Answer

Solution

1. 1

   The unconstrained bliss point is $(10,10)$, but it costs $20$, well within income $40$;

2. 2

   however, the consumer prefers to remain at the bliss point and need not spend the rest.

3. 3

   With strict free disposal of money (no satiation forced by budget), the consumer would

4. 4

   choose $(10,10)$.

5. 5

   However, if the budget must be exhausted ($x + y = 40$, the standard PEA convention here),

6. 6

   maximize $-[(10-x)^2 + (10-y)^2]$ subject to $x+y=40$. Substituting $y = 40 - x$:

7. 7
   $$\max_x \ -\big[(10-x)^2 + (x-30)^2\big].$$
8. 8

   First order condition: $2(10-x) - 2(x-30) = 0 \Rightarrow x = 20$, giving $(20,20)$.

9. 9

   This matches none of (A), (B), (C).

10. 10

    Conclusion: Under the standard PEA convention (budget exhausted), the optimum is

11. 11

    $(20, 20)$, which is none of the listed options.

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