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We are looking for a perception-perfect strategy with $s=(0,0,\dots)$ and $\hat s=(1,1,\dots)$

The agent may believe she will enrol tomorrow if:

$\begin{align} 0+\hat\beta\delta\left(-c_0-c_1+\frac\delta{1-\delta}b\right)&\le-c_0-c_1+\frac{\hat\beta}\delta1-\delta b\\ (1-\hat\beta\delta)(c_0+c_1)&\le\hat\beta\delta b \end{align}$

I know that the LHS refers to the utility the agent thinks she will get if she consumes tomorrow, but I don't know what the RHS is. Can anyone tell me what the RHS refers to?

This is from my economics lecture notes. This is in the context of beta-delta discounting, where $c_0+c_1$ is the cost of doing the task, and $b$ is the benefit from doing the action in all periods following the task.

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    Unfortunately, it doesn't help at all. Those symbols are completely undefined as far as I, or anyone else here, can tell. You should fully write out the question, state what thin$g$s mean, and state what you know. Only then can you hope to receive an answer.2012-12-18

1 Answers 1

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In the second line of the formula we see $ (1 - \beta \delta) (c_0 + c_1) \leq \beta \delta b $.

Divide boths sides by the first factor on the LHS, $ (c_0 + c_1) \leq \frac{\beta \delta }{1 - \beta \delta} \cdot b$.

The RHS can then be interpreted as the value of the benefit discounted as a perpetuity beginning in the next period.