Questions
Dashboard Mock Final
Multiple fill-in-the-blank
Question textThis 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: [table] State | Probability | Endowment G | 0.4 | 4 F | 0.3 | 2 B | 0.3 | 1 [/table] The expected utility is given by [math: u(c0)+β[πG⋅u(cG)+πF⋅u(cF)+πB⋅u(cB)],] u(c_0) +\beta[\pi_G\cdot u(c_G) + \pi_F\cdot u(c_F) +\pi_B\cdot u(c_B)], where the instantaneous utility function is: [math: u(c)=ln(c)]u\left ( c\right ) =\ln (c) (natural logarithm). The consumer’s time discount factor, β, is 0.95. Note: round your answers to 2 decimal places if necessary. 1) At least how many different securities is required for this market to be complete? Answer 1 Question 8[select: , 0, 1, 2, 3, none of these answers].For the rest of this question, consider Arrow-Debreu securities are available. 2) Compute the equilibrium fair weather state price: Answer 2 Question 8[input] 3) Compute the equilibrium traded quantity of the fair weather atomic (Arrow-Debreu) security: Answer 3 Question 8[input] 4) Compute the equilibrium quantity consumed in the bad weather state: Answer 4 Question 8[input] 5) In this Arrow-Debreu economy, maximization of expected utility reflects the assumption of: Answer 5 Question 8[select: , price is taken as given, the prices are maximised, market clearing, agents are selfish, none of these answers] 6) To solve for the Arrow-Debreu equilibrium, we need to do the following EXCEPT: Answer 6 Question 8[select: , set up the Lagrangian, find the first-order-condition for consumptions, find the first-order-condition for asset holdings, find the first-order-condition for asset prices, none of these answers] 7) The agent in this economy is Answer 7 Question 8[select: , risk-averse, risk neutral, risk loving, none of these answers] 8) The stochastic discount factor of the good weather state is Answer 8 Question 8[select: , equal to 0.95, less than 0.95, more than discount factor, none of these answers] 9) Assume now that the instantaneous utility is [math: u(c)=10c]u\left ( c\right ) =10 c and all other parameters remain the same. Compute the discount factor: Answer 9 Question 8[input] 10) Assume again that the instantaneous utility is [math: u(c)=10c]u\left ( c\right ) =10 c and all other parameters remain the same. Compute the risk premium of the good weather atomic (Arrow-Debreu) security: Answer 10 Question 8[input]
View Explanation
Verified Answer
Please login to view
Step-by-Step Analysis
Question 1: At least how many different securities is required for this market to be complete?
- Option: 0. A market cannot be complete with zero securities; this would offer no state-contingent payoffs at all, so it cannot span all possible states. This makes the option incorrect.
- Option: 1. With only one security, you can only hedge or insure against a single payoff pattern, which cannot span all three possible states (G, F, B). Therefore, this is not enough for completeness.
- Option: 2. Similarly, two securities provide at most two independent payoff patterns, still not enough to span three distinct states. This option is incorrect.
- Option: 3. In a three-state world, a complete Arrow-Debreu market requires at least as many independent state-contingent claims as there are states, so three securities can span the three payoffs and achieve completeness. This is the correct reasoning for why three is needed.
- Option: none of these answers. Since three securities is a valid and standard requirement for completeness in a 3-state setting, this option is not correct.
Question 2: Compute the equilibrium fair weather state price.
- The provided answer key indicates 0.10 for the fair weather state price. In Arrow-Debreu terms, the state price (or the price of a one-unit payoff in that state) reflects the discounted marginal utility-weighted value of that state to the representative agent, given the equilibrium allocations across states and the discount factor, beta, and the utility function.
- Conceptually, the state price combines the stochastic dis......Login to view full explanationLog in for full answers
We've collected over 50,000 authentic exam questions and detailed explanations from around the globe. Log in now and get instant access to the answers!
Similar Questions
Consider an investor who lives 2 periods (t and t+1). She has income et in the first period and et+1 in the second period. The investor buys θ shares of an asset at price pt in the first period, and receives an uncertain payoff xt+1=pt+1+dt+1 in the second period. Her investment decision is thus described by the following maximization problem: max θ[u(ct)+β𝔼t(u(ct+1))]. Assuming that the utility function is u(ct)=ct− α 2 c 2 t what is the equation for the price of the asset in period t as a function of tomorrow’s payoffs?
Consider an investor who lives 2 periods ( 𝑡 and 𝑡 + 1 ). She has income 𝑒 𝑡 in the first period and 𝑒 𝑡 + 1 in the second period. The investor buys 𝜃 shares of an asset at price 𝑝 𝑡 in the first period, and receives an uncertain payoff 𝑥 𝑡 + 1 = 𝑝 𝑡 + 1 + 𝑑 𝑡 + 1 in the second period. Her investment decision is thus described by the following maximization problem: 𝑚 𝑎 𝑥 𝜃 [ 𝑢 ( 𝑐 𝑡 ) + 𝛽 𝔼 𝑡 ( 𝑢 ( 𝑐 𝑡 + 1 ) ) ] . Assuming that the utility function is 𝑢 ( 𝑐 𝑡 ) = 1 2 ( 𝑐 𝑡 − 𝛼 ) 2 what is the equation for the price of the asset in period 𝑡 as a function of tomorrow’s payoffs?
Consider an investor who lives 2 periods ( 𝑡 and 𝑡 + 1 ). She has income 𝑒 𝑡 in the first period and 𝑒 𝑡 + 1 in the second period. The investor buys 𝜃 shares of an asset at price 𝑝 𝑡 in the first period, and receives an uncertain payoff 𝑥 𝑡 + 1 = 𝑝 𝑡 + 1 + 𝑑 𝑡 + 1 in the second period. Her investment decision is thus described by the following maximization problem: 𝑚 𝑎 𝑥 𝜃 [ 𝑢 ( 𝑐 𝑡 ) + 𝛽 𝔼 𝑡 ( 𝑢 ( 𝑐 𝑡 + 1 ) ) ] . Assuming that the utility function is 𝑢 ( 𝑐 𝑡 ) = 𝑐 𝑡 𝛼 𝛼 what is the equation for the price of the asset in period 𝑡 as a function of tomorrow’s payoffs?
Consider an investor who lives 2 periods ( 𝑡 and 𝑡 + 1 ). She has income 𝑒 𝑡 in the first period and 𝑒 𝑡 + 1 in the second period. The investor buys 𝜃 shares of an asset at price 𝑝 𝑡 in the first period, and receives an uncertain payoff 𝑥 𝑡 + 1 = 𝑝 𝑡 + 1 + 𝑑 𝑡 + 1 in the second period. Her investment decision is thus described by the following maximization problem: 𝑚 𝑎 𝑥 𝜃 [ 𝑢 ( 𝑐 𝑡 ) + 𝛽 𝔼 𝑡 ( 𝑢 ( 𝑐 𝑡 + 1 ) ) ] . Assuming that the utility function is 𝑢 ( 𝑐 𝑡 ) = 𝑐 𝑡 − 𝛼 2 𝑐 𝑡 2 what is the equation for the price of the asset in period 𝑡 as a function of tomorrow’s payoffs?
More Practical Tools for Students Powered by AI Study Helper
Making Your Study Simpler
Join us and instantly unlock extensive past papers & exclusive solutions to get a head start on your studies!