A consumer is observed making two choices. First, he faces prices p = (1,3) with wealth w = 8 but is limited to purchasing no more than 3 units of good 1. Given this budget set, he chooses the bundle x = (2,2). Second, he faces prices p' = (2, 1) and wealth w' = 8 with no limit on his purchases of either good. Given this budget set, he chooses the bundle x'=(4,0). (a) Identify all revealed preferences given these choices.
please only do: if you can teach explain each partc:
what does it mean? can you show graphs: For these to be optimal choices with such preferences, the indifference curve through a must lie entirely on or above the budget line associated with (p, w), and simi- larly for r' for the budget line associated with (p', w').
how do you know this:Because each of these bundles lies below the other budget line, this implies that the indifference curves must cross, which is impossible.
can you show graphs:
note that (3,1) is a conver combination of x and x', so for conver preferences must be weakly preferred to x (the less preferred bundle between a and a'). But then the bundle (3,5/3) must be strictly preferred z, contradicting that is optimal given the initial budget set
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