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. 
(a1) What is the point elasticity of demand for computers at the new price? Assume the demand curve is linear. 

(a2) Show your work for part (a1) 

(b1) What is the point elasticity of demand for computers at the original price? Again, assume the demand curve is linear. 

(b2) Show your work for part (b1). 

(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. 
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)
(a1)
At new price, Elasticity = (1/3) x (800/13) = 20.51
(b1)
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 midpoint method, which states that
Elasticity = (Change in quantity demanded / Average quantity demanded) / (Change in price / Average price)
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