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# 数学代写|宏观经济学作业代写Macroeconomics代考|The Option Value of Search

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## 宏观经济学作业代写Macroeconomics代考|opportunities

One thing our two-period model is missing is the value of continuing to search. The unemployed workers in period 0 have only one chance to find a job. If they don’t receive a job offer, or if they reject an offer, their payoff in period 1 is just the unemployment benefit, $b$. In a setting with more than two periods there would be multiple opportunities to search. In that case, the opportunity cost of accepting an offer of employment includes the EI benefits, $b$, as well as the expected value of continuing to wait for a better offer.

## 宏观经济学作业代写MACROECONOMICS代考|still illustrate

It turns out we can still illustrate the value of search in our two-period model by focusing on the time 0 values, $V_{0}^{u}$ and $V_{0}^{e}(\cdot)$. Recall from equations (3.3) and (3.5) that these values are determined as follows:
\begin{aligned} V_{0}^{e}(w) &=w+\beta\left{\delta V_{1}^{u}+(1-\delta) V_{1}^{e}(w)\right}, \quad \text { and } \ V_{0}^{u} &=b+\beta\left{\phi \int_{w}^{\bar{w}} \max \left{V_{1}^{e}(w), V_{1}^{u}\right} d F(w)+(1-\phi) V_{1}^{u}\right} \end{aligned}
Using the expressions $V_{1}^{e}(w)=w$ and $V_{1}^{u}=b$, these become
\begin{aligned} V_{0}^{e}(w) &=w+\beta{\delta b+(1-\delta) w}, \quad \text { and } \ V_{0}^{u} &=b+\beta\left{\phi \int_{w}^{\bar{w}} \max {w, b} d F(w)+(1-\phi) b\right} \end{aligned}
Let’s focus on (3.11), and specifically on the expected value in period 1 conditional on receiving an offer:
$$\int_{w}^{\bar{w}} \max {w, b} d F(w)$$

## 宏观经济学作业代写MACROECONOMICS代考|STILL ILLUSTRATE

\begin{aligned} V_{0}^{e}(w) &=w+\beta\left{\delta V_{1}^{u}+(1-\delta) V_{1}^{e}(w)\right}, \quad \text { and } \ V_{0}^{u} &=b+\beta\left{\phi \int_{w}^{\bar{w}} \max \left{V_{1}^{e}(w), V_{1}^{u}\right} d F(w)+(1-\phi) V_{1}^{u}\right} \end{aligned}
Using the expressions $V_{1}^{e}(w)=w$ and $V_{1}^{u}=b$, these become
\begin{aligned} V_{0}^{e}(w) &=w+\beta{\delta b+(1-\delta) w}, \quad \text { and } \ V_{0}^{u} &=b+\beta\left{\phi \int_{w}^{\bar{w}} \max {w, b} d F(w)+(1-\phi) b\right} \end{aligned}
Let’s focus on (3.11), and specifically on the expected value in period 1 conditional on receiving an offer:
$$\int_{w}^{\bar{w}} \max {w, b} d F(w)$$