Question

b. draw a graph and calculate the price elasticity of the demand for chocolate bars if the price goes from $2 to $3, causing you to change your weekly consumption from 8 bars per week to 5. 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 formula

The formula for price - elasticity of demand is $E_d=\frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}}$. The percentage change in quantity demanded is calculated as $\%\Delta Q=\frac{Q_2 - Q_1}{\frac{Q_2+Q_1}{2}}\times100$, and the percentage change in price is calculated as $\%\Delta P=\frac{P_2 - P_1}{\frac{P_2+P_1}{2}}\times100$.

Step2: Calculate percentage change in quantity demanded

$Q_1 = 8$, $Q_2=5$. $\%\Delta Q=\frac{5 - 8}{\frac{5 + 8}{2}}\times100=\frac{- 3}{\frac{13}{2}}\times100=\frac{-3\times2}{13}\times100=\frac{- 600}{13}\approx - 46.15\%$.

Step3: Calculate percentage change in price

$P_1 = 2$, $P_2 = 3$. $\%\Delta P=\frac{3 - 2}{\frac{3+2}{2}}\times100=\frac{1}{\frac{5}{2}}\times100=\frac{2}{5}\times100 = 40\%$.

Step4: Calculate price - elasticity of demand

$E_d=\frac{\%\Delta Q}{\%\Delta P}=\frac{-46.15\%}{40\%}\approx - 1.15$.

To draw the graph:

1. On the x - axis, label the quantity of chocolate bars (ranging from 0 to at least 8). On the y - axis, label the price of chocolate bars (ranging from 0 to at least 3).
2. Plot the initial point $(Q_1,P_1)=(8,2)$ and the new point $(Q_2,P_2)=(5,3)$.
3. Draw a demand curve passing through these two points.

The negative value of price - elasticity of demand indicates an inverse relationship between price and quantity demanded. Since $|E_d|=1.15>1$, the demand for chocolate bars is elastic. This means that a 1% change in price leads to a more than 1% change in the quantity demanded. For a business, this implies that increasing the price will lead to a more than proportionate decrease in the quantity demanded, and total revenue will decrease.

Answer:

The price - elasticity of demand is approximately $-1.15$. The demand for chocolate bars is elastic.