高级微观经济学公式总结Calculationmethodsandexamples

1、精品 料推荐utility calculation methodsnotationcalculation methods1.min v( p, m)utilityu (x)st :pi ximfunction2. v( p , 1),wherem1. max u ( x)st :pi ximpidi1( x,1)mindirect utilityv( p, m)function2. u ( d ( p, m)3. the inverse function ofe( p, u)expenditure1. in 1 pi hi ( p,u)e( p, u)function2. the invers

2、e function ofv( p, m)1. e( p, v(q, m)money metricindirect utilityfunctionmashalliandemandfunctioninversedemandfunctionu( p,q,m)xidi ( p m)pidi 1 ( x m)u( p, q, m)xi ( p, u( p, q, m), i 1,2.n2.piu( q, q, m)m1. max u ( x)st :pi xim2. xiv( p, m)/v( p, m)pim3. xim v( p, m)/nv( p, m)pii1pipi4. xihi ( p,

3、e( p, u)1. min v( p, m)st :pi xim2. piu( x m)/nv(x,m)mi1xixixi3. the inverse functions ofxd ( p, m)1精品 料推荐1. minpi xi hicksianst : u ( x)uxihi ( p u)e( p, u)demandfunction2. xipi3. xi di ( p, e( p, u)cobb douglas utility functionformulaformulautilityuaxy1mashallianxm , y(1)mfunctiondemand functionpx

4、pyindirect utilitya(1)1 minverse demandpxm(1)mfunctionupx p1yfunction, pyyxxpy1uexpenditurepx p1y uhicksian demand) pxe(1afunction(1)1function(1) pxuayapymoney metric1mindirect utilityupx pyqx q1yfunctionleontief utility functionformulaformulautilityumin x, ymashallianx ympyfunctiondemand functionpx

5、pxm , py0xyxindirect utilityuminverse demandpxpymxyfunctionpxpyfunctionxpxmxy0, pyyexpendituree ( pxpy )uhicksian demandx y ufunctionfunctionmoney metricu( pxpy )mindirect utility( qxqy )function2精品 料推荐linear utility functionformulaformulaxm0pxpy, ymashallianpxutilityxympxpyu xydemandfunctionpxfunct

6、ionmx0, ypxpypypxpxmx0, y0xyindirect utilityuminverse demandpxpymx0, y0minpx , py yfunctionfunctionpypxmx0, y0xexpenditurehicksianxu, y0pxpyemin px , py uxy u,pxpydemandfunctionfunctionx0, yupxpymoney metricumin px , py mindirect utilitymin qx ,qy functionces utility functionformulaformula1utilityu(

7、xi)1/mashallianm( 1 )1xipifunction1demand function1 ( 1 )1 njpjindirect utility11inverse demandmxi1umn)1pifunctionj 1(functionnp jj 1 xj1expenditureeuhicksian demandxu( 1 )111pifunctionn1 ()1functioni1( 1 )1 1jpjnjp j( 1 ) 11money metricmnj 1indirect utilityuq j11functionn1j1 ( pj)3精品 料推荐productionf

8、unctioncostfunctionprofitfunctiondemandfunctionconditionaldemandfunctionproduction calculation methodsnotationcalculation methodsf (x)1. from xi ( p,y) to yf (x)c( p, y)1.in1 pi xi ( p, y)1.max pyst : yy( p)2.max pyc( y)st : y03.max pf ( x1 , x2 )w1x1 w2 x2 st : x10x2 01. frommax pyst : yyyiyi ( p)2

9、. frommax pyc( y)st : y01.minpi xi xihi ( p y)st : f ( x)y2. xic( p, y)pi4精品 料推荐production calculation methodsnotationcalculation methodsproductionf (x)1. from xi ( p,y) to y f (x)functioncostc( p, y)1.in1 pi xi ( p, y)function1.max pyprofitst : yy( p)function2.max pyc( y)st : y01. frommax pyst : yy

10、demandyiyi ( p)2. frommax pyc( y)functionst : y03. yi( p)pi1.minpi xi conditionalxixi ( p y)st : f ( x)ydemandc( p, y)function2. xipicobb douglas production functionformulaformulaproductionyax1 x21demand functionfunctionx1w21ycostw1 w21yconditionalac(1)w1function(1)1demand function(1)w1yax2w2aleonti

11、ef production functionformulaformulaproductiondemandp w1w1min x1, x2 x1x2any number pw1w1yfunctionfunction0pw1w15精品 料推荐costc(w1w2 ) yconditionalx1ydemandfunctionx2yfunctionlinear production functionformulaformulax1, x2 0pmin w1 , w2 a1a2productionya1x1a1x2demandpw1,w2functionany numbermina2functiona1x10, x2pmin w1 , w2 a1a2x1y0w1w2, x2a1a2conditionala1costcminw1w2 yw1w2demanda1x1 a1x2yfunctiona1,a1a2a2