All answers should be handwritten. You should provide an explanation for your answers, but the answer should be kept to the point.DO NOT USE CHATGPT!

Consider the graph below that represents the demand curve for a good, the marginal revenue of a potential monopolist, and the marginal cost before an innovation (MC1 = 1) and after a potential innovation of size v (MC2 = 1/7). In the initial period, all firms have the same marginal cost MC1. A single firm can choose to try to innovate. If it is successful, it becomes a monopolist in the second period with marginal cost MC2. Demand MC1 Mc2 Marginal revenue N \\ Q 1. Initially, the market in perfect competition with marginal cost MC1. Show the social surplus and producer surplus on the graph. 2. Show the change in producer surplus in the second period if the firm is successful at innovation and becomes a monopolist. Decompose the producer surplus into two distinet components and interpret them. 3. Suppose that instead the government innovates (or subsidizes research at univer- sities) and distributes the new technology to all firms, so all firms have marginal cost MC2 and there is perfect competition. Show the change in social surplus compared to the initial period. 4. Suppose that the firm is better at innovating than the government, because it has expertise in the specific sector, so the cost of innovation for the firm is lower than for the government. Does the first scenario (bullet point 1) or the second scenario (bullet point 2) lead to higher innovation? How does it depend on and the differential in innovation cost