True/False: In general, a firm's profit is the same regardless of whether it solves a profit maximization or cost minimization problem.

Answer: True. Cost minimization is the "dual problem" of profit maximization. In other words, the maximum profits are the same, whether you use a cost minimization or profit maximization problem.
A detailed proof is probably beyond the scope of most undergraduate courses, but can be found in Mas-Colell, Whinston and Green.

(The output of a cost minimizing and profit maximizing firm need not be the same; consider the case of constant returns to scale.)

True/False: Consider two different firms with identical production functions (but you do not know what the production functions are). The firms are doing static optimization (as opposed to dynamic optimization, where there are many time periods). Suppose one firm chooses to maximize profits and the other firm chooses to minimize costs, subject to producing the profit-maximizing level. Both firms will produce the same output.

Answer: False. Consider the case where both firms have constant returns to scale (CRS) technology, and the zero profit condition holds. Then any amount of output is profit maximizing. For example, one firm could produce 0 units of output, and the other firm could produce 5 units of output, and both firms would have the same profit. Hence the statement is false.

True/False: Consider a standard Hotelling beach model, where consumers are scattered along a one mile beach. These consumers have perfectly inelastic demand as well as positive linear transportation costs. Firms set their location, but price is fixed by the government. The Nash equilibrium location choices will be different from choices that maximize total surplus.

Answer:
True. Nash equilibrium strategy is for both firms to locate at the center of the road (1/2 mile point). The socially optimal strategy, which maximizes total surplus, is for one firm to locate at the 1/4 mile point and for another to locate at the 3/4 mile point.

True/False: Suppose a farmer faces the risk of a natural disaster destroying his rice paddies. If the farmer is risk averse, then the farmer will always take up an insurance contract when offered.

Answer:
False. The farmer may not take up an insurance contract if the premium is too expensive.

True/False: When a monopolist is a perfect price discriminator, total surplus can be increased by changing the price (either lowering or raising the price).

Answer:
False. Perfect price discrimination allows a monopolist to produce at the socially efficient level. Therefore, changing the price would only lower total surplus.

True/False: Last December, oil prices tumbled. Assume all other prices stayed the same. One can reasonably expect that the Consumer Price Index will overstate the change in the cost of living.

Answer:

False. The CPI should understate cost of living changes when prices decrease. Consider that people substitute towards products which use oil as an input. However, the CPI does not take this into account. (The general principle is that CPI does not take into account substitution effects.) What is true is that if the price of oil increased, the CPI would overstate the change in the cost of living.

True/False: Under Leontief preferences, there is no substitution effect as prices change.

Answer:
True. Leontief preferences mean that a consumer treats goods as though they were perfect complements (e.g. left shoes and right shoes). Intuitively, changes in price do not cause consumers to substitute left shoes for right shoes. In fact, the only effect is an income effect: real income goes down when prices increase, and real income increases when prices decrease.

True/False: All games have a Nash equilibrium in pure strategies.

Answer:
False. Matching pennies has no pure strategy Nash equilibrium.

True/False: If a game does not have a Nash equilibrium in pure strategies, then it must have a Nash equilibrium in mixed strategies.

Answer:
True. This is because all games have a Nash equilibrium. (By an advanced mathematical concept known as Kakutani's fixed point theorem. However, it's unlikely you need to know this as an undergraduate).

True/False: With Cobb-Douglas preferences, the cross-price elasticity between any two goods is zero.

Answer:
True. Notice that with Cobb-Douglas preferences, total expenditure on any good is fixed regardless of the good's price. (To verify this, do the Lagrangian.) Hence changes in the price of a good would only lead to changes in quantity demand for that good, and not other goods.