題組內容

2. A utility-maximizing consumer chooses between commodity \( x \) and \( y \) with the utility function \( U(x, y) = \sqrt[3]{x + xy} \) while receiving a total income of 19. Let \( p_x \) denote the price of \( x \), and suppose that the price of \( y \) is 1. Answer the following questions. (14 %)

(a) \( (6\%) \) Find the optimal solutions for \( x \) and \( y \) when \( p_x = 0.4 \) and 0.2. Now suppose that \( p_x \) decreases from 0.4 to 0.2.