Tom has the following utility function "u" over wealth levels "w" (measured in Dollars):

\begin{equation*} u(w) = \sqrt{w} \ \text{for all}\ w \geq 0 \end{equation*}

When choosing between lotteries based on wealth levels, he selects the lottery that provides him with the highest expected utility.

Q: Assuming Tom, at a wealth level of "w", has the opportunity to purchase a lottery ticket at a price of p > 0 (it can be assumed that w > p). The lottery ticket has a probability of 1/10 of winning 1000 USD and the remaining probability of winning nothing. Let $\Bar{p}$ be the price that precisely makes Tom indifferent between purchasing the lottery ticket and not purchasing it. Formulate the equation that determines $\Bar{p}$ (the equation does not need to be solved).