Question

14. Assume the following demand function: Q-400-AP. Find the price range where I Gol > 1 and where Ιει < ! At P= $700, (j) What is demand? (ii) What is D? (iii) Using ED, what would you expect to happen to demand if this firm raised price by a. b. 7%? (fall by what %) (iv) What would you expect to happen to total revenue if this firm raised price by 7%? (go up or down and why)

Answer 1

a) Note that elasticity is given by |ed| = slope x P/Q. Here we have |ed| = 1 when

1 = 0.4 x P/400 - 0.4P

400 - 0.4P = 0.4P

P = 400/0.8 = 500 and Q = 300 units. Maximum or choke price is Q = 0 or 400/0.4 = 1000.

Thus, for prices 0 < P < 500, we have |ed| < 1 and for prices 400 < P < 1000 , we have |ed| > 1.

b) At P = 700, Qd = 400 - 0.4*700 = 120 units

ed = -0.4 x 700/120 = -2.33

When price is higher by 7%, quantity demanded will fall by 7*-2.33 = -16.33%

Total revenue goes down because price is increased by 7% and quantity demanded falls by 16.33%. Hence revenue falls by +7%-16.33% = -9.33%