This is the data that is going to be useful in the question set. Consider the following consumption dataset over X = R^3

i pi wi xi 1 (1, 2, 5) 7 (5, 1, 0) 2 (2, 2, 0.1) 1.5 (0, 0.5, 5) 3 (2, 1, 3) 9 (3, 0, 1) 4 (3, 5, 0.5) 3.5 (0.5, 0, 4) 5 (1, 1, 0.5) 3 (0, 3, 0)

1. List all weak and strict direct revealed preferences satisfied by this dataset. 2. List all weak and strict indirect revealed preferences satisfied by this dataset. 3. Does this dataset satisfy GARP? Explain why or why not.

Answer this questing using data above: More on revealed preference Consider the consumption dataset that we studied in problem 2 of problem set 2. Rank the consumption bundles (0, 3, 0), (2, 2, 1), and (0, 0, 10) in order of preference, assuming that the decision makers preferences rationalize that dataset and are convex and strictly monotone.

You need to use 3 things:

1) The preferences are convex - so can you maybe find a combination of two bundles from xi in the pre-existing dataset that you can combine to look similar to the given bundles? (0,3,0)is already existed, so find the convex combination of original xi bundle for (2,2,1) and (0,0,10)

2) The preferences are monotonic - if you can find this combination and it has less of some goods than one of the given bundles, monotonicity allows you to compare them.

3) Direct revelation: Where any of the given bundles affordable under certain prices & wealth and were not chosen? Then you can make conclude that they are revealed to be worse than the bundle that was chosen.