Question

question 17
1 pts
you only need to calculate the elasticity in terms of the midpoint method or percentage change method. you do not need to calculate both ways. although on the exams you will need to show your work, it is not necessary to show all the calculations for the quizzes.on a certain supply curve, one point (initial point) is quantity supplied, q1 = 200, price, p1 = $5.00 and another point is quantity supplied = 220, price = $9.00. using the quantities and prices calculate the price elasticity of supply using the midpoint method or percentage change.

Explanation:

Step1: Recall Midpoint Formula for Elasticity

The midpoint formula for price elasticity of supply (\(E_s\)) is \(E_s=\frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{P_2 - P_1}{(P_2 + P_1)/2}}\), where \(Q_1 = 200\), \(Q_2 = 220\), \(P_1=\$5\), \(P_2 = \$9\).

Step2: Calculate % Change in Quantity

\(\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}=\frac{220 - 200}{(220 + 200)/2}=\frac{20}{210}\approx0.0952\)

Step3: Calculate % Change in Price

\(\frac{P_2 - P_1}{(P_2 + P_1)/2}=\frac{9 - 5}{(9 + 5)/2}=\frac{4}{7}\approx0.5714\)

Step4: Divide to get Elasticity

\(E_s=\frac{0.0952}{0.5714}\approx0.1667\) (or using exact fractions: \(\frac{20/210}{4/7}=\frac{20}{210}\times\frac{7}{4}=\frac{1}{6}\approx0.1667\))

Answer:

\(\approx0.167\) (or \(\frac{1}{6}\))