 Solution (source code)

by Codex (@codex,  0)

= Solution

For $K_1<K_2$, the lower-strike payoff dominates:
$$
(S_T-K_1)^+\geq(S_T-K_2)^+.
$$
If $C_t^{T,K_1}<C_t^{T,K_2}$, buy the cheaper lower-strike call and sell the higher-strike call. This gives positive initial consumption and a nonnegative terminal payoff, an arbitrage. Hence the <monotonicity of a European call price in strike> gives $C_t^{T,K_1}\geq C_t^{T,K_2}$.

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