108年 - 108 國立臺北大學_碩士班一般入學考試試題_經濟學系：個體經濟學#146586

1. The compensating variation and the equivalent variation are mostly not the same.

2. The supply curve under perfect competition is always positively sloped.

3. A cost-minimizing producer may operate in any region where isoquants slope downward.

4. Sunk costs are fixed costs.

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.

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.

1. _ (3%) In a subgame perfect equilibrium, what is the market price and consumer surplus?

2. _ (2%) For the consumer to accept the contract, what condition should p^c and x satisfy?

3. _ (2%) True or False: There is no contract, (p^c, x), such that the consumer will accept, and Firm C will make a strictly positive profit.

4. _ (3%) Suppose that the consumer has signed the contract, and Firm D has entered into the market. When Firm D sets its price at $p^D$, what condition should p^c, d, and p^D satisfy for the consumer to breach the contract and purchase from Firm D?

5. _ (6%) To maximize profit, what value of the penalty d should Firm C choose? And what is its optimal profit?

6. _ (6%) Describe the best response of consumer E as a function of the acceptance or rejection decision of other two consumers.

7. _ (3%) Find out all the pure strategy Nash equilibrium of the game played by consumers.

1. ______ (4%) Agent \( H \) has a utility function \( u^H = \min\{x_1^H, x_2^H\} \); Agent \( I \) has a utility function \( u^I = \min\{x_1^I, x_2^I\} \).

2.______ (3%) Agent \( J \) has a utility function \( u^J = \min\{x_1^J, x_2^J\} \); Agent \( K \) has a utility function \( u^K = \max\{x_1^K, x_2^K\} \).

3. ______ (3%) Agent \( L \) has a utility function \( u^L = \max\{x_1^L, x_2^L\} \); Agent \( M \) has a utility function \( u^M = \max\{x_1^M, x_2^M\} \).