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# Answer to Question #79193 in Economics of Enterprise for vivian

Question #79193
a) Yesterday, the price of a packet of sachet water was ȼ3.00, and Sompa was willing to buy 10 packets. Today, the price has gone up to ȼ3.75 a packet, and Sompa is now willing to buy 8 packets. Is Sompa's demand for sachet water elastic or inelastic? What is her point elasticity of demand at the original price? What is the mid-point elasticity of demand?

a) P1 = 3.00, Q1 = 10 packets, P2 = 3.75, Q2 = 8 packets.
The price elasticity of demand is: Ed = (8 - 10)/(3.75 - 3)*(3.75 + 3)/(8 + 10) = -1, so the demand is unit elastic.
Her point elasticity of demand at the original price is: Ed = a*P1/Q1 = a*3/10.
According to the equation of the line using two points:
(P - 10)/-2 = (Q - 3)/0.75
-2Q + 6 = 0.75P - 7.5
P = -8/3Q + 18
a = -8/3.
Ed = -8/3*3/10 = -0.8.
The mid-point elasticity of demand formula gives the same result as the first formula, so Ed = 1.

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