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

## Question:

(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?

## Step by Step Answer:

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