中级微è§�ç»�æ&mic

中级微è§�ç»�æ&mic - VARIAN VARIAN...

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VARIAN ’ VARIANà¤G 2,Budget Constraint 0.Describe budget constraint 0. Algebra : x y P X P Y I + = B(p 1 , … , p n , m ) ={ (x 1 , … , x n ) | x 1 0, … , x n 0 and p 1 x 1 + … + p n x n m } 1. Graph. 1. Describe changes in budget constraint 2.Government programs and budget constraints 3.Non-linear budget lines ² ³ “S±± ´ µP± Quantity DiscountAQuantity PenaltyAOne Price Negative The Food Stamp ProgramAUniform Ad Valorem Sales TaxesR }oX X yX X 8 The Food Stamp Program G F 100 100 F + G = 100: before stamps. Budget set after 40 food stamps issued. 140 The family’s budget set is enlarged. 40 Shapes of Budget Constraints with a Quantity Discount m = $100 50 100 20 Slope = - 2 / 1 = - 2 (p 1 =2, p 2 =1) Slope = - 1/ 1 = - 1 (p 1 =1, p 2 =1) 80 x 2 x 1
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VARIAN 8 X ^ 3. Preferences Describe preferences ( strict preference; indifference; weak preference & 8 Indifference curves ( & ˚P ) ±±±±±±±±± ˚ ²P±±±±±±±±± X Well-behaved preferences( Monotonicity G : More of any commodity is always preferred ( i.e. no satiation and every commodity is a good). Convexity (( ): Mixtures of bundles are (at least weakly) preferred to the bundles themselves. Marginal rate of substitution ( & ) MRS= dx 2 /dx /dx 1 z + ; 8 ± ”P x 1 z + ; 8 ; x 2 z + ; 8 ; z + A 4. Utility 0. Utility function (.±±± . 0. Definition 1. Monotonic transformation . . ±±± . p ¸ ²P±±±± ³ ´ µ ² P±±±± p ´ ²P±±± q ;q ; ±±±±±±x V(x 1 ,x 2 ) = x 1 + x 2 . A W(x 1 ,x 2 ) = min{x 1 ,x 2 }. A U(x 1 ,x 2 ) = f(x 1 ) + x 2 A U(x 1 ,x 2 1 a x 2 b = + ; z üq “S±± 1. Marginal rate of substitution . ±± . ± 2 Well-Behaved Preferences -- Convexity. x 2 y 2 x 1 y 1 x y z =(tx 1 +(1-t)y 1 , tx 2 +(1-t)y 2 ) is ¶referred to x and y for all 0 < t < 1. Indifference Curves x 2 x 1 z x y . x y z Marg. Rates-of-Substitution for Quasi-linear Utility Functions x 2 x 1 Each curve is a vertically shifted co¶y of the others. MRS is a constant along any line for which x 1 is constant. MRS = - f(x 1 ’) MRS = -f(x 1 ·) x 1 x 1 · 2 1 1 1 2 / ( ). / dx U x MRS f x U x = = - = -
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VARIAN 8 ^ 8 ; U(x 1 ,x 2 ) k 8 , Üá* MRSA 5. Choice 4.Rational constrained choice 5.Computing ordinary demands 2. Interior solution n n& n 3. Corner solution n n 4. “Kinky” solution &&&&&&&= ¸ ±…&&&& t& &&&& &&R nW Max U(x 1 ,x 2 ) s.t. 1 1 2 2 PX PY I + = ˚ ±…&&&&&& &&W ¸ U(x 1 ,x 2 ) = x 1 + x 2 $ A& Cobb-Douglas= K * * 1 2 1 2 ( , ) , ( ) ( ) am bm x x a b p a b p = + + ¨ cobb-douglas > ' ; 8 A 6. Demand 2.Own-price changes 2. Price offer curve n L ² ³ ´ µ n n The curve containing all the utility-maximizing bundles traced out as p 1 changes, with p 2 and y constant, is the p 1 - price offer curven 3. Ordinary 3 1 2 1 2 0 U U dx dx x x + = 1 2 1 2 ( , ) a b U x x x x = x 2 x 1 x 1 *(p 1 ’’’) x 1 *(p 1 ’) x 1 *(p 1 ’’) p 1 x 1 *(p 1 ’) x 1 *(p 1 ’’’) x 1 *(p 1 ’’) p 1 p 1 ’’ p 1 ’’’ x 1 * Own-Price Changes Ordinary demand curve for commodity 1 p 1 price offer curve Fixed p 2 and y.
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中级微è§�ç»�æ&amp;mic - VARIAN VARIAN...

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