四、十九世紀科學之犯罪學崛起，一路發展至當前之廿一世紀，新創之犯罪學理論幾乎以「科際整合」(Interdisciplinary integration)之姿出現。試問：何謂「科際整合」？並請舉出兩個廿一世紀才產出的知名之科際整合的犯罪學理論及其內容。

(a) \( (2\%) \) Explain why \( x \) is an economic good for Mary.

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

(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 \( x^{} \).

(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.

(b) \( (4\%) \) What is the substitution effect of this reduction in price?

(c) \( (4\%) \) What is the compensating variation of this reduction in price?

3-1. Uniform Price per Session (10%)Suppose in this part of the question that the Planet Gym takes a simple pricing strategy: to set a uniform price per session. Given this form of pricing strategy, it maximizes its profit. Please find Planet Gym's supply of gym sessions. Please accompany your answer with a consistent figure (graph).

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).

3-3. The Optimal Pricing Strategy (6%)From what you have found in 3-1 and 3-2, what is the optimal pricing strategy for the Planet Gym? Is the optimal pricing strategy efficient from the social perspective? Is the optimal pricing strategy also the best for the customers? Briefly explain.¹ This assumption might not be realistic, but it allows us to focus on what we are really interested to analyze.

(a) \( (3\%) \) only labor?

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