ä¸­çº§å¾®è§�ç»�æ&mic

# ä¸­çº§å¾®è§�ç»�æ&mic - VARIAN VARIAN...

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 = = - = -
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 32

ä¸­çº§å¾®è§�ç»�æ&mic - VARIAN VARIAN...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online