Question

c. draw a graph and calculate the price elasticity of the supply for concert tickets if the price goes from $50 to $60, causing you to change your weekly consumption from 10 tickets per week to 15. show all work and explain what the outcome means to a business! (hint: refer to the above video process first before completing this section)

Explanation:

Step1: Recall price - elasticity of supply formula

The formula for price - elasticity of supply ($E_s$) is $E_s=\frac{\%\text{ change in quantity supplied}}{\%\text{ change in price}}$. The percent - change in quantity supplied ($\%\Delta Q_s$) is calculated as $\frac{Q_2 - Q_1}{Q_1}\times100\%$, and the percent - change in price ($\%\Delta P$) is calculated as $\frac{P_2 - P_1}{P_1}\times100\%$.

Step2: Calculate percent - change in quantity supplied

Given $Q_1 = 10$ and $Q_2=15$. Then $\%\Delta Q_s=\frac{Q_2 - Q_1}{Q_1}\times100\%=\frac{15 - 10}{10}\times100\%=\frac{5}{10}\times100\% = 50\%$.

Step3: Calculate percent - change in price

Given $P_1 = 50$ and $P_2 = 60$. Then $\%\Delta P=\frac{P_2 - P_1}{P_1}\times100\%=\frac{60 - 50}{50}\times100\%=\frac{10}{50}\times100\%=20\%$.

Step4: Calculate price - elasticity of supply

$E_s=\frac{\%\Delta Q_s}{\%\Delta P}=\frac{50\%}{20\%}=2.5$.

For graphing:

1. On the x - axis, label the quantity of concert tickets (ranging from at least 0 to 15). On the y - axis, label the price of concert tickets (ranging from at least 0 to 60).
2. Plot the initial point $(Q_1,P_1)=(10,50)$ and the new point $(Q_2,P_2)=(15,60)$.
3. Draw a supply curve that passes through these two points. A positive - sloped straight line can be used for simplicity in this case, assuming a linear supply relationship in this price - quantity range.

The interpretation of $E_s = 2.5$: A price - elasticity of supply of 2.5 means that for a 1% increase in the price of concert tickets, the quantity supplied of concert tickets increases by 2.5%. It indicates that the supply of concert tickets is elastic, meaning that suppliers are relatively responsive to price changes.

Answer:

The price - elasticity of supply is 2.5. The graph has a positive - sloped line passing through the points (10,50) and (15,60) with quantity on the x - axis and price on the y - axis.