1. Suppose that V (S, t) = S^b for a negative real number b, that V satisfies the BlackScholes equation, and that = 0.4, r = 0.05, = 0. Solve for b. Show your work. 2. Suppose that r = 0.05 and = 0. Find all real constants b such that V (S, t) = S + b satisfies the BlackScholes equation. Show your work. 3. Suppose that for a certain stock, the volatility = 0.25, the risk-free interest rate is r = 0.05, and the Sharpe ratio is 0.6. (a) Find the numerical value of the expected annualized return of the stock. (b) If, instead, the Sharpe ratio is 0.2, then what is ? Show your work.