Consider a monopolist with the following demand curve: P = 210 Q. Assume the fixed costs of the monopolist are equal to 0 because the monopolist has been in business so long. The monopolist has a constant MCM = 30 for levels of output 90. If q> 90, MCM is infinite. a. Solve for the profit- maximizing level of output, price, and profit for the monopolist. b. Suppose a potential entrant has an option to enter the market for a sunk cost of $3000. If it enters, the potential entrant's MCPE = 30 for output 45 units. If qpE > 45, MCPE is infinite. If the entrant does enter, it produces qpE = 45. Assuming that the monopolist accommodates entry, solve for the output and profits to the monopolist and the potential entrant. c. Suppose the monopolist has the option to increase its capacity up to a maximum of 135 units and lower its marginal cost to 25 (infinity after qM = 135 ) for a sunk cost of $1600. If the monopolist chooses to make this investment and then accommodates entry of the potential entrant with qPE = 45, solve for the output, price, and profits to the monopolist and the potential entrant. d. Assume the entrant chooses not to enter, but the monopolist spends the $1600 to expand as described in part (c). Solve for the monopolist's output and profit.