Practice Quiz 6 Solutions — Exchange Rates & PPP
Setup: S = $/£ = 1.25. Latte costs $5.50 in LA, £3.80 in London. US inflation 3%, UK inflation 4%.
(a) PPP-implied exchange rate and pound valuation?
Absolute PPP (law of one price applied to lattes):
\[S_{PPP} = \frac{P_{US}}{P_{UK}} = \frac{5.50}{3.80} = 1.4474 \text{ \$/£}\]The PPP-implied rate is $1.45/£, but the market rate is only $1.25/£. Since it costs fewer dollars to buy a pound in the market than PPP suggests, the pound is undervalued (equivalently, the dollar is overvalued) relative to PPP.
(b) Relative PPP: predicted percentage change in S = $/£?
The log-linear approximation to relative PPP:
\[\%\Delta S \approx \pi_{US} - \pi_{UK} = 3\% - 4\% = -1\%\]S = $/£ is predicted to fall by 1% — meaning the pound will weaken (depreciate) against the dollar. This makes sense: the UK has higher inflation, so its currency loses purchasing power faster.
(c) Intuition for why the higher-inflation currency depreciates?
If prices rise faster in one country, its goods become relatively more expensive — to maintain purchasing power parity, the exchange rate must adjust so that the higher-inflation country’s currency buys less foreign currency (depreciates).