Consider a two-good economy, and a consumer with strictly convex preferences. Prices in this economy are al- ways positive. We observe that the consumer makes two following choices.

At price (1; 2), the consumer chooses (2; 3). At price (2; 1), the consumer chooses (1; 6).

a. Observing the consumer making choices in the supermarket, you are unable to observe her wealth level. What can you say about the consumers wealth w? b. How would the consumer rank (2; 3) and (1; 6)? c. Are the consumers choices consistent with rational preference? d. Suppose the consumer chooses (4; 2) under the price 1/2 ; 3 .How does the consumer rank (4; 2) and (1; 6)? e. How does the consumer rank ( 5/2 ; 4) and (4; 2)?