Questions: Consider Abdul and Bridget's production functions: Abdul's catch: y^A = h^A(α - β(h^A + h^B)) Bridget's catch: y^B = h^B(α - β(h^A + h^B)) Select the SIX correct statements The higher the value of the parameter, the more fishes Bridget can catch in an hour. If Abdul fishes zero hours and Bridget fishes 10 hours, Bridget will catch 10β fishes. These production functions tell us that both Abdul and Bridget experience increasing marginal disutility of effort. These production functions indicate interdependence between Abdul and Bridget. If Abdul fishes zero hours and Bridget fishes 10 hours, Bridget will catch 10α - 100β fishes. These production functions indicate that fishing is subject to 'decreasing productivity'; These production functions convey the information that there is an externality in this game. These production functions involve no externality, indicating that this is likely to be an 'Invisible Hand' game. If Abdul fishes five hours and Bridget fishes 10 hours, Bridget will catch 10α fishes. As Bridget's fishing hours increase, everything else remaining constant, the number of fishes Abdul can catch increases. As Bridget's fishing hours increase, everything else remaining constant, the number of fishes Abdul can catch decreases.

To determine the correct statements, we need to analyze the given production functions for Abdul and Bridget:

Abdul's catch:
\[ y^{A} = h^{A} \left(\alpha - \beta \left(h^{A} + h^{B}\right)\right) \]

Bridget's catch:
\[ y^{B} = h^{B} \left(\alpha - \beta \left(h^{A} + h^{B}\right)\right) \]

These functions suggest that the number of fish caught by each person depends on their own hours of fishing (\(h^A\) for Abdul and \(h^B\) for Bridget) and the total hours both spend fishing (\(h^A + h^B\)).

Let's evaluate each statement:

1. The higher the value of the parameter, the more fishes Bridget can catch in an hour.

   • This statement is incomplete as it does not specify which parameter. If it refers to \(\alpha\), then it is true because a higher \(\alpha\) increases the potential catch. If it refers to \(\beta\), it is false because a higher \(\beta\) reduces the catch due to increased competition.

2. If Abdul fishes zero hours and Bridget fishes 10 hours, Bridget will catch \(10 \beta\) fishes.

   • Incorrect. If \(h^A = 0\) and \(h^B = 10\), then \(y^B = 10(\alpha - \beta \cdot 10) = 10\alpha - 100\beta\).

3. These production functions tell us that both Abdul and Bridget experience increasing marginal disutility of effort.

   • Incorrect. The functions do not directly address disutility of effort; they focus on the catch, which decreases with more total hours fished due to the \(-\beta(h^A + h^B)\) term.

4. These production functions indicate interdependence between Abdul and Bridget.

   • Correct. The catch for each depends on the total hours fished by both, indicating interdependence.

5. If Abdul fishes zero hours and Bridget fishes 10 hours, Bridget will catch \[10 \alpha-100 \beta\] fishes.

   • Correct. As calculated earlier, \(y^B = 10(\alpha - \beta \cdot 10) = 10\alpha - 100\beta\).

6. These production functions indicate that fishing is subject to 'decreasing productivity'.

   • Correct. As \(h^A + h^B\) increases, the term \(-\beta(h^A + h^B)\) reduces the catch, indicating decreasing productivity.

7. These production functions convey the information that there is an externality in this game.

   • Correct. The actions of one affect the outcome of the other, indicating an externality.

8. These production functions involve no externality, indicating that this is likely to be an 'Invisible Hand' game.

   • Incorrect. There is an externality as the catch of one affects the other.

9. If Abdul fishes five hours and Bridget fishes 10 hours, Bridget will catch \(10 \alpha\) fishes.

   • Incorrect. If \(h^A = 5\) and \(h^B = 10\), then \(y^B = 10(\alpha - \beta \cdot 15) = 10\alpha - 150\beta\).

10. As Bridget's fishing hours increase, everything else remaining constant, the number of fishes Abdul can catch increases.

    • Incorrect. As \(h^B\) increases, the term \(-\beta(h^A + h^B)\) reduces Abdul's catch.

11. As Bridget's fishing hours increase, everything else remaining constant, the number of fishes Abdul can catch decreases.

    • Correct. As explained above, Abdul's catch decreases with more total hours fished.

Summary of Correct Statements:

• These production functions indicate interdependence between Abdul and Bridget.
• If Abdul fishes zero hours and Bridget fishes 10 hours, Bridget will catch \[10 \alpha-100 \beta\] fishes.
• These production functions indicate that fishing is subject to 'decreasing productivity'.
• These production functions convey the information that there is an externality in this game.
• As Bridget's fishing hours increase, everything else remaining constant, the number of fishes Abdul can catch decreases.