Exercise 3, Questions 1-4 ALL
OSIF pdv' Exereise 3, (17 points) Consider a [monopolist firm that faces the demand QB : 2P + 10. l. (1 point] Find the inverse demand function and derive the revenue function of the rm, R(Q) That is, express the revenue as a function of the quantity Q (and not of the price). . Suppose that the monopolist's total production cost are linear and take the form: mm = Q + 3,5. The monopolist is capacity constrained and cannot produce more than 10 quantities. Thus. the domain of the cost function. prot function and revenue function is [0, 10]. (a) (1 point.) Find the monopolist's prot function, \"((2). (h) (2 points) Find and sketch the marginal revenue function. MMQ}, the marginal cost function MC(Q}, and the marginal profit function l'I'[Q) in one graph. If there are intersections with the vertical axis and with the horizontal axis. please highlight them clearly. (c) (1 point) In your graph1 highlight the part of the domain where the prot function 11\".?) is convex and that where \"((2) is concave. Also highlight the part of the domain where the revenue function HQ) is convex and that where 309) is concave.2 3. Assume now that cost are quadratic and take the form: C(Q) = 0.5Q2 +0 The domain of the cost functionI prot function and revenue function is [0,10]. (a) (1 point) Find the monopolist's prot function, \"((2) (h) (3 points) Find and sketch the marginal revenue function1 MR(Q}. the marginal cost function M0052}, and the momma! prot function {HQ} in one graph. If there are intersections with the vertical axis and with the horizontal axis. please highlight them clearly. (c) (1 point] In your graph. highlight the part of the domain where the prot function 11(0) is convex and that where l'I('Q} is concave. Moreover. highlight the part of the domain where the cost function C(Q) is convex and that where C(Q) is concave. ALso highlight the part of the domain where the revenue function R(Q} is convex and that where R(Q) is concave.\" E Q3+F.pdf 6 / 6 93% ... (e, (I point) In your graph, highlight the part of the domain where the proju function II(Q) is convex and that where II(Q) is concave. Moreover, highlight the part of the domain where the cost function C(Q) is convex and that where C(Q) is concave. Also highlight the part of the domain where the revenue function R(Q) is convex and that where R(Q) is concave. 4. Assume now that cost take the form: C(Q) = Q3 -2.5Q2 +6Q. The domain of the cost function, profit function and revenue function is [0, 10]. "It might well be the case that one (or all) of these functions are either convex or concave over the entire domain. "It might well be the case that one (or all) of these functions are either convex or concave over the entire domain. (a) (1 point) Find the monopolist's profit function, II(Q). (b) (4 points) Find and sketch the marginal revenue function, MR(Q), the marginal cost function MC(Q), and the marginal profit function II'(Q) in one graph. If there are intersections with the vertical axis and with the horizontal axis, please highlight them clearly. (c) (2 points) In your graph, highlight the part of the domain where the profit function II(Q) is convex and that where II(Q) is concave. Moreover, highlight the part of the domain where the cost function C(Q) is convex and that where C(Q) is concave. Also highlight the part of the domain where the revenue function R(Q) is convex and that where R(Q) is concave
