Question

3. (25) Suppose that St. Patrick's Day has brought you lots of luck. You have come up with thoe novel idea of shamrock-shaped resin paperweights with an Arizona Bark Scorpion set inside. Not surprisingly, you have monopoly status in this market. You face the following cost function: C() 50020Q Q(p) 120-р (b) (5) Show your answers to (a) graphically on two, side-by-side graphs. The left graph should Market demand is given by: a) (5) What is your revenue maximizing Q and p? Draw a box around your answers. include demand and marginal revenue. The right graph should show total revenue. Page 1 of 2 (c) (5) What is your profit maximizing Q and p"? Draw a box around your answers. (d) (5) Show your answer to (c) on a single graph that includes demand and marginal revenue. (e) (5) In this scenario, how much larger are profits under profit maximization versus revenue maximization?

Answer 1

Q = 120 - p

p = 120 - Q

(a) Revenue is maximized when Marginal revenue (MR) is zero.

Total revenue (TR) = p x Q = 120Q - Q²

MR = dTR/dQ = 120 - 2Q

When MR = 0,

120 - 2Q = 0

2Q = 120

Q* = 60

p* = 120 - 60 = 60

(b)

From demand function,

When Q = 0, p = 120 (Vertical intercept) & when p = 0, Q = 120 (Horizontal intercept).

From MR function,

When Q = 0, p = 120 (Vertical intercept) & when p = 0, Q = 120/2 = 60 (Horizontal intercept).

TR curve is inverse-U shaped.

In following graph, D & MR are shown in left panel and TR is shown in right panel.

(c) Profit is maximized when MR equals MC.

MC = dC(Q)/dQ = 20

120 - 2Q = 20

2Q = 100

Q* = 50

p* = 120 - 50 = 70

(d) In following graph, profit is maximized at point A where MR intersects MC with price p* = P0 (= 70) and quantity Q* = Q0 (= 50).

NOTE: As HOMEWORKLIB Answering policy, first 4 parts are answered.