Consider a prediction market with a LMSR market maker with two outcomes, so that

$C(y)=ln(e^{y_0}+e^{y_1})$

Recall that after the conclusion of this market traders will receive a payment of $$1$ for each share of

the security they own for the outcome that occurs.

What is the cost for a trader that wants to buy one share of both securities $($that is a trader who wants

to simultaneously purchase one share of security $0$ and one share of security $1)?$ How does your answer

compare to the trader's expected utility for owning the two shares?

Plz do not use AI to solve!