label demand as elastic, unit elastic, or inelastic for each scenario. use the midpoint method when…

label demand as elastic, unit elastic, or inelastic for each scenario. use the midpoint method when applicable to calculate the price elasticity of demand.\na. contain yourself!, a plastic container company, raises the price of its signature lunchbox container from $3.00 to $4.00. as a result, the quantity sold drops from 20,000 to 15,000.\nb. economists working for the united states have determined that the elasticity of demand for gasoline is 0.5.\nc. capital metro decides to increase bus fare rates from $2.00 to $2.21. consequently, the number of passengers who decide to take the bus in austin drops from an average of 70,000 riders a day to an average of 61,000 riders a day.

label demand as elastic, unit elastic, or inelastic for each scenario. use the midpoint method when applicable to calculate the price elasticity of demand.\na. contain yourself!, a plastic container company, raises the price of its signature lunchbox container from $3.00 to $4.00. as a result, the quantity sold drops from 20,000 to 15,000.\nb. economists working for the united states have determined that the elasticity of demand for gasoline is 0.5.\nc. capital metro decides to increase bus fare rates from $2.00 to $2.21. consequently, the number of passengers who decide to take the bus in austin drops from an average of 70,000 riders a day to an average of 61,000 riders a day.

Answer

Explanation:

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

The mid - point formula for price elasticity of demand ($E_d$) is $E_d=\frac{\frac{Q_2 - Q_1}{(Q_2+Q_1)/2}}{\frac{P_2 - P_1}{(P_2+P_1)/2}}$, where $Q_1$ and $Q_2$ are initial and new quantities, and $P_1$ and $P_2$ are initial and new prices. If $|E_d|> 1$, demand is elastic; if $|E_d| = 1$, demand is unit - elastic; if $|E_d|<1$, demand is inelastic.

Step2: Solve part a

$P_1 = 3$, $P_2=4$, $Q_1 = 20000$, $Q_2 = 15000$. First, calculate the percentage change in quantity: $\frac{Q_2 - Q_1}{(Q_2+Q_1)/2}=\frac{15000 - 20000}{(15000 + 20000)/2}=\frac{- 5000}{17500}\approx - 0.286$. Then, calculate the percentage change in price: $\frac{P_2 - P_1}{(P_2+P_1)/2}=\frac{4 - 3}{(4 + 3)/2}=\frac{1}{3.5}\approx0.286$. $E_d=\frac{-0.286}{0.286}=- 1$. Since $|E_d| = 1$, the demand is unit - elastic.

Step3: Solve part b

Given $E_d = 0.5$. Since $|E_d|=0.5<1$, the demand for gasoline is inelastic.

Step4: Solve part c

$P_1 = 2$, $P_2 = 2.21$, $Q_1 = 70000$, $Q_2 = 61000$. Percentage change in quantity: $\frac{Q_2 - Q_1}{(Q_2+Q_1)/2}=\frac{61000 - 70000}{(61000 + 70000)/2}=\frac{-9000}{65500}\approx - 0.137$. Percentage change in price: $\frac{P_2 - P_1}{(P_2+P_1)/2}=\frac{2.21 - 2}{(2.21+2)/2}=\frac{0.21}{2.105}\approx0.1$. $E_d=\frac{-0.137}{0.1}=-1.37$. Since $|E_d| = 1.37>1$, the demand is elastic.

Answer:

a. Unit - elastic b. Inelastic c. Elastic