Question

Short Problem. 12 points: 26. (a) Write out the complete formula for the Price Elasticity of Demand. Now, given the following information on changes in the price and quantity of a good, calculate the PED using the midpoint method, for both possible price increases, (b) that is, show how you calculate PED once as price increases from P=1 to P-3, and again (c) as price increases from P-3 to P-5. For each price increase, is the good elastic, inelastie, or unit elastic? P (gooda (good) Elastic, Inelastic, or Unit Elastic?

Answer 1

a) Price elasticity of demand = %change in quantity demanded / %change in price

Price elasticity of demand using mid-point method = {(Q2 - Q1) / [(Q2+Q1) / 2]} / {(P2 - P1) / [(P2+P1) / 2]}

P2 = New price level

P1 = Initial price level

b)

• P1 = Initial price level = 1

P2 = New price level = 3

Q1 = Initial quantity = 8

Q2 = New quantity demanded = 6

PED using mid-point method = {(Q2 - Q1) / [(Q2+Q1) / 2]} / {(P2 - P1) / [(P2+P1) / 2]}

= {(6 - 8) / [(6+8) / 2]} / {(3 - 1) / [(3+1) / 2]} = -0.28 / 1 = -0.28

We can ignore the negative sign due to the negative relationship between price and quantity demanded. Thus elasticity is 0.28 which means demand is inelastic as elasticity of demand between 0 and 1 is inelastic demand.

• P1 = Initial price level = 3

P2 = New price level = 5

Q1 = Initial quantity = 6

Q2 = New quantity demanded = 4

PED using mid-point method = {(Q2 - Q1) / [(Q2+Q1) / 2]} / {(P2 - P1) / [(P2+P1) / 2]}

= {(4 - 6) / [(4+6) / 2]} / {(5 - 3) / [(5+3) / 2]} = -0.4 / 0.5 = -0.8

We can ignore the negative sign due to the negative relationship between price and quantity demanded. Thus elasticity is 0.8 which means demand is inelastic as elasticity of demand between 0 and 1 is inelastic demand.