題組內容

  1. Mary buys commodity \( x \) and \( y \) that maximize her utility \( U(x, y) = \alpha x + y \) with \( \alpha > 0 \). Let her income be \( I \), the price of \( x \) be \( p_x \), and the price of \( y \) be \( p_y \). Answer the following questions in terms of \( \alpha, p_x, p_y \) and \( I \). (12%)

(c) \( (4\%) \) Suppose that one optimal solution \( x^{} \) is nonzero and independent of \( p_y \). Find Mary's price elasticity and income elasticity of demand for \( x \) under \( x^{} \).