Please answer in words and be specific and give some explanations

Part 2 (45 points) Consider a real intertemporal model with investment in Chapter 11 with the following modification. Suppose that the government introduces a "stimulus" policy, and the firm receives a subsidy of s in the current period per unit of investment it makes. 1. Assuming the other structure of the firm's problem is identical to the textbook model, write down the firm's profit for today and tomorrow under this policy. Then, derive the present value of its lifetime profit. 2. Before deriving the firm's optimal investment rule, describe how this subsidy would affect the firm's optimal investment decision using its lifetime profit function you derived above. 3. Derive the firm's optimal investment rule as we did in class, and analyze how the sub- sidy affects the optimal investment decision by comparing it with the rule (11.16) in the textbook. Intuitively explain why this effect occurs. Was your analysis above correct? 4. This subsidy is an additional government expenditure to the original model. There could potentially be several ways to finance it, including some additional tax scheme other than the lump sum tax on the consumers assumed in the standard model. Choose one and explain how it works. Also, analyze the pros and cons of your choice as much as you can/want from the perspectives of the complete real intertemporal model in Chapter 11