Question 25 of 25intermediate🔧 ApplyNumerical4 marks

At the market price of Rs 10, a firm supplies 4 units of output. The market price increases to Rs 30. The price elasticity of the firm’s supply is 1.25. What quantity will the firm supply at the new price?

Correct Answer

The firm will supply 14 units at the new price of Rs 30.

Exercise: EXERCISES | Q: 27 | (Page 18)
For More Understanding

Explanation

This question tests the application of the price elasticity of supply formula. The student needs to understand that elasticity measures the responsiveness of quantity supplied to price changes. Using the percentage change method, we first calculate the percentage change in price, then use the elasticity value to find the percentage change in quantity, and finally determine the new quantity supplied.

Solution Steps

  1. Step 1: Given values - Initial Price (P₁) = Rs 10, Initial Quantity (Q₁) = 4 units, New Price (P₂) = Rs 30, Price Elasticity of Supply (eₛ) = 1.25

  2. Step 2: Calculate Percentage Change in Price - %ΔP = [(P₂ - P₁) / P₁] × 100 = [(30 - 10) / 10] × 100 = (20/10) × 100 = 200%

  3. Step 3: Apply Elasticity Formula - eₛ = (% Change in Quantity Supplied) / (% Change in Price). Therefore, 1.25 = (%ΔQ) / 200

  4. Step 4: Calculate Percentage Change in Quantity - %ΔQ = 1.25×2001.25 \times 200 = 250%

  5. Step 5: Find New Quantity - %ΔQ = [(Q₂ - Q₁) / Q₁] × 100. So, 250 = [(Q₂ - 4) / 4] × 100. This gives (Q₂ - 4) / 4 = 2.5. Therefore, Q₂ - 4 = 10, and Q₂ = 14 units.

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