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The image contains utility functions and an equilibrium allocation problem related to two individuals, Amanda and Bernd. Let me break it down:

1. **Amanda's Utility Function**:
   - Amanda's utility function \( u^A(x_1^A, x_2^A) \) over the goods \( x_1^A \) and \( x_2^A \), where both quantities are non-negative (\( x_1^A, x_2^A \geq 0 \)), is given by:
   \[
   u^A(x_1^A, x_2^A) = 5 \cdot (x_1^A)^2 \cdot x_2^A
   \]
   This means Amanda's utility depends quadratically on \( x_1^A \) and linearly on \( x_2^A \).

2. **Bernd's Utility Function**:
   - Bernd's utility function \( u^B(x_1^B, x_2^B) \) over the goods \( x_1^B \) and \( x_2^B \), with the same condition \( x_1^B, x_2^B \geq 0 \), is given by:
   \[
   u^B(x_1^B, x_2^B) = \min(x_1^B, x_2^B)
   \]
   Bernd's utility is the minimum of the two goods, meaning he values the good he has less of the most.

3. **Equilibrium Allocation**:
   - The equilibrium allocation \( x^* \) for Amanda and Bernd is given as:
   \[
   x^* = \left(x_1^A = 6, x_2^A = 3\right) \quad \text{and} \quad \left(x_1^B = 3, x_2^B = 3\right)
   \]
   This means Amanda has 6 units of good 1 and 3 units of good 2, while Bernd has 3 units of each good.

This setup suggests a problem involving welfare economics, possibly aimed at finding Pareto efficient allocations or equilibrium.

Would you like further clarification on specific parts or an analysis of the equilibrium allocation?

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Here are 5 related questions to deepen your understanding:

1. How do the different forms of utility functions impact Amanda's and Bernd's preferences over goods?
2. How can we determine if the given allocation is Pareto efficient?
3. What are the implications of Amanda's utility function being quadratic in \( x_1^A \)?
4. How does Bernd's "min" utility function affect his consumption choices?
5. What would happen to the equilibrium if the total supply of goods changed?

**Tip**: For analyzing equilibrium allocations, always check whether marginal utilities are equalized across agents for each good.

Amandas Nutzenfunktion über die Gütermengen x1A, x2A ≥ 0 ist gegeben durch u^A(x1A, x2A) = 5 * (x1A)^2 * x2A. Bernds Nutzenfunktion über die Gütermengen x1B, x2B ≥ 0 ist gegeben durch u^B(x1B, x2B) = min(x1B, x2B). Es sei x*A = (6, 3) und x*B = (3, 3) eine Gleichgewichtsallokation.

Analyze utility functions of Amanda and Bernd to determine equilibrium allocation. This problem involves calculating utility based on quadratic and min functions and exploring Pareto efficiency. Suitable for undergraduate students in economics.

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