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Consumers buy 50 units of a product when the price is £1.50 - Leaving Cert Economics - Question 3 - 2007

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Consumers buy 50 units of a product when the price is £1.50. When the price is reduced to £1 consumers buy 90 units. Using an appropriate formula, calculate the cons... show full transcript

Worked Solution & Example Answer:Consumers buy 50 units of a product when the price is £1.50 - Leaving Cert Economics - Question 3 - 2007

Step 1

Calculate the Change in Quantity Demanded

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Answer

The initial quantity demanded (Q1) is 50 units and the new quantity demanded (Q2) is 90 units. The change in quantity demanded (ΔQ) is:

ΔQ=Q2−Q1=90−50=40 ΔQ = Q2 - Q1 = 90 - 50 = 40

Step 2

Calculate the Change in Price

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Answer

The initial price (P1) is £1.50 and the new price (P2) is £1. The change in price (ΔP) is:

ΔP=P2−P1=1.00−1.50=−0.50ΔP = P2 - P1 = 1.00 - 1.50 = -0.50

Step 3

Calculate the Average Quantity Demanded

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Answer

The average quantity demanded (Q_avg) is calculated as:

Qavg=Q1+Q22=50+902=70Q_{avg} = \frac{Q1 + Q2}{2} = \frac{50 + 90}{2} = 70

Step 4

Calculate the Average Price

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The average price (P_avg) is calculated as:

Pavg=P1+P22=1.50+1.002=1.25P_{avg} = \frac{P1 + P2}{2} = \frac{1.50 + 1.00}{2} = 1.25

Step 5

Calculate the Price Elasticity of Demand

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Answer

The price elasticity of demand (PED) is calculated using the formula:

PED=(ΔQ/Qavg)(ΔP/Pavg)PED = \frac{(ΔQ / Q_{avg})}{(ΔP / P_{avg})}

Substituting the values:

PED=(40/70)(−0.50/1.25)=4070×1.25−0.50=40×1.2570×−0.50=50−35=−1.43PED = \frac{(40 / 70)}{(-0.50 / 1.25)} = \frac{40}{70} \times \frac{1.25}{-0.50} = \frac{40 \times 1.25}{70 \times -0.50} = \frac{50}{-35} = -1.43

Step 6

Interpret the Price Elasticity of Demand

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Answer

The calculated PED is -1.43, which indicates that demand is elastic since the absolute value is greater than 1. This means that consumers respond significantly to price changes. Since the PED is negative, this confirms that the product is a normal good.

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