Suppose a firm's total revenue function and total cost function are given by: R(q) = 70q q² where R: R+ → R C(q) = q² - 30q+ 100 where C: R+ → R 1. What is the type of the firm facing this particular revenue function? 2. Based on the given information, can you deduce the inverse demand function? 3. Solve this firm's profit maximization problem. Make sure to clearly indicate the profit maximizing solution at the end (i.e. q,p*,& n(q)). 4. Find the supply function for this particular firm. Is it equal to the market supply? Please explain. Hint: Supply function can either be defined by an exact quantity or it can be defined by a set of possible quantities. 5. Suppose that the barrier to entry for this market has been removed by a change in regulation. You wish to start a new business in this market. What is the type of the new firm in this case? 6. Solve this new firm's profit maximization problem. Make sure to clearly indicate the profit maximizing solution at the end (i.e. q*,p*,& n(q*)). Hint: DO NOT use the inverse demand function. Example in Section 11.2 was finding for the point of intersection between the inverse demand function and MC. Your answers might not be in clean numbers as opposed to part 3. 7. Find the supply function for this new firm. Is it equal to the market supply? Please explain. Hint: Supply function can either be defined by an exact quantity or it can be defined by a set of possible quantities. 8. By part 5, what would be the initial market price p demanded by consumers? Please explain. Then, using this market price p, solve q* and 7(q) for this new firm. 9. Do you think that this market price p is going to stay the same in the long-run? Please explain. 10. Compare your answers in Part 3 (i.e. the original firm's q* and 7(q")) and Part 8 (i.e. the new firm's q* and π(q)). Is π(q*) the same for two firms? If so, why does one firm enjoy better profit than the other? Please explain. 11. Please draw marginal revenue, marginal cost, and supply curve for both firms in the same graph. Let subscript m denote the monopolist's curves and let subscript c denote the competitive firm's curves. Hint: For the competitive firm's supply curve, draw as if we are not given the market price p.