= Solution
{c}
Write $\tau=T-t$. In the <Black-Scholes formula>, both $d_1$ and $d_2$ depend on $x,K$ only through $\log(x/K)$. Replacing them by $\lambda x,\lambda K$ leaves that ratio unchanged. Each prefactor in the put formula acquires the same factor $\lambda$, giving
$$
p(t,\lambda x;\lambda K,T)
=\lambda Ke^{-r\tau}\Phi(-d_2)-\lambda x\Phi(-d_1)
=\boxed{\lambda p(t,x;K,T).}
$$
This is degree-one <homogeneity> of the <European put option> price in its spot and strike together.
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