Question

16. Suppose that \( \mathcal{C}_{1} \) and \( \mathcal{C}_{2} \) are two companies that control some particular given market. Each time period, \( \mathcal{C}_{1} \) retains 70 per cent of its market share, but loses 30 per cent to \( \mathcal{C}_{2} \), whilst \( \mathcal{C}_{2} \) retains 50 per cent of its market share, but loses 50 per cent to \( \mathcal{C}_{1} \). Which one of the following statements is correct, assuming these conditions hold each time period indefinitely into the future? In the long run, \( \mathcal{C}_{1} \) captures \( \frac{3}{4} \) and \( \mathcal{C}_{2} \) captures \( \frac{1}{4} \) of the market. In the long run, \( \mathcal{C}_{1} \) captures \( \frac{2}{3} \) and \( \mathcal{C}_{2} \) captures \( \frac{1}{3} \) of the market. In the long run, \( \mathcal{C}_{1} \) captures \( \frac{4}{7} \) and \( \mathcal{C}_{2} \) captures \( \frac{3}{7} \) of the market. In the long run, \( \mathcal{C}_{1} \) captures \( \frac{5}{8} \) and \( \mathcal{C}_{2} \) captures \( \frac{3}{8} \) of the market. In the long run, \( \mathcal{C}_{1} \) captures \( \frac{5}{7} \) and \( \mathcal{C}_{2} \) captures \( \frac{2}{7} \) of the market.

          16. Suppose that \( \mathcal{C}_{1} \) and \( \mathcal{C}_{2} \) are two companies that control some particular given market. Each time period, \( \mathcal{C}_{1} \) retains 70 per cent of its market share, but loses 30 per cent to \( \mathcal{C}_{2} \), whilst \( \mathcal{C}_{2} \) retains 50 per cent of its market share, but loses 50 per cent to \( \mathcal{C}_{1} \).
Which one of the following statements is correct, assuming these conditions hold each time period indefinitely into the future?
In the long run, \( \mathcal{C}_{1} \) captures \( \frac{3}{4} \) and \( \mathcal{C}_{2} \) captures \( \frac{1}{4} \) of the market.
In the long run, \( \mathcal{C}_{1} \) captures \( \frac{2}{3} \) and \( \mathcal{C}_{2} \) captures \( \frac{1}{3} \) of the market.
In the long run, \( \mathcal{C}_{1} \) captures \( \frac{4}{7} \) and \( \mathcal{C}_{2} \) captures \( \frac{3}{7} \) of the market.
In the long run, \( \mathcal{C}_{1} \) captures \( \frac{5}{8} \) and \( \mathcal{C}_{2} \) captures \( \frac{3}{8} \) of the market.
In the long run, \( \mathcal{C}_{1} \) captures \( \frac{5}{7} \) and \( \mathcal{C}_{2} \) captures \( \frac{2}{7} \) of the market.

16. Suppose that 𝒞1 and 𝒞2 are two companies that control some particular given market. Each time period, 𝒞1 retains 70 per cent of its market share, but loses 30 per cent to 𝒞2, whilst 𝒞2 retains 50 per cent of its market share, but loses 50 per cent to 𝒞1.
Which one of the following statements is correct, assuming these conditions hold each time period indefinitely into the future?
In the long run, 𝒞1 captures (3)/(4) and 𝒞2 captures (1)/(4) of the market.
In the long run, 𝒞1 captures (2)/(3) and 𝒞2 captures (1)/(3) of the market.
In the long run, 𝒞1 captures (4)/(7) and 𝒞2 captures (3)/(7) of the market.
In the long run, 𝒞1 captures (5)/(8) and 𝒞2 captures (3)/(8) of the market.
In the long run, 𝒞1 captures (5)/(7) and 𝒞2 captures (2)/(7) of the market.

Added by Randy R.

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