Question $2.$

$[25]2-$a$)$ By relying on arbitrage free assumption, show that for strike prices $0P_{K_2}^A-P_{K_1}^A{K}_2-K_1(0,S(0)$;$T)K_1,$ both inequal$-$

ities hold:

$0P_{K_2}^A-P_{K_1}^A{K}_2-K_1$

$We$ omitted $(0,S(0)$;$T)$ for brevity, $asitis$ fixed. $[Note$ that these are American contracts.$]$