50 units of good X is demanded at a price of 10 per unit. When price changes the Quantity demanded rises by 20 units. Calculate the new price of good X. The coefficient of elasticity of demand as unity.

6

The correct answer is option (2) : 6

• Initial quantity demanded (Q1) = 50 units
• Initial price (P1) = ₹10 per unit
• Increase in quantity demanded (ΔQ) = 20 units
• Elasticity of demand (Ed) = 1 (unitary elastic)
• The new Price P2 will be less than P1 because of the law of demand which states that when the price decreases, the quantity demanded increases. In this case, the quantity has increased so the price will decrease. Thus, change in price (ΔP) will be 10-P1.

We know unitary elasticity (Ed = 1) means that the percentage change in quantity demanded is equal to the percentage change in price (with opposite signs).

Here's how to find the new price (P2):

Calculate the percentage change in quantity demanded (%ΔQ):= (ΔQ / Q1) * 100 (%ΔQ)

= (20 units / 50 units) * 100 (%ΔQ)

= 40%

Since the elasticity is unitary (Ed = 1), the percentage change in price (%ΔP) will also be 40% but with a negative sign (price decreases to increase quantity demanded).

(%ΔP) = -40%

We can now use the initial price (P1) and the percentage change in price (%ΔP) to find the new price (P2):

P2 = P1 + (P1 * %ΔP) / 100

P2 = ₹10 + (₹10 * -40%) / 100

P2 = ₹10 - ₹4

P2 = ₹6

Alternatively,

Ed = (ΔQ / ΔP) * (P1/Q1)

1 = (20/ΔP) * 10/50

1= 4/ 10-P2

10-P2 = 4

P2 = 10-4

P2 = 6

ΔP = -4