5. Leontief utilities violate the "more is better" assumption.

6. The elasticity of demand is never greater than zero.

7. Economic rent may be the same as economic profit.

8. The tangent condition always holds in finding optimal choices.

9. When demand and supply change simultaneously, the changes in equilibrium price and equilibrium quantity are not determinate without knowing the relative magnitude of the shocks.

10. Shephard's lemma relates the demand functions to the indirect utility function.

II. The production function of Firm A is $$q^A = \min\{2L, 2K\}.$$ Firm A is a price taker at the factor market. The unit price of L is 1, and the unit price of K is r > 0. The inverse demand at the product market is p = 1 - Q, where p is the market price and Q the market quantity. 1. (3%) What is the cost function of Firm \(A\)?

2. (4%) If Firm \( A \) is a monopoly firm at the product market, what is its profit-maximizing output? Another firm, Firm B, faces the same input prices as Firm A, but produces the same product with a different product function, $$q^B = (\sqrt{L} + \sqrt{K})^2.$$

3. (4%) What is the cost function of Firm \(B\)?

4. (4%) Suppose that Firm \( A \) and Firm \( B \) engage in Bertrand competition and simultaneously choose their own price. Find out the equilibrium market price and profit of the two firms.

III. A monopoly firm, Firm C, has a constant marginal cost $2. A potential entrant, Firm D, is considering whether to enter into the market. Entry requires a fixed cost $f, with 0 < f < 1/2. By paying f, Firm D can enter into the market and offer the same product as Firm C at a lower (constant) marginal cost $1/2. (Firms have no other cost.) There is only one consumer in the market, who purchases at most one unit of the product. The consumption value of the product is $4. Consider the following game: Firm D first decides whether to spend f to enter into the market. If Firm D does not enter, then Firm C maintains its monopoly and charges the monopoly price; but if Firm D enters, the two firms engage in Bertrand competition and simultaneously offer a price to the consumer, who then makes the purchasing decision. In this part of questions, note that: (i) A consumer does not face any budget constraint. He makes the purchasing decision to maximize consumer surplus; and if he doesn't buy, consumer surplus is zero. (ii) Upon indifference between the offer of the two firms, a consumer will buy from Firm D. (iii) Firm D will enter and make a sale as long as its profit is not strictly negative. 1. _ (3%) In a subgame perfect equilibrium, what is the market price and consumer surplus?

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