Karl and Clara maximize their respective utilities subject to budget constraints; they shop at the same grocery store that sells only apples and bananas. Karl’s utility function is given by UK (xA,xB) = xA +2xB, where xA denotes his consumption of apples and xB his consumption of bananas. Clara’ sutility function is UC (x A, x B) = 3 x A + 2xB.

(a) When the store observes that Karl leaves with some apples, can they infer that Clara also buys some apples? How?

(b) When the store observes that Karl leaves with some bananas, can they infer that Clara also buys some bananas? How?

(c) The store is interested in setting the prices of apples and bananas in such a way that both consumers buy strictly positive amounts of both goods. Can you advise the store on what those prices might be?