题目
题目
单项选择题

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?

选项
A.𝑝 𝑡 = 𝔼 𝑡 [ 𝛽 ( 𝑐 𝑡 + 1 𝑐 𝑡 ) 1 − 𝛼 𝑥 𝑡 + 1 ]
B.𝑝 𝑡 = 𝔼 𝑡 [ 𝛽 𝑐 𝑡 + 1 𝑐 𝑡 𝑥 𝑡 + 1 ]
C.𝑝 𝑡 = 𝔼 𝑡 [ 𝛽 ( 𝑐 𝑡 𝛼 𝛼 ) 𝑥 𝑡 + 1 ]
D.𝑝 𝑡 = 𝔼 𝑡 [ 𝛽 ( 𝑐 𝑡 + 1 𝑐 𝑡 ) 𝛼 − 1 𝑥 𝑡 + 1 ]
E.𝑝 𝑡 = 𝔼 𝑡 [ 𝛽 ( 𝑐 𝑡 + 1 𝛼 𝛼 ) 𝑥 𝑡 + 1 ]
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思路分析
We start by restating the problem setup and the candidate answers to ensure clarity about what we are evaluating. - The investor chooses theta in period t to maximize a two-period utility that depends on current consumption c_t and expected future utility from c_{t+1}. - The utility function is u(c) = c^α, with α > 0 (and presumably less than 1 to reflect risk preferences, though the exact range isn’t specified here). The question asks for the equation that prices the asset in period t as a function of tomorrow’s payoffs. - The answer options present candidate expressions for p_t as an efficiently expected discounted value that depends on ct, ct+1, x_t, etc., with β as the discount factor and the payoff structure for x_{t+1} given by x_{t+1} = p_t+1 + d_t+1 (i.e., the asset’s payoff depends on the price today plus a dividend). Option 1: p_t = E_t[ β ( ct + 1/ct ) 1 − α x_t + 1 ] - This expression mixes ct with a term 1/ct in a way that is not dimensionally consistent with the usual pricing of assets derived from the Euler equation under u(c) = c^α. It also......Login to view full explanation

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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?

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