Question

1. Felix chooses between clothing, q1, and food, q2. His initial income is $5,000 a month, p1 = 500, and p2 = 50. At his initial bundle, he consumes q1 = 2 and q2 = 80. Later, his income rises to $6,000 and the price of clothing rises to p1 = $750, but the price of food does not change. (p2 = 50). As a result, he reduces his consumption of clothing to q1 = 1. Using a revealed preference reasoning, can you determine how he ranks the two bundles?

Answer 1

Initially His Income = 5000 and prices are p1 = 500 and p2 = 50.and he consumes q1 = 2 and q2 = 80.

Later, his income rises to $6,000 and the prices are p1 = $750 and p2 = 50 and he consumes q1 = 1 so

q2 = (6000 - 1*750)/50 = 105.

Lets check that with initial budget and initial prices can he afford the new bundle (q1,q2) = (1,105)

Amount required to buy new bundle with initial prices are 500*1 + 50*105 = 5750 which is greater than his initial income( = 5000). Hence this new bundle is not affordable under initial conditions. Hence he purchased initial bundle and new Bundle is not affordable at that time. Hence we can not say which Bundle is revealed preferred at this point.

Now,

Lets check that with New budget and New prices can he afford the old bundle (q1,q2) = (2,80)

Amount required to buy old bundle with new prices are 750*2 + 50*80 = 5500 which is lesser than his new income( = 6000). Hence this old bundle is affordable under new conditions. Hence he purchased new bundle when old Bundle is still affordable.

Hence, New Bundle i.e. (1,105) is revealed preferred over Old Bundle(i.e. (2,80)