A firm earns a revenue of Rs 50 when the market price of a good is Rs 10. The market price increases to Rs 15

Exercises · Q25

Q. A firm earns a revenue of Rs 50 when the market price of a good is Rs 10. The market price increases to Rs 15 and the firm now earns a revenue of Rs 150. What is the price elasticity of the firm's supply curve?

West Bengal WbchseTextbookSubjective· 3mImportance★★★★★

68% · 25/37 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Concept understanding — Price Elasticity Of Demand

Price Elasticity of Demand: From the Market to Your Pocket

Think about the last time the price of something you buy regularly went up. Maybe it was petrol, or onions, or your favourite snack. Did you stop buying it altogether? Did you buy a little less? Or did you grumble and keep buying the same amount?

That difference in your behaviour is exactly what Price Elasticity of Demand (PED) measures. It answers one simple question: When the price changes, how much does the quantity demanded change?

The Intuition First

Some goods are necessities — things you cannot easily do without. If the price of life-saving insulin rises, a diabetic patient will still buy almost the same amount. Their demand is insensitive to price.

Other goods are luxuries or have close substitutes. If the price of a particular brand of packaged juice doubles, you can easily switch to another brand, or drink water instead. Your demand is sensitive to price.

PED is just a number that captures this sensitivity. It tells sellers and policymakers: "If you change the price by 1%, by what percentage will the quantity demanded change?"

The Precise Definition (NCERT Standard)

The NCERT textbook defines Price Elasticity of Demand as:

E_d = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}

Or, more formally:

E_d = \frac{\Delta Q / Q}{\Delta P / P} = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}

Where:

$E_d$ = Price elasticity of demand (a pure number, no units)
$Q$ = Original quantity demanded
$\Delta Q$ = Change in quantity demanded ( $Q_{new} - Q_{old}$ )
$P$ = Original price
$\Delta P$ = Change in price ( $P_{new} - P_{old}$ )

Watch out

The Law of Demand says price and quantity move in opposite directions. So $\Delta Q$ and $\Delta P$ have opposite signs, making $E_d$ always negative. Economists usually drop the negative sign and talk about the absolute value (e.g., "elasticity is 2" means $E_d = -2$ ).

The Five Types of Elasticity

The value of $E_d$ tells you the nature of the good:

|---|---|---|---|---|

| $|E_d| = 0$ | Perfectly inelastic | Quantity demanded does not change at all when price changes | Life-saving drugs, salt (in very small quantities) |

| $0 < |E_d| < 1$ | Inelastic demand | Quantity changes by a smaller percentage than price | Petrol, electricity, basic food items |

| $|E_d| = 1$ | Unitary elastic | Quantity changes by exactly the same percentage as price | A theoretical midpoint; rare in real life |

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

For a business: Elasticity determines what happens to total revenue when you change price.

Important

Total Revenue (TR) = Price × Quantity. If demand is elastic ( $|E_d| > 1$ ), a price decrease raises total revenue (because quantity rises by a larger percentage). If demand is inelastic ( $|E_d| < 1$ ), a price increase raises total revenue (because quantity falls by a smaller percentage). …

Start your 14-day free trial to unlock the full solution →

Price elasticity of supply measures how responsive quantity supplied is to a change in price. Recovering the quantities from the revenue data ( $Q_1 = 5$ , $Q_2 = 10$ ) and applying the percentage (point) method the chapter uses — with base values $P_1$ and $Q_1$ — gives $e_s = 2$ , so supply is elastic.

The price elasticity of supply ( $e_s$ ) is the percentage change in quantity supplied divided by the percentage change in price. Because firms generally supply more as price rises, this elasticity is normally positive.

Step 1 — Recover the quantities

We are given revenue, not quantity. But revenue is price times quantity, $R = P \times Q$ , so $Q = R/P$ :

At the initial price $P_1 = 10$ , revenue is $50$ , so $Q_1 = \frac{50}{10} = 5$ units.
At the new price $P_2 = 15$ , revenue is $150$ , so $Q_2 = \frac{150}{15} = 10$ units.

The firm supplies 5 units at Rs 10 and 10 units at Rs 15.

Step 2 — Apply the chapter's elasticity method

Section 4.7 computes the price elasticity of supply from the base (initial) values $P_1$ and $Q_1$ — exactly as in the cricket-ball worked example, where $e_s$ came out to $2$ . We do the same here.

e_s = \frac{\dfrac{Q_2 - Q_1}{Q_1} \times 100}{\dfrac{P_2 - P_1}{P_1} \times 100}

Percentage change in quantity: $\dfrac{Q_2 - Q_1}{Q_1} \times 100 = \dfrac{10 - 5}{5} \times 100 = 100\%$ . …

Start your 14-day free trial to unlock the full solution →

←Previous questionQ24 — There are three identical firms in a market. The following table shows…→Next questionQ26 — The market price of a good changes from Rs 5 to Rs 20. As a result, th…

Q.A firm earns a revenue of Rs 50 when the market price of a good is Rs 10. The market price increases to Rs 15 and the firm now earns a revenue of Rs 150. What is the price elasticity of the firm's supply curve?

Step 1 — Recover the quantities

Step 2 — Apply the chapter's elasticity method

🎓Unlock everything free for 14 days

Unlock everything free for 14 days