Let’s consider a market in which two firms compete as quantity setters, and the market
demand is given by Q = 4,000 − 40P . Firm 1 has a constant marginal cost equal to
$20, while firm 2 has a constant marginal cost equal to $40.
(a) Find the Cournot equilibrium quantities. (4)
(b) Suppose that instead of choosing quantities, these two firms compete by choosing
prices simultaneously. Find the Bertrand equilibrium prices. (5)
Suppose that the domestic demand for television sets is given by Q = 40,000 −180P ,
and the domestic supply is given by Q = 20P . Television sets can currently be freely
imported at the world price of $160. What is the domestic deadweight loss if the
government introduces a $20 tariff per television set? (8)
政府預計兩年內開辦長期照護保險,假設需要長期照護的人每人每年所需費用為
一百萬元新台幣,而罹病或行動不便需長期照護的機率是千分之一。某人效用函
數為U(I ) = I1/2,且符合N-M效用理論,I 代表所得。試問:
(1) 此人的風險貼水(risk premium)是多少? (4%)
(2) 政府辦此保險,在收支平衡下,只另收10%行政費用,一年保費至少應向此
人收多少? (4%)
(3) 如果可以自由投保,此人最高願意出多少保費來購買此保險? (3%)
(4) 如果可以自由投保,但效用函數為U(I ) = I 2 ,在與(2)相同保費下,是否會購
買此保險? (3%)
(5) 報載政府欲強制全民加入長期照護保險,理由何在?與資訊不對稱有無關
聯? (4%)
某公司使用F1 及F2 兩種生產要素生產X 產品,其生產函數為齊序生產函數
(homothetic production function),F1 及F2 要素價格相同,每單位皆為10 元。已
知上個月該公司生產80 單位的X ,在成本最小下的F1 及F2 使用組合分別是
(20,60)。試求解下列(如無法求解請解釋其原因):
(1) 如果該公司生產X 的產量為100, 150, 190 時,分別使用了90, 120, 150 單位的
F2 要素,試問在成本最小下的F1 要素使用量分別是多少? (4%)
(2) 求此公司的產出擴張途徑函數(output expansion path) (4%)
(3) 求此公司一生產時F1 及F2 的邊際技術替代率(MRTS) (4%)
(4) F1 或F2 有無可能是劣等要素? (4%)
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