Question

Please show work.

When the prices were ($5, $1), Vanessa chose the bundle (x, y) = (6, 3). Now at the new prices, (px, py), she chooses the bundle (x, y) = (5, 7). For Vanessa’s behavior to be consistent with the weak axiom of revealed preference, it must be that

a. 4py < px.

b. px < 4py.

c. 5py < px.

d. py = 5px.

e. None of the above.

Answer 1

At prices = ($5, $1) , Venessa choose the bundle A i.e (6,3) .

and at new prices =(px,py) , she chooses the bundle B i.e (5,7)

Total cost of A at ($5,$1) = 5(6) + (1)(3) = $33.

Total cost of B at ($5,$1) = 5(5) + 7(1) = $32.

It implies that bundle B has less cost , and feasible but not chosen at original prices. (It implies that it is directly revealed preferred).

For Weak axiom to be satisfied ,at new prices when B is chosen , A must not be feasible.( Because if A is feasible then B is directly revealed preferred to A.)

So,at new prices A must not be feasible implies that total cost of A at new prices is more than total cost of B at new prices.

Or in other words, total cost of B at new prices is less than total cost of A at new prices.

From this, we get

(5)px + 7(py) < (6) px + (3) py

4py < px

Hence, the option (A) is correct.