Question

Microeconomics

Posted 2 months ago

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When the price of socks was $\$ 4$ per pair, Theo's Sock-Stravaganza supplied 10,000 pairs of socks. When the price of socks was $\$ 5$ per pair, it supplied 17,500 pairs of socks.
What is the price elasticity of supply for socks?
Choose 1 answer:
(A) 2.4
(B) 0.33
(C) 3
(D) 7
(E) 1.5
```

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Answer from Sia

Posted 2 months ago

Solution

a

Definition of Price Elasticity of Supply: The price elasticity of supply (PES) measures the responsiveness of the quantity supplied of a good to a change in its price. It is calculated using the formula: $PES = \frac{\% \Delta Q_s}{\% \Delta P}$

b

Calculate Percentage Change in Quantity Supplied: The initial quantity supplied ($Q_1$) is 10,000 pairs, and the new quantity supplied ($Q_2$) is 17,500 pairs. The percentage change in quantity supplied is calculated as: $\% \Delta Q_s = \frac{Q_2 - Q_1}{Q_1} \times 100 = \frac{17,500 - 10,000}{10,000} \times 100 = 75\%$

c

Calculate Percentage Change in Price: The initial price ($P_1$) is $4, and the new price ($P_2$) is$5. The percentage change in price is calculated as: $\% \Delta P = \frac{P_2 - P_1}{P_1} \times 100 = \frac{5 - 4}{4} \times 100 = 25\%$

d

Calculate Price Elasticity of Supply: Using the percentage changes calculated, the price elasticity of supply is: $PES = \frac{\% \Delta Q_s}{\% \Delta P} = \frac{75\%}{25\%} = 3$

Answer

(C) 3

Key Concept

Price Elasticity of Supply

Explanation

The price elasticity of supply measures how much the quantity supplied of a good responds to a change in its price. In this case, the quantity supplied of socks increased by 75% when the price increased by 25%, resulting in a price elasticity of supply of 3.

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