Answer

Solution

1. 1

   Consumer A: Bundle $a_1 = (3,8)$, $a_2 = (8,3)$.

2. 2
   $$\begin{aligned} \text{Month 1 budget:}\ & p^1 \cdot a_1 = 2(3)+3(8) = 30,\quad p^1 \cdot a_2 = 2(8)+3(3) = 25 < 30. \\ \text{Month 2 budget:}\ & p^2 \cdot a_2 = 3(8)+2(3) = 30,\quad p^2 \cdot a_1 = 3(3)+2(8) = 25 < 30. \end{aligned}$$
3. 3

   Both bundles are directly revealed preferred to each other, violating WARP.

4. 4

   Consumer B: Bundle $b_1 = (6,6)$, $b_2 = (4,9)$.

5. 5
   $$\begin{aligned} p^1 \cdot b_1 &= 12+18 = 30, & p^1 \cdot b_2 &= 8+27 = 35 > 30. \\ p^2 \cdot b_2 &= 12+18 = 30, & p^2 \cdot b_1 &= 18+12 = 30 \le 30. \end{aligned}$$
6. 6

   In month 2, $b_1$ was affordable and $b_2$ was chosen, so $b_2 \succsim b_1$.

7. 7

   In month 1, $b_2$ was not affordable, so no contradictory revelation exists. Consumer $B$

8. 8

   satisfies WARP.

9. 9

   Hence consumer $B$ satisfies WARP but $A$ does not.

Answer structure / marking notes

Content note