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# (Solved): 1. Charlie and Paul have preferences over novels (x1 ) and science books (x2 ) occupying their books ...

1. Charlie and Paul have preferences over novels (x1 ) and science books (x2 ) occupying their bookshelves, and this year they each plan on spending \$500 on books. Their preferences are represented by the utility functions u C (x) = x 3/5 1 x 2/5 2 and u P (x) = x 8 1 x 2 2 respectively. (a) Depending on the market prices, could Charlie or Paul ever choose 0 books in either genre? (b) If Charlie and Paul face the same market prices, who will buy more novels? (c) Calculate each of their demands in a market where the market price for novels is \$20 and the market price for science books is \$25. (d) Another friend Milton has book preferences over novels, science, and current events (x3 ) represented by the utility function u M (x) = x 5 1 x 3 2 x 2 3 . If Milton also has \$500 and faces the same market prices as Charlie and Paul, who will buy the most science books? (e) Does your answer to the previous question change if all 3

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