Sure! The price elasticity of demand (PED) using the mid-point (or arc elasticity) formula is calculated as:
\[ PED = \frac{\text{% change in quantity demanded}}{\text{% change in price}} \]
Using the mid-point method:
\[ \text{% change in quantity demanded} = \frac{\text{New Quantity - Initial Quantity}}{\text{((New Quantity + Initial Quantity) / 2)}} \]
\[ \text{% change in price} = \frac{\text{New Price - Initial Price}}{\text{((New Price + Initial Price) / 2)}} \]
Plugging in your values:
Initial Quantity (Q1) = 50,000
New Quantity (Q2) = 49,000
Initial Price (P1) = $8
New Price (P2) = $9
\[ \text{% change in quantity demanded} = \frac{49,000 - 50,000}{(49,000 + 50,000) / 2} = \frac{-1,000}{49,500} = -0.0202 \] or -2.02%
\[ \text{% change in price} = \frac{9 - 8}{(9 + 8) / 2} = \frac{1}{8.5} = 0.1176 \] or 11.76%
\[ PED = \frac{-2.02\%}{11.76\%} = -0.1718 \]
Given that the absolute value of this elasticity measure is less than 1, this means the product is inelastic. This is typical for many goods that are considered necessities or have few substitutes, like cigarettes for many people.
For the graph:
1. Plot the vertical axis (Y-axis) as "Price" and the horizontal axis (X-axis) as "Quantity".
2. You have two points to plot: (50,000, $8) and (49,000, $9).
3. Draw a downward sloping line connecting these two points.
4. Label this line as "Demand".
The curve would slope downward from left to right, consistent with the law of demand. Given that the quantity decreased by a small percentage relative to the percentage increase in price, this further confirms the inelastic nature of the product visually on the graph.
To conclude, the price elasticity of demand for the pack of cigarettes, based on the data provided, is inelastic.