Question

fall 2022 exam 1 chapters 1,4,5,6,7,8,13
table 5 - 2

price	quantity
$200	20
$150	70
$100	100
$50	150
$0	190

1. refer to table 5 - 2. using the midpoint method, if the price falls from $150 to $100, the elasticity of demand is:

a. 0.6.
b. 0.9.
c. 1.1.
d. 2.
short answers

1. use the figure below to answer the following questions.

in the absence of any price controls (meaning the market is in equilibrium), find total surplus created. show work.

Explanation:

Step1: Recall mid - point formula for price elasticity of demand

The mid - point formula for price elasticity of demand ($E_d$) is $E_d=\frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}}$, where $\%\text{ change in quantity demanded}=\frac{Q_2 - Q_1}{\frac{Q_2+Q_1}{2}}\times100$ and $\%\text{ change in price}=\frac{P_2 - P_1}{\frac{P_2+P_1}{2}}\times100$. When the price falls from $P_1 = 150$ to $P_2=100$, from the table, $Q_1 = 70$ and $Q_2 = 100$.

Step2: Calculate the percentage change in quantity demanded

$\%\text{ change in quantity demanded}=\frac{Q_2 - Q_1}{\frac{Q_2+Q_1}{2}}\times100=\frac{100 - 70}{\frac{100 + 70}{2}}\times100=\frac{30}{\frac{170}{2}}\times100=\frac{30}{85}\times100\approx35.29\%$

Step3: Calculate the percentage change in price

$\%\text{ change in price}=\frac{P_2 - P_1}{\frac{P_2+P_1}{2}}\times100=\frac{100 - 150}{\frac{100+150}{2}}\times100=\frac{- 50}{\frac{250}{2}}\times100=\frac{-50}{125}\times100=-40\%$

Step4: Calculate the price elasticity of demand

$E_d=\frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}}=\frac{35.29\%}{-40\%}\approx - 0.9$. We take the absolute value, so $|E_d|=0.9$

Answer:

b. 0.9