# 高级经济学理论 Adv. Econometric Theory ECON3012

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$$\Delta \mu_{t}=\beta_{p}\left(\bar{U}^{c}-U_{t-1}^{c}\right)+\gamma\left(\bar{\mu}-\mu_{t-1}\right),$$
where $\gamma>0$. Inserted into the formula for price inflation this in sum gives:
$$\Delta p_{t}=\beta_{p}\left(\bar{U}^{c}-U_{t-1}^{c}\right)+\gamma\left(\bar{\mu}-\mu_{t-1}\right)+\left(\Delta w_{t}-n_{x}\right) .$$
In terms of the logged wage share $v_{t}=-\mu_{t}$ we get
$$\Delta p_{t}=\beta_{p}\left(\bar{U}^{c}-U_{t-1}^{c}\right)+\gamma\left(v_{t-1}-\bar{v}\right)+\left(\Delta w_{t}-n_{x}\right) .$$

## ECON3012 COURSE NOTES ：

Inserting the Taylor rule
$$i=\rho_{o}+\pi+\beta_{r_{1}}(\pi-\bar{\pi})+\beta_{r_{2}}\left(v-v_{o}\right), \quad \beta_{r_{1}}, \beta_{r_{2}}>0$$
into the effective demand equation
$$y=\frac{n+g-i_{1}\left(i_{o}-\pi\right)}{(1-v)\left(1-i_{1}\right)+(1-c) v}$$
$$\bar{y}=-\frac{i_{1} \beta_{r_{2}}\left(v-v_{o}\right)}{(1-v)\left(1-i_{1}\right)+(1-c) v}$$
to our former calculations – in the place of the $\beta_{w_{2}}$ term now. This term gives rise to the following additional partial derivative
$$\tilde{y}{v}=-\frac{i \beta{r_{2}}}{\left(1-v_{o}\right)\left(1-i_{1}\right)+(1-c) v_{o}}$$