2. (5%) Under the set-up of question 1 but with the monopolist operating at an output level with point price elasticity of demand equal to 3. If the government imposes a quantity tax of $4 per unit of output, then the price will increase (2).

3. (5%) Suppose that a representative firm in a perfectly competitive industry has the production function $f(x_1, x_2) = \min\{x_1, x_2\}^n$ with $0 < \alpha < 1$, where $x_1$ and $x_2$ are the amounts of inputs 1 and 2, respectively. Denote $w_1$ and $w_2$ the prices of inputs 1 and 2, respectively. Suppose that this firm chooses the amounts of inputs 1 and 2 to minimize its costs for producing $y$ units of output. The long run cost function of this firm is (3a) and the long-run supply function of this firm is (3b). 3a

3b

4. (5%) Consider a representative firm in a perfectly competitive market using three inputs to produce its output: labor \((L)\), capital \((K)\), and material \((M)\). The production function is given by \(f(L, K, M) = L^2 K^2 M^2\). Suppose the unit price of labor, capital, and material are \(w = 1\), \(r = 1\), and \(m = 1\), respectively. Each firm is assumed to solve the cost minimization problem given the capital level \(K = 1\). The short-run cost function of each firm is (4a) with efficient scale (4b). 4a

4b

5. (5%) As in question 4, the short-run supply function of each firm is (5a) and the market supply function is (5b) if there are 100 identical firms in this industry. 5a

5b

6. (5%) Consider the following two-player game. Player 1 can choose \( T \), \( M \), or \( B \), while player 2 can choose \( L \), \( C \), or \( R \). The payoffs under players' various action profiles are given below. All the Nash equilibria including the mixed-strategy ones are (6).

7. (5%) There is an industry with three firms, each having zero marginal cost and zero fixed cost. The inverse demand function faced by these three firms is $P(q_1, q_2, q_3) = 60 - (q_1 + q_2 + q_3)$. Suppose that these three are Cournot competitors. Then, the Cournot-Nash equilibrium is (7a) with equilibrium profits of three firms (7b). 7a

7b

8. (5%) Consider the three firms and inverse demand function as assumed in question 7. But now suppose that firm 1 can commit to a certain level of output in advance. Afterwards, firms 2 and 3 will choose their outputs to maximize their profits independently and simultaneously. The subgame perfect Nash equilibrium is (8a) with equilibrium profits of three firms (8b). 8a

115年 - 115 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#146554

112年 - 112 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#146556

112年 - [無官方正解]112 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#146523

111年 - 111 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#146584

110年 - 110 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#146585

110年 - [非官方正解]110 國立臺灣大學_碩士班招生考試_經濟學研究所:個體經濟學#123412

110年 - 110 國立政治大學_碩士班暨碩士在職專班招生考試_ 經濟學系:個體經濟學#105665

110年 - 110 國立中央大學_碩士班招生考試_經濟學系/不分組(一般生):個體經濟學#105315

110年 - 110 國立清華大學碩士班考試入學試題_經濟學系:個體經濟學#105241

110年 - 110 國立中山大學_碩士暨碩士專班招生考試_經濟所:個體經濟學#104433