Consider the following production function of future investments: f(e, K) = ek.5. K is the level of investment and e is the fraction of the firm sold in an equity offering. The manager may be optimistic about the performance of the assets in place and any future investments. Specifically, an optimistic manager overestimates the output by a factor, s. The optimistic manager expects the output to be, (1 + s)f(.). a. The manager decides what fraction of the firm to sell and how much to invest going forward. Write down the equation to describe the manager's maximization problem. [3 marks] b. Derive the optimal investment policy for a rational manager as well as an optimistic manager. How does managerial optimism affect firm investment? Provide empirical support. [10 marks] C. Derive the optimal financing policy for an optimistic manager. How does optimism affect financing policy? Illustrate your answer with empirical support. Consider the following production function of future investments: f(e, K) = ek.5. K is the level of investment and e is the fraction of the firm sold in an equity offering. The manager may be optimistic about the performance of the assets in place and any future investments. Specifically, an optimistic manager overestimates the output by a factor, s. The optimistic manager expects the output to be, (1 + s)f(.). a. The manager decides what fraction of the firm to sell and how much to invest going forward. Write down the equation to describe the manager's maximization problem. [3 marks] b. Derive the optimal investment policy for a rational manager as well as an optimistic manager. How does managerial optimism affect firm investment? Provide empirical support. [10 marks] C. Derive the optimal financing policy for an optimistic manager. How does optimism affect financing policy? Illustrate your answer with empirical support