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: You are doing econometric analysis. If your dependent variable only takes on values of zero or one (for "no" and "yes"), and your independent variable has a continuous distribution, then regressing the dependent variable on the independent variable will unbiased coefficient and standard error estimates.

Answer:
False. There are many problems with such regressions. For example, the model will very likely suffer from severe heteroskedasticity, making standard error estimates biased.

True/False: Suppose you are analyzing panel data and are unsure whether the fixed effect and independent variables are correlated. Then, it is best to use fixed effect models.

Answer:
True. Random effects models impose the strong assumption that the fixed effect and independent variables are uncorrelated. These coefficients may be biased if the assumptions does not hold. Therefore, it is best to play safe and use fixed effects model. You potentially sacrifice some efficiency if your assumption is not correct, but your estimates are unbiased if all other assumptions are met.

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.