In this paper we addressed the problem of determining the optimal replicating strategy for a European call option under differential transactions costs. We derived an upper boundary for the cost factor in a market where all Investors face the same factor. This upper boundary ensures the efficiency of the stock price as well as the bond price process. It turned out that exact replication is optimal in the presence of only one transactions cost factor. Hence, the option is redundant. Nevertheless the bid price is below the ask price with prices in this ränge being arbitrage-free. With an increasingly finer partition of the binomial tree the condition of dominance becomes more stringent, so that the cost factor must be rather small. Furthermore, the bid price increases and the ask price decreases with a finer partition.