Denote by p(K) = p(K,T) the fair price (at time t = 0) of a European call option with strike price K and exercise date T. Show that the function p(K) is strictly increasing. That is, show that for every 0 < K1 < K2, one has p(K1) < p(K2).
(Hint: arguing by contradiction assume that the inequality does not hold and find an arbitrage opportunity using the two European call options.)