Suppose you live in a world with three islands and where currencies are unknown. Each island is specialized in mining a precious or rare earth metal that is the commodity used for transaction on each of those islands. Island one (I1) mines rhodium (R); island two (I2) mines Silver (S), and island three (I3) mines Gold (G). There exists a network of three precious metal dealers, D1, D2, and D3, with each one making a market in one of these metals with prices quoted per ounce.

 

a. Suppose dealer D1 is currently quoting to exchange 1.4260oz of rhodium per ounce of gold, and dealer D2 is exchanging 1.6230oz of silver per ounce of gold. Using only those two dealers, how many ounces of silver do you need to receive one ounce of rhodium? 

 

b. Suppose dealer D3 is quoting you to exchange 1.1250oz of silver for one ounce of rhodium. Given this quote and neglecting transaction costs would you say that there is an arbitrage opportunity? What would be the direct quote that excludes any arbitrage?

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To determine the number of ounces of silver needed to receive one ounce of rhodium using dealers D1 ... View the full answer