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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,a1a2a2functionyw1w2x10, x2a2a1a2CES production functionFormulaFormulaProductiony(xi)1/Demand functionfunction111CostcyConditionaly()1n111xiwi1function1()demand function1 ( 1 )1jwj njwj6
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