# 高级货币经济学 Adv. Monetary Economics ECON3008

If market agents do not suffer from money illusion, a change in $P$ and a change in $Y^{n}$ by the multiple $\lambda$ will change the demand for money by the same amount (homogeneity hypothesis of money demand):
$$\lambda \cdot L^{n}=f\left(\lambda \cdot P, r_{B}, r_{E}, \frac{\dot{P}}{P}, \lambda \cdot Y^{n}\right) .$$
If holds true for any arbitrary realisation of the parameter $\lambda$, we can, for instance, define $\lambda=1 / Y^{\pi}$. Substituting this expression in yields:
$$\begin{gathered} \frac{1}{Y^{n}} \cdot L^{n}=f\left(\frac{P}{Y^{n}}, r_{B}, r_{E}, \frac{\dot{P}}{P}, 1\right) \text { and, by rearranging } \ L^{n}=f\left(\frac{P}{Y^{n}}, r_{B}, r_{E}, \frac{\dot{P}}{P}, 1\right) \cdot Y^{n} . \end{gathered}$$

## ECON3008 COURSE NOTES ：

$$n R_{t}^{(n)}=(n-1) E_{t} R_{t+1}^{(n-1)}+r_{t}+T_{t}^{(n)}$$
one period yields:
$$(n-1) R_{t+1}^{(n-1)}=(n-2) E_{t+1} R_{t+2}^{(n-2)}+r_{t+1}+T_{t+1}^{(n-1)}$$
When we take expectations of by writing $E_{t} E_{t+1}=E_{t}$ and substituting in yields:
$$n R_{t}^{(n)}=(n-2) E_{t} R_{t+2}^{(n-2)}+E_{t}\left(r_{t+1}+r_{t}\right)+E_{t}\left(T_{t+1}^{(n-1)}+T_{t}^{(n)}\right) .$$