1. Mary buys commodity $x$ and $y$ that maximize her utility $U(x, y) = ax + y$ with $a > 0$. Let her income be $I$, the price of $x$ be $px$, and the price of $y$ be $py$. Answer the following questions in terms of $a, px, py$ and $I$. (12%) (a) (2%) Explain why x is an economic good for Mary.

3. Pricing Strategy of a Monopoly (26%) Planet Gym is the only gym in town. Providing a session of workout to a customer is at a marginal cost of $c$. This marginal cost is perfect information. The gym is large enough so that even in peak hours there is no externality between the customers.¹ Planet Gym has two forms of feasible pricing strategies. It can set a uniform price per session for all customers with free entrance, or it can set a two-part tariff with a membership fee and a price per session conditional on paying the membership fee. The market demand of gym session at price $p$ per session is $q = \Delta - \delta \cdot p$. The market demand is perfect information. To guarantee existence of an equilibrium, assume that $\Delta > \delta \cdot c$. 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).

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