Calculating the Elasticity of Demand

To calculate the elasticity of demand, we can use the formula:

Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)

In this case, we are given that when the price of commodity A falls from 10 to 5 per unit, its quantity demanded doubles. Let's calculate the percentage change in quantity demanded and price.

Percentage Change in Quantity Demanded = ((New Quantity Demanded - Initial Quantity Demanded) / Initial Quantity Demanded) * 100
Percentage Change in Price = ((New Price - Initial Price) / Initial Price) * 100

Using the given information, we can substitute the values into the formulas:

Percentage Change in Quantity Demanded = ((2 - 1) / 1) * 100 = 100%
Percentage Change in Price = ((5 - 10) / 10) * 100 = -50%

Now we can calculate the elasticity of demand:

Elasticity of Demand = (100% / -50%) = -2

Interpreting the Elasticity of Demand

The calculated elasticity of demand is -2. This negative value indicates that commodity A has a price elastic demand. When the price decreases by 1 unit (from 10 to 5), the quantity demanded increases by 2 units.

The magnitude of the elasticity (-2) tells us that the demand for commodity A is relatively responsive to price changes. A 1% decrease in price leads to a 2% increase in quantity demanded.

Calculating the Price at which Quantity Demanded Falls by 50%

To calculate the price at which quantity demanded falls by 50%, we need to find the new price when the quantity demanded is reduced by 50%. Let's assume the initial quantity demanded is Q and the initial price is P.

Quantity Demanded at 50% Reduction = (Initial Quantity Demanded - 50% of Initial Quantity Demanded) = Q - (0.5 * Q) = 0.5Q

Now, we can set up the equation using the elastic demand formula:

Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)

-2 = ((0.5Q - Q) / Q) / ((New Price - P) / P)

Simplifying the equation:

-2 = (-0.5Q / Q) / ((New Price - P) / P)
-2 = -0.5 / ((New Price - P) / P)

-2 = -0.5P / (New Price - P)
-2(New Price - P) = -0.5P
-2New Price + 2P = -0.5P
-2New Price = -2.5P
New Price = -2.5P / -2
New Price = 1.25P

Therefore, when the price is reduced to 1.25 times the initial price (1.25P), the quantity demanded will fall by 50%.

Summary

- The elasticity of demand for commodity A is calculated to be -2, indicating price elastic demand.
- A 1% decrease in price leads to a 2% increase in quantity demanded.
- The price at which the quantity demanded falls by 50% is 1.25 times the initial price

Elasticity of demand = 2.