A seller of potatoes sells 80 quintals a day when the price of potatoes is Rs. 4 per kg. The price elasticity of supply of potatoes is known to be 2. How much quantity of potatoes will the seller supply when price rise to Rs. 5 per unit ? a. 40 kg b. 80 kg c. 120 kg d. 160 kg?

Question

Answer

Solution:

To find out the quantity of potatoes the seller will supply when the price rises to Rs. 5 per unit, we need to use the concept of price elasticity of supply.

Price Elasticity of Supply (PES):
Price elasticity of supply measures the responsiveness of the quantity supplied of a commodity to a change in its price. It is calculated using the formula:

PES = (% Change in Quantity Supplied) / (% Change in Price)

Given that the price elasticity of supply of potatoes is known to be 2, we can use this information to calculate the change in quantity supplied when the price changes.

Calculating the Change in Quantity Supplied:
Let's assume the initial quantity supplied by the seller is Q1 and the initial price is P1. It is given that the seller sells 80 quintals (1 quintal = 100 kg) of potatoes when the price is Rs. 4 per kg.

So, Q1 = 80 quintals = 80 * 100 kg = 8000 kg
P1 = Rs. 4 per kg

Now, let's assume the price increases to P2 = Rs. 5 per kg. We need to find the change in quantity supplied, denoted as ∆Q.

Using the formula for price elasticity of supply, we have:

PES = (∆Q / Q1) / (∆P / P1)

2 = (∆Q / 8000) / (1 / 4)

2 = (∆Q / 8000) * 4

8 = ∆Q / 8000

∆Q = 8 * 8000
∆Q = 64000 kg

This means that the seller will supply an additional quantity of 64000 kg when the price of potatoes rises to Rs. 5 per kg.

Calculating the Total Quantity Supplied:
To find the total quantity supplied at the new price of Rs. 5 per kg, we add the additional quantity to the initial quantity supplied:

Total Quantity Supplied = Q1 + ∆Q
Total Quantity Supplied = 8000 kg + 64000 kg
Total Quantity Supplied = 72000 kg

Therefore, the seller will supply a total quantity of 72000 kg of potatoes when the price rises to Rs. 5 per kg.

Answer:
The quantity of potatoes the seller will supply when the price rises to Rs. 5 per unit is 72000 kg (option d).

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