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 台湾大学博士班入学考试试题 (转贴) -- 借本试题做海归黄埔军校入学考试, 高人大比武现在开始! |
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台湾大学博士班入学考试试题 (转贴) -- 借本试题做海归黄埔军校入学考试, 高人大比武现在开始! -- 安普若 - (3376 Byte) 2003-9-28 周日, 11:57 (1676 reads) |
安普若
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作者：安普若 在 海归黄埔军校 发贴, 来自【海归网】 http://www.haiguinet.com
國立台灣大學 八十七 學年度 博士班入學考試試題
科目：個體經濟學
Note: Problems 1-3.(50%); Problem 4.(25%), and Problem 5.(25%).
1.The production function of a competitive producer (a price taker) is homothetic given by q = H(f (XI, X2)), where Y = f (XI, X2) is a CRTS production function with the cost function YO(WL, W2) and H(f) is strictly monotonic increasing with inverse f = H-'(q) =- h(q), both H and h twice differentiable.
(a)Derive the cost function c(w, q) in terms of h and 0 for the competitive producer.
(b)Suppose that both the two inputs are variable. For given input prices (iVl, CV2), find the inverse of the supply function p = D-'(q; ivl, CV2) ≡g(q; ?bl, Z7V2) of the producer.
2.The indirect utility function is v(p, rn) = (2p1-1 + p2-1)m.
(a)Find the demand function.
(b)Find the expenditure function and Hickslan demand functions.
3.Consider the utility function U(Xl, X2, Z) =(√x1 + √x2)2z2 +
(√x1 +√x2)4z.
(a)Show that the utility is functionally separable.
(b)Find the quantitiy index X = f(Xl,X2) and the price index
P = g(Pl,P2)-
(c)Given that the price of z is pz = 1, find the demand for X as a function of P.
4.Suppose there are two states of the world, wet and fine, and that the firm's output for given input is greater in the fine state than in the wet state but that the price of its output is greater in the wet state. Assume that there is no futures market but that the firm could buy insurance against the wet state at an actuarially fair price. How does the existence of such insurance affect
(a)the firm's choice of input level;
(b)the firm's expected utility.
5.Analyze the effect of changes in the loss (L), the accident probabilities (7ri), i=h (high-risk type), I (low-risk type); and the degree of risk aversion of insureds upon the cover of low-risk type in the separating equilibrium contracts.
作者：安普若 在 海归黄埔军校 发贴, 来自【海归网】 http://www.haiguinet.com
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