The market price of a good changes from Rs 5 to Rs 20. As a result, the quantity supplied by a firm increases by 15 units. The price elasticity of the firm’s supply curve is 0.5. Find the initial and final output levels of the firm.
Initial output level = 10 units; Final output level = 25 units
Explanation
This question tests the application of the price elasticity of supply formula. The formula from the textbook is: eS = (ΔQ/Q) × (P/ΔP), where ΔQ is the change in quantity, Q is the initial quantity, P is the initial price, and ΔP is the change in price. Students need to substitute the given values and solve for the unknown initial quantity.
Solution Steps
Step 1: Identify given values: Initial Price (P₁) = Rs 5, Final Price (P₂) = Rs 20, Change in Quantity (ΔQ) = 15 units, Price Elasticity of Supply (eₛ) = 0.5
Step 2: Calculate Change in Price: ΔP = P₂ - P₁ = 20 - 5 = Rs 15
Step 3: Apply the formula for price elasticity of supply: eₛ = (ΔQ/Q₁) × (P₁/ΔP)
Step 4: Substitute values: 0.5 = (15/Q₁) × (5/15)
Step 5: Simplify: 0.5 = (15/Q₁) × (1/3) = 5/Q₁
Step 6: Solve for Initial Output (Q₁): Q₁ = 5/0.5 = 10 units
Step 7: Calculate Final Output (Q₂): Q₂ = Q₁ + ΔQ = 10 + 15 = 25 units