I am currently reading David Romer's Advanced Macroeconomics for self study. Could someone please kindly explain to me how to derive (10.21) from chapter 10 in more detail than the textbook?
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1 Answer
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You can derive (10.20) just applying expectation of $p_t$ repeatedly.
For details:
$p_t =\frac{r-\gamma V}{1+r}+\frac{f \eta_t }{1+r}+ \frac{E_t (p_{t+1} )}{1+r} =\frac{r-\gamma V}{1+r} + \frac{r-\gamma V }{(1+r)^2}+\frac{f \eta_t }{1+r}+ \frac{E_t (p_{t+2} )}{(1+r)^2}=\frac{r-\gamma V}{1+r} + \frac{r-\gamma V }{(1+r)^2}+\frac{r-\gamma V }{(1+r)^3}+\frac{f \eta_t }{1+r}+ \frac{E_t (p_{t+3} )}{(1+r)^3}=\cdots$
If you contiune this to infinite you can get (10.20).
