In response to a change in the price of good x from $10 to $6, the quantity demanded of good x increases from 100 to 150 units. what is the price elasticity of demand for good x? (use the midpoint formula and express as a decimal - e. g. 0.2)

- 0.80

Explanation:

Price elasticity of demand describes the extent to which the quantity demanded of good X changes as result of a change in its own price.

The midpoint formula for price elasticity of demand is presented and used as follows:

Percentage change in quantity = %ΔQ = [Q2 - Q1] / [(Q2 + Q1) ÷ 2] × 100

Percentage change in quantity = %ΔP = [P2 - P1] / [(P2 + P1) ÷ 2] × 100

Midpoint price elasticity of demand = %ΔQ / %ΔP

Where:

Q2 = New quantity of good X = 150

Q1 = Initial quantity of good X = 100

P2 = New price of good X = $6

P1 = Initial price of good X = $10

Therefore,

Percentage change in quantity = %ΔQ = [150 - 100] / [(150 + 100) ÷ 2] × 100

                                                                = [50/(250 ÷ 2)] × 100

                                                                 = (50/125) × 100

                                                                 = 40.00%

Percentage change in quantity = %ΔP = [$6 - $10] / [($6 + $10) ÷ 2] × 100

                                                                = [-$4/($16 ÷ $2)] × 100

                                                                 = (-$4/$8) × 100

                                                                 = - 50.00%

Price elasticity of demand = 40% / 50% = - 0.80

The elasticity of demand of -0.80 less than 1. That indicate that the quantity demand is inelastic. That is the change in the degree of change in the quantity demanded of good X is lower than the degree of change in its price.

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