Suppose that you own a land. The market value of the land will be ale0.6-0.16? att times from now, where I is the investment amount (for example the number of trees you plant) at time t = 0 and a > 0 is a given number. The cost of investing I amount is 12. In other words, if you spend 12 dollars in your land now, then the value becomes ale0.6-0.162 t times from now. The interest rate of continuously compounding is r = 0.2. Note that you can choose I and the harvest time together. Let the value you maximize be denoted by U, that is, U(I,t) = [(the present value of a 1e0.670.1t) 12). at (a) Obtain the optimal harvest time and the investment amount. (b) Let the optimized value of U be denoted by U(a). Using the envelop theorem, show that (a) is a increasing function in a. Suppose that you own a land. The market value of the land will be ale0.6-0.16? att times from now, where I is the investment amount (for example the number of trees you plant) at time t = 0 and a > 0 is a given number. The cost of investing I amount is 12. In other words, if you spend 12 dollars in your land now, then the value becomes ale0.6-0.162 t times from now. The interest rate of continuously compounding is r = 0.2. Note that you can choose I and the harvest time together. Let the value you maximize be denoted by U, that is, U(I,t) = [(the present value of a 1e0.670.1t) 12). at (a) Obtain the optimal harvest time and the investment amount. (b) Let the optimized value of U be denoted by U(a). Using the envelop theorem, show that (a) is a increasing function in a