QUESTIONS
1.) Individuals $A$ and $B$ think the probability that a future event will occur is $p$ and $q$ respectively. $A$ and $B$ have risk capital $X$ and $Y$. $A$ and $B$ invest so as to maximize the expected log of their capital. What price $r$ for the contract will assure that the sum of the demand for the contract from $A$ and $B$ is 0?2.) A future event has $n$ possible outcomes each with associated contract $c_{i}$ which will pay off 1 unit if the $i$th possibility occurs while the other $n-1$ contracts will become worthless. Each contract has a market price $m_{i}$ and the market is efficient: $\sum_{i}^{n} m_{i}=1$.
You believe the true probability of the $i$th possibility occurring is $q_{i}$ for $i=1,...,n$ (where the $q_{i}$ also sum to 1). You have $X$ units to invest and you wish to do this in such a way that the expected value of the logarithm of your capital is maximized. How many of each of the $n$ contracts should you buy?
