Question

2. Assume that the prices of a standard basket of goods and services in different countries are as follows . United States $40o .Canada C$500 . United Kingdom £220 .Japan Y60,000 a. What are the implied PPP exchange rates? b. How would the presence of a high sales tax in Britain, such as the value added tax (VAT), influence your guess of where the actual value of S($/E) would be vis-à-vis the PPP value of S($/E)?

Answer 1

Part (a)

Implied exchange rate = P₂ / P₁ where P_i = Price of the standard basket of goods and services in the country i

There are six possible exchange rate between the 4 countries:

Country	Price (P)
USA	PUSA = $ 400
Canada	PCan = C$ 500
United Kingdom	PUK = £ 220
Japan	PJ = ¥ 60,000

Exchange rate: $ / C $ = P_USA / P_Can = 400 / 500 = 0.80 to be interpreted as $ 0.8 = C$ 1

Exchange rate: $ / £ = P_USA / P_UK = 400 / 220 = 1.82 to be interpreted as $ 1.82 = 1 £

Exchange rate: $ / ¥ = P_USA / P_J = 400 / 60,000 = 0.00667 to be interpreted as $ 0.00667= ¥ 1

Exchange rate: C$ / £ = P_Can / P_UK = 500 / 220 = 2.27 to be interpreted as C$ 2.27 = 1 £

Exchange rate: C$ / ¥ = P_Can / P_J = 500 / 60,000 = 0.00833 to be interpreted as C$ 0.00833= ¥ 1

Exchange rate: £ / ¥ = P_UK / P_J = 220 / 60,000 = 0.00367 to be interpreted as £ 0.00367= ¥ 1

Part (b)

If any government levies higher sales taxes, say VAT, the goods and services will sell at a relatively higher price in such countries. Because the price is now inclusive of the tax as well. Thus, presence of different level of  taxes in different countries lead to distortion in the PPP implied exchange rates.

In our example, let's say UK has higher sales tax. So, the prices in UK will quoted relatively higher. So, any exchange rate derived by application of PPP theory using P_UK in denominator will be lower than actual value. Hence, the actual value of S ($ / £) will be higher than the PPP value of S ($ / £)