Purchasing power parity
Absolute PPP sets the exchange rate to the ratio of price levels: E_PPP = P_dom / P_for. The real exchange rate q = E_market · P_for / P_dom equals 1 at PPP, so any gap is over- or under-valuation.
Quote convention: E = domestic currency per 1 unit of foreign currency. A higher E means the domestic currency has depreciated.
PPP-implied rate E_PPP1.00dom / foreign
Domestic currency isat PPPq = 1.00
Real exchange rate q 1.00Market vs PPP +0.0%
Domestic price level P_dom100
Foreign price level P_for100
Market exchange rate E_market1.00
The market rate sits exactly on the PPP line, so q = 1 and the domestic currency is fairly valued against PPP. Raise P_dom and watch E_PPP rise: domestic inflation depreciates the currency.
Relative PPP. Over time the rate moves with the inflation gap: %ΔE ≈ pi_dom − pi_for, exactly E1 / E0 = (1 + pi_dom) / (1 + pi_for). Faster domestic inflation pushes E up, depreciating the currency.
Try this. Raise P_dom to 120 with P_for at 100: E_PPP climbs to 1.20, so domestic inflation depreciates the currency. Then move E_market above and below that 1.20 line to flip the verdict between under- and over-valued.
Discussion: PPP is a long-run anchor, not a day-to-day rule. Why can a currency stay over- or under-valued for years? Think about non-traded goods, trade costs, and persistent productivity gaps.