Question

12. Given the demand function is Q 180 5P, find the following: a The revenue finction b. The revnue maximizing output and price c. The own-price elasticity of demand at P $80 d. The level ofe and P where the own-price elasticity of demand (ED) is equal to one, in absolute value. What is the nature of total revenue when lEDl 1? 13. Assume that the demand function is Q demand at each of the following prices a. b. $7 c. $20 100-3P. Calculate the own-price elasticity of 14. Assume the following demand function: Q = 400-4P Find the price range where lepl >1 and where lEpl AtP= $700 1. a. b. What is demand? (ii) What is 60? (ii) Using ED. what would you expect to happen to demand if this firm raised price by 7967 (fall by what %) (iv) What would you expect to happen to total revenue if this finn raised price by 7%? (go up or down and why) 15. Assume TR (Q) 150 + 500-502 and TC(Q) = 100 + 60 Create a table in Excel showing TR(Q), MRC), TC(Q), MC (Q), π(Q), and marginal profit, as Q goes from 0 to 10 in increments of1 a. b. Identify the level of 2 that maximizes profit. c. At the level of Q that maximizes profit, what is the relation between MR and MC? d. At the level of Q that maximizes profit, what is marginal profit? e. Check your answer in part b using calculus. 16. Given the following profit function: π(x) x3-6x2-3x + 25 where x is the number of days of producing the good. a-interpret π(5) b. interpret ㎡(5) c. based on b, what woul d. Using information from a-c, would predicted sales on day 6 be an overestimate or under estimate? Explain? d you predict sales to be on day 6

Answer 1

(12)

Q = 180 - 0.5P

0.5P = 180 - Q

P = 360 - 2Q

(a) Revenue (TR) = P x Q = 360Q - 2Q²

(b) Revenue is maximized when dTR/dQ = 0.

dTR/dQ = 360 - 4Q = 0

4Q = 360

Q = 90

P = 360 - (2 x 90) = 360 - 180 = 180

(c) When P = $80, Q = 180 - (0.5 x 80) = 180 - 40 = 140

Elasticity = (dQ/dP) x (P/Q) = -0.5 x (80/140) = -0.29

(d) When absolute value of elasticity is 1,

(dQ/dP) x (P/Q) = -1

-0.5 x (P/Q) = -1

0.5 x (P/Q) = 1

P/Q = 2

P / (180 - 0.5P) = 2

P = 360 - P

2P = 360

P = 180

Q = 180 - (0.5 x 180) = 180 - 90 = 90

Revenue = 180 x 90 = 16,200

Since elasticity equals 1 at mid-point of demand curve, total revenue is maximized at this point.

NOTE: As per Answering Policy, 1st question is answered.