True of False?
E=exchange rate
Suppose E $/euros = 3/2 and E $/pounds = 2, and there is no trade friction, the no arbitrage condition implies
that E pounds/euros = 2
False. Think it through.
You have $/euros = 3/2 which means $3 = 2E. Also, you have 2E=1L. Ergo, $3=1L.
so the arbitrage condition should be E pounds/euros=3/4. ( i got this by multiplying 1/2 and 3/2 )
Is this correct?
To determine whether the statement is true or false, we need to understand the concept of exchange rates and the no arbitrage condition.
Exchange rates represent the price of one currency in terms of another currency. In this case, E $/euros indicates the exchange rate between US dollars ($) and euros (€), and E $/pounds represents the exchange rate between US dollars and British pounds (£).
The no arbitrage condition is an economic principle that states there should be no opportunity for risk-free profits in the foreign exchange market. In other words, if the exchange rates are not in equilibrium, it could create an arbitrage opportunity where one could make risk-free profits by exploiting the price differences between different currencies.
Now, let's analyze the given information:
E $/euros = 3/2 (US dollars per euro)
E $/pounds = 2 (US dollars per pound)
The statement suggests that the no arbitrage condition implies E pounds/euros = 2 (the exchange rate between British pounds and euros).
To determine if this condition holds, we need to consider the cross-rate between the pounds and euros using the given exchange rates.
To calculate the cross-rate E pounds/euros, we can use the formula:
E pounds/euros = (E $/pounds) / (E $/euros)
Using the given values, we can substitute the exchange rates:
E pounds/euros = (2) / (3/2) = 4/3
Since the calculated cross-rate E pounds/euros is not equal to 2, the statement is false. The no arbitrage condition does not imply that E pounds/euros = 2 in this case.
To recap: The correct value for E pounds/euros, using the given exchange rates, is 4/3, not 2.