If the quantity supplied increases from 98 to 118 if the price rises from 4 to 12, what is the price elasticity of supply according to the arc (or midpoint) method? [Round your answer to 2 decimal places]
Question
If the quantity supplied increases from 98 to 118 if the price rises from 4 to 12, what is the price elasticity of supply according to the arc (or midpoint) method? [Round your answer to 2 decimal places]
Solution
The price elasticity of supply using the arc method is calculated as follows:
Elasticity = [(Q2 - Q1) / ((Q2 + Q1) / 2)] / [(P2 - P1) / ((P2 + P1) / 2)]
Where: Q1 = initial quantity supplied = 98 Q2 = final quantity supplied = 118 P1 = initial price = 4 P2 = final price = 12
Substituting these values into the formula, we get:
Elasticity = [(118 - 98) / ((118 + 98) / 2)] / [(12 - 4) / ((12 + 4) / 2)] Elasticity = [20 / 108] / [8 / 8] Elasticity = 0.185 / 1 Elasticity = 0.185
So, the price elasticity of supply is 0.19 (rounded to two decimal places).
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