other parameters remain the same. Compute the discount factor:
10) Assume again that the instantaneous utility is u (c)
fair weather atomic (Arrow-Debreu) security:
= 10c and all other parameters remain the same. Compute the risk premium of the
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