Answer to Question #160941 in Microeconomics for Albert

Question

The price of oil is $30 per barrel and the price elasticity is constant and equal to-0.5. An oil embargo reduces the quantity available by 20 percent. Use the arc elasticity formula to calculate the percentage increase in the price of oil.

Answer 1

$Price \; elasticity = \frac { \frac{Q_2 – Q_1}{0.5 \times (Q_1 + Q_2)} }{ \frac{P_2 – P_1}{0.5 \times (P_2 + P_1)} } \\ -0.5 = \frac {-0.2} { \frac{P_2 – 30}{0.5 \times (P_2 + 30)} } \\ \frac{P_2 - 30}{P_2 + 30} = \frac{0.2 \times 0.5}{0.5} \\ \frac{P_2 - 30}{P_2 + 30} = 0.2 \\ P_2 - 30 = 0.2P_2 + 6 \\ 0.8P_2 = 36 \\ P_2 = 45$

Hence price is increased to $45

In terms of arc elasticity, price is increased by 33.33% and in terms of absolute change, price is increased by 50%.