MIT14_01SCF11_exam01_sol - u = x + y P = 5 - 1 Q 2 P = 20 -...

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Unformatted text preview: u = x + y P = 5 - 1 Q 2 P = 20 - Q QD 1 10 - 2P = 0 , P 5 , P >5 P 5 Q 15 30 Image by MIT OpenCourseWare. QD = 20 - P 2 QD M = QD 1 + D Q2 30 - 3P = 20 - P , P 5 , P >5 20 - Q P = 10 - 1 Q 3 Q 15 Q > 15 QS = 2 + P p = 5 QS = 7 < 15 = QD QS = QD 2 + P = 20 - P P = 9 Q = 11 1 U (b, n) = 3 min(n, b) U (b, n) = 3 min(3n, b) 3 Bracelets (1, 3) Necklaces Image by MIT OpenCourseWare pn = 2 pb = 2 b = 3n 2n + 2b = 32 2n + 6n n = = 32 3 n = 4 b = 12 u = 12 pn = 10 10n + 6n = 32 n = 2 b = 6 u = 6 2 10 + 6 2 = 32 nb2 b2 2nb b = = 2 2 2n 2(2n) + 2n = 32 n = 16 b = 32 u = 16 ( 32 )2 = 512 3 3 3 3 27 b2 2nb b = = 10 2 10n 2(10n) + 10n = 32 16 n = 16 b = 160 u = 15 ( 160 )2 = 15 15 15 2560 225 16 162 4 16 162 100 16 162 4 - ) )/( 27 27 53 27 16 162 (4 53 - 100) = 27 53 = 485.4 = ( Bracelets (1, 3) Necklaces Image by MIT OpenCourseWare. LD = 34 - 4w w LS = L + 2w L L = 10 LS = LD 34 - 4w = 10 + 2w w = 4 L = 18 D = dLD w 4 16 8 = -4 =- =- dw L 18 18 9 w L = 16 L = 16 34 - 4w = 16 + 2w w = 3 L = 22 w = 4 w > w LD = 18 LS = 24 LS - LD = 6 W LD LS 18 Unemployment 24 L Image by MIT OpenCourseWare. = 1 LS (p+ ) = LD 16 + 2(w + ) = 34 - 4w w = 16 = 8 w + = 6 3 8 11 3 + 1 = 3 X Y U (X, Y ) = X 0.2 Y 0.8 $ X Y $ $ X Y X Y M UX = 0.2(Y /X)0.8 M UY = 0.8(X/Y )0.2 M RSY X = -M UX /M UY = -Y /4X X Y X Y Y X (X , Y ) M RSY X = -PX /PY -Y /4X = -10/20 = -Y /4X = -1/2 = 2Y = 4X = Y = 2X I = PX X + PY Y = 100 = 10X + 20Y (X , Y ) 100 = 10X + 20(2X) = 100 = 50X = X = 2 Y = 2X = 2(2) = Y = 4 -PX /PY M RSY X = -PX /PY Y = 2X 100 = 20X +40Y (X , Y ) = (1, 2) X Y X Y PX , PY I M RSY X = -PX /PY = -Y /4X = -PX /PY = PY Y = 4PX X I = PX X + PY Y X Y I = PX X + 4PX X = 5PX X = X (PX ; I) = I/(5PX ) $100 X (PX ; I = 100) = 20/PX Y X PY Y = 4PX X = Y = (4PX X)/PY = Y = (4PX [I/(5PX )])/P Y Y (PY ; I) = 4I/(5PY ) $100 Y (PY ; I = 100) = 80/PY Y $ $ Y X PY X = 2 Y Y = 80/PY = 80/10 = 8 Y X Y BCsub BC1 IC0 Y Y 10 8 Total effect Inc IC1 4 Sub BC su BC b 0 BC IC0 1 2 10 Image by MIT OpenCourseWare. X $10 8 Y 8($10) = $80 MIT OpenCourseWare http://ocw.mit.edu Fall 2011 14.01SC Principles of Microeconomics For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. ...
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