题目
题目

Dashboard Mock Final

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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]

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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 explanation

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