Consider the example given on pages 3-12 and 3-13. Suppose $k_{v}=k_{c}=0$, that is both costs and rewards are immediate. Let the remaining parameters be unchanged, so that $v_{t}=$ $\{8,20,0\}, c_{t}=\{0,9,1\}, \beta=\frac{1}{2}, \delta=1$. Suppose the decision-maker is partially naïve and believes $\hat{\beta}\beta$. For which value of $\hat{\beta}$ does the decision-maker's choice violate the dominance property?
A) $\hat{\beta}=\frac{1}{2}$
B) $\hat{\beta}=\frac{8}{11}$
C) $\hat{\beta}=\frac{4}{11}$
D) $\hat{\beta}=1$.

Question

Consider the example given on pages 3-12 and 3-13. Suppose $k_{v}=k_{c}=0$, that is both costs and rewards are immediate. Let the remaining parameters be unchanged, so that $v_{t}=$ $\{8,20,0\}, c_{t}=\{0,9,1\}, \beta=\frac{1}{2}, \delta=1$. Suppose the decision-maker is partially naïve and believes $\hat{\beta}>\beta$. For which value of $\hat{\beta}$ does the decision-maker's choice violate the dominance property?
A) $\hat{\beta}=\frac{1}{2}$
B) $\hat{\beta}=\frac{8}{11}$
C) $\hat{\beta}=\frac{4}{11}$
D) $\hat{\beta}=1$.

Quizplus · Accepted Answer

Given that $k_v = k_c = 0$, the costs and rewards are immediate, and with the parameters provided, the dominance property is violated when the decision-maker overestimates the discount factor $\beta$, thinking it is higher than it actually is. The correct choice of $\hat{\beta}$ that leads to a violation of the dominance property, given the context and parameters, is $\hat{\beta} = \frac{8}{11}$. This is because, with this overestimation, the decision-maker would incorrectly assess the present value of future rewards and costs, leading to a choice that does not maximize their actual discounted utility.

Consider the Example Given on Pages 3-12 and 3-13 kv=kc=0k_{v}=k_{c}=0kv​=kc​=0 , That Is Both Costs and Rewards Are Immediate

Consider the Example Given on Pages 3-12 and 3-13 $k_{v}=k_{c}=0$ , That Is Both Costs and Rewards Are Immediate