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.

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Accepted Answer

> [!TLDR]
> This problem uses the concept of Price Elasticity of Supply to determine how a firm's output changes in response to a price change. Given the elasticity and the change in price and quantity, we find the initial output was 10 units and the final output was 25 units.

The Price Elasticity of Supply ($E_s$) measures the responsiveness of the quantity supplied of a good to a change in its price. It tells us, in percentage terms, how much the quantity supplied will change for a given percentage change in price. A higher elasticity value indicates that producers are more responsive to price changes, meaning they can significantly increase or decrease production when prices fluctuate. Conversely, a lower elasticity value (like 0.5 in this case) suggests that producers are less responsive, and quantity supplied does not change proportionally much with price changes.

In this specific problem, an elasticity of 0.5 means that a 1% increase in price leads to only a 0.5% increase in the quantity supplied. This indicates an inelastic supply, which is common for goods where production capacity is limited or takes time to adjust.

> [!FORMULA]
> The Price Elasticity of Supply ($E_s$) is calculated as:
> $$E_s = \frac{\% 	ext{ Change in Quantity Supplied}}{\% 	ext{ Change in Price}} = \frac{\frac{\Delta Q}{Q_1}}{\frac{\Delta P}{P_1}}$$
> where $Q_1$ is the initial quantity, $\Delta Q$ is the change in quantity, $P_1$ is the initial price, and $\Delta P$ is the change in price.

Let's use the given information to find the initial and final output levels.

1.  **Identify the given values:**
    *   Initial Price ($P_1$) = Rs 5
    *   Final Price ($P_2$) = Rs 20
    *   Change in Quantity Supplied ($\Delta Q$) = 15 units (since it increases by 15 units)
    *   Price Elasticity of Supply ($E_s$) = 0.5 …

Q.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.

Concept understanding — Price Elasticity Of Demand

Price Elasticity of Demand: From the Market to Your Pocket

The Intuition First

The Precise Definition (NCERT Standard)

The Five Types of Elasticity

Why Does This Matter? (The "So What?")

Q.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.

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