Consider a monopolist firm, facing the demand QD = −aP +b, where a > 0 and b > 0 are real numbers. The monopolist’s total production costs are linear and take the following form: C(Q) = cQ + d, wh

Consider a monopolist firm, facing the demand QD = −aP +b, where a > 0 and b > 0 are real numbers. The monopolist’s total production costs are linear and take the following form: C(Q) = cQ + d, where c > 0 and d > 0 are real numbers and the domain of C is [0,∞). 1. (1 points) Derive the monopolist’s revenue function, R(Q). 2. (1 points) Derive the monopolist’s profit function, Π(Q). 3. (1 points) What is the shape of the profit function, Π(Q)? Explain your answer. 4. Assume now that costs are quadratic and have the form C(Q) = gQ2 + d, where d > 0 and g are some real number. The domain of C is [0, ∞). (a) (2 points) For which choice of the parameters, g and d > 0, are the profits inverse u-shaped? Your answer might depend on a or b. (b) (2 points) For which choice of the parameters, g and d > 0, are the profits u-shaped? Your answer might depend on a or b. (c) (2 points) Assume a = 1. Choose particular values for the parameters, g and d > 0, that are consistent with your answer from part (b) and sketch the cost function. (d) (2 points) Assume a = 1. Choose particular values for the parameters, g and d > 0, that are consistent with your answer from part (a) and sketch the cost function. (e) (1 points) Based on your sketches of the cost function, is there any case you find reasonable? Explain your answer (Max 2 sentences).