a) Covered interest rate parity (CIRP) links the spot exchange rate of a currency to its forward rate and the interest rates of currency regions: $(1+i) = (1 + i^*)S/F$, where $i$ is domestic interest rate, $i^*$ is the foreign interest rate, $S$ is the spot exchange rate, and $F$ is the forward interest rate. Use the rules of log and approximation $\log(1+x) \approx x$ to derive the approximation $i \approx i^* - (F - S)/S$. Tips: take logs of both sides of CIRP, use the rules of logs and observe that $F/S = 1 + (F - S)/S$.
b) Assume that the price level $P$ is related to expected prices $P^e$ by equation: $P = A(1 + \theta)P^e$, where $\theta$ is a mark-up parameter, and $A$ is a constant. Let us now assume that $P$, $P^e$, and $\theta$ are functions of time $t$. Moreover, let $\pi(t)$ denote the inflation, i.e. $\pi(t) = P'(t)/P(t)$, and let $\pi^e(t)$ stand for the expected inflation, respectively. Log-differentiate both sides of the equation to get a relation for inflation, inflation expectations and the mark-up $\theta$.
