# Here is a table that illustrates some observed prices and choices for three different goods at three

## Question:

Here is a table that illustrates some observed prices and choices for three different goods at three different prices in three different situations.

(a) We will fill in the table below as follows. Where i and j stand for anyof the letters A, B, and C in Row i and Column j of the matrix, write the value of the Situation-j bundle at the Situation-i prices. For example, in Row A and Column A, we put the value of the bundle purchased in Situation A at Situation A prices. From the table above, we see that in Situation A, the consumer bought bundle (2, 1, 3) at prices (1, 2, 8). The cost of this bundle A at prices A is therefore (1Ã—2)+(2Ã—1)+(8Ã—3) = 28, so we put 28 in Row A, Column A. In Situation B the consumer bought bundle (3, 4, 2). The value of the Situation-B bundle, evaluated at the situation-A prices is (1 Ã— 3) + (2 Ã— 4) + (8 Ã— 2) = 27, so put 27 in Row A, Column B. We have filled in some of the boxes, but we leave a few for you to do.
(b) Fill in the entry in Row i and Column j of the table below with a D if the Situation-i bundle is directly revealed preferred to the Situation-j bundle. For example, in Situation A the consumer€™s expenditure is \$28. We see that at Situation-A prices, he could also afford the Situation-B bundle, which cost 27. Therefore the Situation-A bundle is directly revealed preferred to the Situation-B bundle, so we put a D in Row A, Column B. Now let us consider Row B, Column A. The cost of the Situation-B bundle at Situation-B prices is 32. The cost of the Situation-A bundle at Situation-B prices is 33. So, in Situation B, the consumer could not afford the Situation-A bundle. Therefore Situation B is not directly revealed preferred to Situation A. So we leave the entry in Row B, Column A blank. Generally, there is a D in Row i Column j if the number in the ij entry of the table in part (a) is less than or equal to the entry in Row i, Column i. There will be a violation of WARP if for some i and j, there is a D in Row i Column j and also a D in Row j, Column i. Do these observations violate WARP?
(c) Now fill in Row i, Column j with an I if observation i is indirectly revealed preferred to j. Do these observations violate the Strong Axiom of Revealed Preference?

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