A consumer with income I=120 facing prices pX = 4 and pY = 8 for two goods X and Y (for each good she prefers more to less) chooses optimally to consume 12 units of X. If the prices change and now pX = 6 and pY = 4, what is the possible range for her optimal X consumption? (like, x >/ 7 or 10 >/ x >/7…etc. Use indifference curve analysis on a graph to reason about the possible locations of the new optimal bundle.)

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