(b) (6%) Derive and graph Mary's demand curve for x

題組內容

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%)

3-2. Two-Part Tariff (10%)Suppose in this part of the question that the Planet Gym adopts a two-part tariff: to set a membership fee and a price per session for customers who have paid the membership fee. The membership fee is required for entrance. Given this form of pricing strategy, the Planet Gym maximizes its profit. Please find the optimal membership fee, the optimal price per session, and the equilibrium gym sessions traded. Please accompany the above answers with a consistent figure (graph).

題組內容

(b) \( (6\%) \) Derive and graph Mary's demand curve for \( x \)

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