Question

In a bold attempt to test the market, Megan lowered the price of her best selling computer from $950 to $800 and her sales rose from 8 a day to 13 a day.

(a-1) What is the point elasticity of demand for computers at the new price? Assume the demand curve is linear.
(a-2) Show your work for part (a-1)
(b-1) What is the point elasticity of demand for computers at the original price? Again, assume the demand curve is linear.
(b-2) Show your work for part (b-1).
(c) Without any data on cost, can you make a suggestion on the strategy Megan should take if these two options are the only options she is considering? Explain. Suggest a broad general rule regarding elasticity and pricing that Megan could rely on even if she doesn’t have cost data.

Answer 1

Linear demand equation: Q = a - bP

When P = $950, Q = 8 and when P = $800, Q = 13.

8 = a - 950b........(1)

13 = a - 800b......(2)

(2) - (1) yields:

150b = 5

b = 5/150 = 1/30

a = 8 + 950b [From (1)] = 8 + 950 x (1/3) = (24 + 950)/3 = 974/3

Demand equation: Q = (974/3) - (P/3)

Elasticity = (dQ/dP) x (P/Q) = -(1/3) x (P/Q)

(a-1)

At new price, Elasticity = (-1/3) x (800/13) = -20.51

(b-1)

At original price, Elasticity = (-1/3) x (950/8) = -39.58

(c)

Since absolute value of elasticity is higher at original price, demand is more elastic at original price. With elastic demand, a price decrease will increase total revenue. So lowering price to $800 is a correct decision based on elasticity.

However, a broader measure of elasticity is the mid-point method, which states that

Elasticity = (Change in quantity demanded / Average quantity demanded) / (Change in price / Average price)