Question

(c) f(z, y) =ェ-3y-ry, subject toェ+9 = 6 (d) f(x,y) , subject to a +y (e) f(x, v) -+, subject to +y'- Applications 4. Jane is running a lemonade stand at the farmer's market. The farmer's market only (20 allows one stand, so she faces no competition. She currently sells lemonade for $1. Tarzan tells her that this price is too high and suggests that if she lowers the price she can sell more lemonade. Jane does not know her costs, but she does know that her marginal cost is positive. The inverse demand for lemonade is P 3-0.01Q2 (a) What is Jane's revenue as a function of quantity? (b) What price will maximize revenue? (c) Is Tarzan right? How will lowering the price affect profits? Page 1 of 2

Answer 1

P = 3 - 0.01 Q^2 total revenue(TR) = P times Q = (3.0 .001 theta^2)Q = 3 theta - 0.01 theta^3 Total revenue = 3 theta - 0.01 theta^3 b) Marginal revenue (MR) = dTR/d theta MR = 3 - 0.03 theta^2 To maximize revenue put MR = 0 3 - 0.03 theta^2 = 0 0.03 theta^2 = 3 theta^2 = 100 rightdoublearrow theta = 10 Put theta = 10 in P = 3 - 0.01 theta^2 P = 3 - 0.01(10)^2 = 3 - 1 = 2 Price that neill maximize revenue = $ 2 c) Tarzan is not right. Lowering the price neill lower the profits because $2 > $1