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107年 - 107 東吳大學_暑假轉學生招生考試_經濟學系三年級：經濟數學#105575

科目：研究所、轉學考(插大)◆經濟數學 | 年份：107年 | 選擇題數：0 | 申論題數：15

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所屬科目：研究所、轉學考(插大)◆經濟數學

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申論題 (15)

(a) Derive the slope of the IS curve.
(b) Derive the slope of the LM curve.
(c) Derive the following two comparative-static derivatives: dY */ dG0 and dr*/ dG0 .
 (a) 4x + 3y - 2z = 1
      x + 2 y = 6 
      3x + z = 4 
(b) -x+y+z=a
x-y+z=b
x+y-z=c

3. Compute the determinant of A , where 61d7966e08cff.jpg . How many solutions does  the homogeneous equation Ax = 0 have?

(a) Check whether the conditions of the implicit-function theorem are satisfied. If so, write the equilibrium identity.
(b) Find (dY * dG0 ) and discuss its economic implications.
5. Determine whether q = 2u 2 = 3v2 - w2 + 6uv - 8uw - 2vw is either positive or negative definite.
(a) z = xy , subject to x + 2 y = 2 .
(b) z = x( y + 4) , subject to x + y = 8 .
(c) z = x - 3 y - xy , subject to x + y = 6 .
(d) z = 7 - y + x 2 , subject to x + y = 0 .
(a) f ( x) = a
(b) f ( x) = a + bx (b ≥ 0)