A consumer spends €200 monthly on Product A when its price is €2 and continues to spend €200 monthly when its price increases to €2.50 - Leaving Cert Economics - Question 3 - 2010

Next, we calculate the quantity demanded when the price is €2.50 using the same formula:

$\text{Quantity Demanded} = \frac{200}{2.50} = 80 \text{ units}$

Now, we find the change in quantity demanded and price:

• Change in Quantity: $\Delta Q = Q_2 - Q_1 = 80 - 100 = -20 \text{ units}$

• Change in Price: $\Delta P = P_2 - P_1 = 2.50 - 2 = 0.50$

Next, we will find the average quantity and average price:

• Average Quantity: $\text{Average Quantity} = \frac{Q_1 + Q_2}{2} = \frac{100 + 80}{2} = 90 \text{ units}$

• Average Price: $\text{Average Price} = \frac{P_1 + P_2}{2} = \frac{2 + 2.50}{2} = 2.25$

Finally, we calculate the price elasticity of demand using the elasticity formula:

$\text{PED} = \frac{\Delta Q}{\Delta P} \times \frac{P_{avg}}{Q_{avg}}$

Substituting the values:

$\text{PED} = \frac{-20}{0.50} \times \frac{2.25}{90} = -1.00$

The calculated price elasticity of demand is -1.00. This indicates that the demand for Product A is unit elastic, meaning that a 1% increase in price results in a 1% decrease in quantity demanded. This conforms to the law of demand, where price increases lead to a decrease in quantity demanded.