Hello! kindly provide detailed proof and analysis. Thanks!

3. Consider an industry with market demand characterized by: P = 6300 3Q. Suppose the market is currently served by a large collection of rms all with constant marginal costs: M C = 4200. (a) What will be the initial price in this market? (b) Suppose one rm is able to innovate and drive their own costs down to V ' = 3600. What price and quantity would this rm want to set to maximize prots as a single-price monopolist if it were to have the market to itself? (0) Suppose one rm is able to innovate and drive their own costs down to M C = 3600. What price and quantity will this rm actually set and what are the rm's prots? Is this a large or small innovation? (d) Given that there's a large collection of rms in the market and given that one rm has innovated to reduce its costs, what will be the output and prots of this innovating rm when it chooses to practice rst degree price discrimination after having driven its costs down to MC = 3600