Please help with these 3 questions

Question 1 Hold-up with investment by the downstream rm. [20 points] Consider the holdup problem discussed in class. Change the game so that the timing/ actions are now: 1. Stage 1: o Downstream rm makes investment choice. Investment increases the value to consumers such that we have v(I) o Upstream rm makes product; 2. Stage 2: o Downstream rm sells at 17(1) 0 Set unit input payment from Downstream to Upstream rm p(I), so that prots are split evenly. v(I) is such that v' (I) > 0, v\" (I) c. 1. What is the price arising out of the second stage, given that rms split gains from trade equally (as in class)? Show your working. 2. What is the objective function solved by the downstream rm in determining their investment level in the rst stage? 3. Solve for the optimal investment and compare it to the investment made by the integrated rm. Is it higher or lower? Explain. The point of this question is to show that hold up also arrises if it is the downstream rm that makes the investment