Question

Please show work.

At prices (p1, p2) = ($4, $1), George buys the bundle (x1, x2) = (10, 20). At prices (p′1, p′2) = ($1, $4), he buys the bundle (x′1, x′2) = (4, 14). At prices (p′′1, p′′2), he buys the bundle (x′′1, x′′2) = (20, 10). If his preferences satisfy the strong axiom of revealed preferences, then it must be that

a. 10p′′1 < 10p′′2.

b. 10p′′1 < 8p2.

c. 8p1 > 8p2.

d. p′′1 = p′′2.

e. None of the above.

Answer 1

Given three price sets and along with them three bundles of goods chosen by the consumer.

firstly, one should find the cost incured for each bundle with respect to the price sets given

At

Cost of bundle A

Cost of bundle B

Cost of bundle C

bundle B is more feasible than bundle A but it is revealed that bundle A is preferred so A is directly revealed preferred to B. bundle C is not feasible so will not be considered at this price set.

Similarly at

Cost of bundle A

Cost of bundle B

Cost of bundle C

Here, bundle B and bundle C incur same costs but it is revealed that B is preferred to C and bundle A is not feasible in this case. So, bundle B is directly revealed preferred to bundle C.

Now, in order to satisfy strong axiom of revealed preferences which implies weak axiom aling with transitivity means bundle A should be indirectly revealed prefered to bundle C which will be the case when cost of buying bundle C is greater than for bundle A.

Given price set

Cost of bundle A

Cost of bundle B

Cost of bundle C

now cost of bundle A must be less than bundle C so that strong axiom of revealed preference is satisfied

option e is the answer