CBSE Class 12 Economics Chapter 4: Elasticity of Demand NCERT Solutions

Solution: Price elasticity of demand is a measure that quantifies how much the quantity demanded of a particular good or service changes in response to a change in its price. It essentially indicates the degree of responsiveness of consumers to price fluctuations in the market. A higher elasticity value signifies greater responsiveness, while a lower value indicates less responsiveness.

Solution:

We are given the following information:

• Original Price (P) = ₹ 4
• Original Quantity Demanded (Q) = 25 units
• New Price (P₁) = ₹ 5
• New Quantity Demanded (Q₁) = 20 units

First, we calculate the change in price and the change in quantity demanded:

• Change in Price (ΔP) = New Price - Original Price = ₹ 5 - ₹ 4 = ₹ 1
• Change in Quantity Demanded (ΔQ) = New Quantity - Original Quantity = 20 units - 25 units = -5 units

The formula for price elasticity of demand (Ed) is:

$$Ed\; =\; \backslash frac\{\backslash text\{\%\; Change\; in\; Quantity\; Demanded\}\}\{\backslash text\{\%\; Change\; in\; Price\}\}\; =\; \backslash frac\{\backslash Delta\; Q\; /\; Q\}\{\backslash Delta\; P\; /\; P\}\; =\; \backslash frac\{\backslash Delta\; Q\}\{\backslash Delta\; P\}\; \backslash times\; \backslash frac\{P\}\{Q\}$$

Now, we substitute the values into the formula:

$$Ed\; =\; \backslash frac\{-5\}\{1\}\; \backslash times\; \backslash frac\{4\}\{25\}$$

$$Ed\; =\; -5\; \backslash times\; \backslash frac\{4\}\{25\}$$

$$Ed\; =\; -\backslash frac\{20\}\{25\}$$

$$Ed\; =\; -0.8$$

The price elasticity of demand is -0.8. Since the absolute value of elasticity (|-0.8| = 0.8) is less than 1, the demand for the good is relatively inelastic. The negative sign indicates the inverse relationship between price and quantity demanded.

Solution:

We are given the demand function $Q\; =\; 10\; -\; 3P$. We need to find the price elasticity of demand at $P\; =\; \backslash frac\{5\}\{3\}$.

First, let's find the quantity demanded at this price:

$$Q\; =\; 10\; -\; 3\; \backslash times\; \backslash left(\; \backslash frac\{5\}\{3\}\; \backslash right)$$

$$Q\; =\; 10\; -\; 5$$

$$Q\; =\; 5$$

Now, we need to find the derivative of quantity (Q) with respect to price (P) to determine the slope of the demand curve at this point. For a linear demand function $Q\; =\; a\; -\; bP$, the derivative $\backslash frac\{dQ\}\{dP\}$ is a constant, -b.

In our case, $Q\; =\; 10\; -\; 3P$, so:

$$\backslash frac\{dQ\}\{dP\}\; =\; -3$$

The formula for price elasticity of demand (Ed) using calculus is:

$$Ed\; =\; \backslash frac\{dQ\}\{dP\}\; \backslash times\; \backslash frac\{P\}\{Q\}$$

Now, substitute the values of $\backslash frac\{dQ\}\{dP\}$, P, and Q:

$$Ed\; =\; (-3)\; \backslash times\; \backslash frac\{5/3\}\{5\}$$

$$Ed\; =\; -3\; \backslash times\; \backslash frac\{5\}\{3\; \backslash times\; 5\}$$

$$Ed\; =\; -3\; \backslash times\; \backslash frac\{1\}\{3\}$$

$$Ed\; =\; -1$$

The price elasticity of demand at $P\; =\; \backslash frac\{5\}\{3\}$ is -1. This indicates that the demand is unitary elastic at this price point, meaning the percentage change in quantity demanded is exactly equal to the percentage change in price.

Solution:

We are given:

• Price Elasticity of Demand (Ed) = -0.2
• Percentage change in Price = +5% (an increase)

We need to find the percentage change in quantity demanded.

The formula for price elasticity of demand is:

$$Ed\; =\; \backslash frac\{\backslash text\{\%\; Change\; in\; Quantity\; Demanded\}\}\{\backslash text\{\%\; Change\; in\; Price\}\}$$

We can rearrange this formula to solve for the percentage change in quantity demanded:

$$\%\; Change\; in\; Quantity\; Demanded\; =\; Ed\; \backslash times\; \%\; Change\; in\; Price$$

Now, substitute the given values:

$$\%\; Change\; in\; Quantity\; Demanded\; =\; (-0.2)\; \backslash times\; (+5\%)$$

$$\%\; Change\; in\; Quantity\; Demanded\; =\; -1\%$$

Therefore, the demand for the good will go down by 1%. The negative sign indicates a decrease in quantity demanded, which is consistent with an increase in price.

Solution:

We are given that the price elasticity of demand (Ed) for a good is -0.2. This value is less than 1 in absolute terms (|-0.2| < 1), which means the demand for the good is inelastic.

When demand is inelastic, a change in price leads to a proportionally smaller change in quantity demanded. Specifically, if the price of the good increases, the quantity demanded will decrease, but by a smaller percentage than the price increase.

We are told there is a 10% increase in the price of the good.

Since the demand is inelastic (Ed = -0.2), the percentage decrease in quantity demanded will be:

$$\%\; \backslash text\{\; Change\; in\; Quantity\; Demanded\}\; =\; Ed\; \backslash times\; \%\; \backslash text\{\; Change\; in\; Price\}$$

$$\%\; \backslash text\{\; Change\; in\; Quantity\; Demanded\}\; =\; (-0.2)\; \backslash times\; (+10\%)\; =\; -2\%$$

So, the quantity demanded will decrease by 2%.

Now let's consider the effect on total expenditure (Total Expenditure = Price × Quantity Demanded):

• The price has increased by 10%.
• The quantity demanded has decreased by 2%.

Since the percentage increase in price (10%) is greater than the percentage decrease in quantity demanded (2%), the total expenditure on the good will increase.

Conclusion: Total expenditure on the good will rise.

Solution:

We are given:

• Percentage decrease in Price = 4% (so, % Change in Price = -4%)
• Percentage increase in Total Expenditure = 2%

We know the relationship between price changes, elasticity, and total expenditure:

• If demand is elastic (|Ed| > 1), a price decrease leads to an increase in total expenditure.
• If demand is inelastic (|Ed| < 1), a price decrease leads to a decrease in total expenditure.
• If demand is unitary elastic (|Ed| = 1), total expenditure remains unchanged.

In this case, the price of the good has decreased, and the total expenditure on the good has increased. This situation occurs when the demand is elastic.

Let's verify this using the formula for elasticity. We need to find the percentage change in quantity demanded.

Let the initial price be P and the initial quantity be Q. Total Expenditure (TE) = P × Q.

New Price = P - 0.04P = 0.96P

Let the new quantity be Q'.

New Total Expenditure = (0.96P) × Q'

We are given that the new total expenditure is 2% higher than the original total expenditure:

New TE = TE + 0.02TE = 1.02TE

$$1.02(P\; \backslash times\; Q)\; =\; (0.96P)\; \backslash times\; Q\text{'}$$

Now, solve for Q':

$$Q\text{'}\; =\; \backslash frac\{1.02\; P\; \backslash times\; Q\}\{0.96\; P\}\; =\; \backslash frac\{1.02\}\{0.96\}\; Q\; \backslash approx\; 1.0625\; Q$$

The percentage change in quantity demanded is:

$$\%\; \backslash text\{\; Change\; in\; Quantity\; Demanded\}\; =\; \backslash frac\{Q\text{'}\; -\; Q\}\{Q\}\; \backslash times\; 100\; =\; \backslash frac\{1.0625\; Q\; -\; Q\}\{Q\}\; \backslash times\; 100\; =\; 0.0625\; \backslash times\; 100\; =\; +6.25\%$$

Now, calculate the price elasticity of demand:

$$Ed\; =\; \backslash frac\{\backslash text\{\%\; Change\; in\; Quantity\; Demanded\}\}\{\backslash text\{\%\; Change\; in\; Price\}\}\; =\; \backslash frac\{+6.25\%\}\{-4\%\}$$

$$Ed\; =\; -1.5625$$

Since the absolute value of elasticity (|-1.5625| = 1.5625) is greater than 1, the demand is elastic.

Conclusion: The elasticity of demand is elastic.

Solution: Price elasticity of demand refers to the degree of responsiveness of the quantity demanded of a commodity to a change in its price. It measures how much the quantity demanded changes for a given percentage change in price.

Solution: The price elasticity of demand is always negative because of the fundamental law of demand, which states that there is an inverse relationship between the price of a good and the quantity demanded of that good, assuming all other factors remain constant. When the price increases, the quantity demanded decreases, and when the price decreases, the quantity demanded increases. This inverse relationship results in a negative value when calculating elasticity using the formula.