Question

Two firms, X and Y, are operating in a perfectly competitive market. The price elasticity of supply of X and Y are respectively 0.5 and 1.5. Then

• A. if the market price increases by 1 %, X supplies 0.5 % less quantity
• B. Y experiences a slower increase in marginal cost in comparison to X
• C. if market price increases by 0.5 %, X supplies 1 % more quantity
• D. Y experiences a rapid increase in marginal cost in comparison to X

Answer 1

The Correct Option is B

To solve the problem, we need to understand the concept of price elasticity of supply and how it affects the behavior of firms in a perfectly competitive market.

The price elasticity of supply (\(\text{PES}\)) is a measure of how much the quantity supplied of a good changes in response to a change in its price. It is given by the formula:

\(\text{PES} = \frac{\%\ \text{change in quantity supplied}}{\%\ \text{change in price}}\) 

Given:

• Firm X has a price elasticity of supply of 0.5.
• Firm Y has a price elasticity of supply of 1.5.
• The market price increases by 1%.

Let's analyze the impact on the quantity supplied by both firms:

1. For Firm X:
   • \(\text{PES}_X = 0.5\)
   • Using the formula, the change in quantity supplied by X when the price increases by 1% is:

\(\%\ \text{change in quantity supplied} = \text{PES}_X \times \%\ \text{change in price} = 0.5 \times 1\% = 0.5\%\)

1. For Firm Y:
   • \(\text{PES}_Y = 1.5\)
   • Similarly, the change in quantity supplied by Y when the price increases by 1% is:

\(\%\ \text{change in quantity supplied} = \text{PES}_Y \times \%\ \text{change in price} = 1.5 \times 1\% = 1.5\%\)

Now, let's consider the options:

• If the market price increases by 1%, X supplies 0.5% less quantity: Incorrect, as X will supply 0.5% more quantity, not less.
• Y experiences a slower increase in marginal cost in comparison to X: Correct, because a higher elasticity of supply indicates that Y can increase its supply more easily without a significant increase in marginal cost compared to X. Therefore, Y's marginal cost increases more slowly.
• If the market price increases by 0.5%, X supplies 1% more quantity: Incorrect, as with a PES of 0.5, X would supply 0.25% more quantity for a 0.5% increase in price (not 1%).
• Y experiences a rapid increase in marginal cost in comparison to X: Incorrect, this is opposite to what the elasticity values suggest. Y would have a less rapid increase in marginal costs compared to X.

Therefore, the correct answer is that Y experiences a slower increase in marginal cost in comparison to X.