1. **State the problem:** Given the utility function $$u(x_1, x_2) = 2x_2$$, interpret and analyze it. 2. **Interpretation:** The utility function depends only on the variable $$x_2$$ multiplied by 2, meaning utility is solely affected by changes in $$x_2$$ and independent of $$x_1$$. 3. **Properties:** - For any fixed $$x_1$$, increasing $$x_2$$ increases utility linearly. - Changing $$x_1$$ does not affect utility. 4. **Example:** If $$x_2 = 3$$, then $$u = 2 \times 3 = 6$$. 5. This function can represent preferences where only $$x_2$$ matters for satisfaction.