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Advanced microeconomics

Advanced microeconomics. a- General equilibrium and Welfare ; 1- Microeconomic Theory , J.M. Henderson , R.E. Quandt CH 9 - Multi-market Equilibrium CH 10 – Topics in Multi-market equilibrium CH 11 - Welfare Economics

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Advanced microeconomics

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  1. Advanced microeconomics a- General equilibrium and Welfare ; 1- Microeconomic Theory , J.M. Henderson , R.E. Quandt CH 9 - Multi-market Equilibrium CH 10 – Topics in Multi-market equilibrium CH 11 - Welfare Economics 2 - Microeconomic Theory, P.R.G. Layard and A.A. Walters; CH 1 - Welfare economics CH 2 - General equilibrium CH 3 - Application to Public Finance CH 4 - Application to International Trade CH 1 welfare

  2. Advanced microeconomics 3- Microeconomic Theory, A. Mas-Collel , M. D. Winston , J . R . Green . CH 15 - General equilibrium theory Ch 16 - Equilibrium and its basic welfare properties CH 17 - Positive Theory of Equilibrium CH 18 - Some foundations for competitive equilibrium CH 20 - Equilibrium and Time CH 21 - Social Choice Theory CH 22 - Elements of Welfare economics 4- A Course In Microeconomics Theory . D . M . Kreps . CH 5 - Social choice and Efficiency CH 6 - Pure Exchange and General Equilibrium . CH 1 welfare

  3. Advanced microeconomics b- Uncertainty 1- Microeconomic Theory, P.R.G. Layard and A.A. Walters; CH 13 Uncertainty . 2- Microeconomic Theory, A. Mas-Collel , M. D. Winston , J . R . Green CH 13 Adverse selection signaling and screening Ch 14 the principal agent problem CH 19 General Equilibrium under uncertainty 3- A Course In Microeconomics Theory . D . M . Kreps . CH 3 Choice under uncertainty C- Information Economics 1- A Course In Microeconomics Theory . D . M . Kreps . CH 16 Moral Hazard and Incentives CH 17 Adverse selection and market signaling . CH 18 The revelation principle and mechanism design 2- Microeconomic Theory, A. Mas-Collel , M. D. Winston , J . R . Green CH 23 Incentives and Mechanism design CH 1 welfare

  4. Advanced microeconomics d- Original selected articles in microeconomics , 1- Joan Robinson , The Polar Case of Competition and monopoly . 2- R. Coase The Problem of Social Cost 3- Demesetez, Towards a Theory of Property Right . 4- Arrow , Difficulty in the concept of social welfare function . 5- Yew-Kawng , some fundamental issues in social welfare . 6- Peter Hammond , Welfare Economics. CH 1 welfare

  5. Advanced microeconomics 7- Frutz , Machlup , Theories of firm ; marginalist , behavioral ,managerial, 8- Robins , Denis , Muller , The corporation , competition and invisible hand . 9- F. M. Bator , The Anatomy of Market Failture . 10 – Arrow , The organization of Economic Activity 11 – W. Vickery , Some implication of the Marginal Cost Pricing . 12- Arrow, The Potential and Limits of Market in Resource Allocation 13- R. McKean , The nature of Cost Benefit Analysis. CH 1 welfare

  6. Introduction To draw policy conclusions from the facts we need normative theory. For this reason welfare economics can be chosen to be the first chapter that could be studied in the microeconomics . This issue deals with three main questions ; 1- How should a particular society’s resources ideally be used . What social organization is best for this goal ? 2- How can we tell any change we make is for the better ? 3- What would be the property of acceptable social welfare function ? CH 1 welfare

  7. Society's Economic Problem Two important issues : 1- How should factors be allocated among products ? This will determine the quantityof each product , and the techniqueswhich they are produced with . 2-How should the products be distributed among different citizens . Conclusions could be drawn from a simple model ; Two persons ; A & B Two homogenous devisable factors ; L & K Two homogenous divisible commodities X & Y CH 1 welfare

  8. Society's Economic Problem Max W=w(uA , uB) need not to be defined exactly S.T. uA= uA(xA,yA) (1)taste limits the happiness uB= uB(xB,yB) (2)taste limits the happiness x=x(Kx , Lx ) (3) technology limits the production y=y(Ky , Ly ) (4) technology limits the production X= xA + xB(5) Y = yA+ yB(6) K = Kx+ Ky (7) L = Lx + Ly (8) Eight constraints and eight unknowns, xA,xB,yA,yB,Kx,Ky,Lx,Ly CH 1 welfare

  9. Society's Economic Problem First order conditions ; 1- UAx(xA,yA)/ UAy(xA,yA)=UBx (xB,yB)/UBy(xB,yB) MRSAx,v = MRSBx,y efficient consumption 2- XL(Kx,Lx)/ XK (Kx,Lx)= YL(Ky,Ly)/ YK (Ky,Ly) RTSxL,K=RTSyL,K efficient production 3- UAx(xA,yA)/ UAy(xA,yA)= YK (Ky,Ly)/ XK (Kx,Lx) MRSAx,v= RPTx,y mix effeiciency 4- UAx(xA,yA)/ UBx (xB ,yB)=WUB(uA,uB)/ WUA (uA,uB), or UAx(xA,yA) WUA (uA,uB) = UBx (xB ,yB) WUB(uA,uB) UAy(xA,yA) WUA (uA,uB) = UBy(xB ,yB) WUB(uA,uB) value of one unit of xor y consumed by A or B should be the same from social point of view. A situation is efficient or pareto optimal( 1 ,2 ,3 holds ) if it is impossible to make one person better off except by making some one else worse off. CH 1 welfare

  10. Conditions for efficiency Efficient consumption ; Max UA( xA , YA) S.T. UB(xB , YB) = u0 xA + xB = x yA + yB = y L = UA( xA , YA) +λ[ u0-u( x - xA , y – yA ) ] LxA= UxA + λUxB = 0 LyA= Uy A + λUy B = 0 MRSx,yA = MRS x,y B Both A and B place the same relative value on x and y CH 1 welfare

  11. Conditions for efficiency At point A , MRSxyA>MRSxyB . X has more relative value to A and y has more relative value to B. A will give up Y for x and B will give up x for y till MRSxyA = MRSxyB. Efficient consumption requires all individuals place the same relative value on all products xB O OB A yA yB UB1 UA 1 N N M M UB0 MN : locus of efficient points on contract curve AMN ; efficiency area ََ UA0 O OA xA CH 1 welfare

  12. Conditions for efficiency uB M uB1 Utility possibility frontier N uB0 In this way we could find the locus of all efficient points for consumption ; MRSA and MRSB are the same at points M and N uA uA0 uA1 CH 1 welfare

  13. Efficient production Allocation of given factors among factors of production in such a way that ; for given production level of commodity Y , the output of commodity X be the maximum possible. Max X=X(Kx , Lx) S.T. Y0=Y(Ky,Ly) Lx+Ly=L Kx+Ky=K P.O.→ ( XL / XK ) = RTSLKx = RTSLKy =( YL / YK ) Labor and Capital are engaged in producing those goods in which they have comparative advantage CH 1 welfare

  14. Qy Efficient production K At point p ; RTSLKx > RTSLKy Labor has more productivity in producingx than y , so it has comparative advantage in producing x. more Lshould be allocated for producing x . We should move from p to Q x1 R p y0 x0 Q y1 Ox L R & Q are efficient points , since RTS for X & Y are the same .they belong to the locus of all efficient points on the production possibility frontier CH 1 welfare

  15. Production possibility frontier Locus of all efficient points of production : For every level of x maximum amount of Y could be attained Y Efficient production Q Y1 MRTxy = -dY/dX = MCx/MCy Opportunity cost of producing one unit of x in terms of Y R Y0 x X0 X1 CH 1 welfare

  16. Product mix efficiency Production is efficient Y PPF Consumption is efficient OB Y0 Consumer needs = production ability Product mix efficiency requires that the subjective value of x in terms of y (MRSxy) be equal to marginal opportunity cost of x in terms y (MRTxy). uA0 MRSxyA = MRSxyB = MRTxy uB0 X OA X0 CH 1 welfare

  17. Oy K=Kx +Ky =KA+KB L=Lx + Ly =LA + LB K y0 Kx X x0 PPF Ox Social justice &social optimum Lx L x0 y0 OA UA0 yA uB0 Y xA OB Y0 x0 UB O UB0 W=W(uA,uB) = social welfare function uA UPF(x0,y0) UA0 UA UPF(x1,y1) CH 1 welfare

  18. Social justice &social optimum W=W(UA,UB) , dW=0 , WUA dUA +WUBdUB = 0 Slope of social welfare function = -(duB/duA)=WUA/WUB slope of UPF = -(duB/duA)=-(duB/dx)/(duA/dx)=-(duB/dy)/(duA/dy) At point O (bliss point ) ; (WUA/WUB) =-(UBx/UAx)=-(UBy/UAy) WUAUAx=-WUBUBxWUAUAy=-WUBUBy WUAUAx+WUBUBx = 0 WUAUAy+WUBUBy=0 Social value of an extra amount of x(or y) giving to A should be the same mount as taking it away from B . CH 1 welfare

  19. Social justice & Social optimum Once point O (bliss point) is chosen, three basic question can be answered when XA, XB, YA,YBare defined , FOR WHOME when Lx, Ly, Kx , Kyare defined , WHAT & HOW In judging about the point of bliss we have not taken into account the question of equality . In other words we have considered the question of efficiency in isolation from equality . Later on we will refer to this point as dichotomy between production (allocation of inputs) and distribution (equity). CH 1 welfare

  20. freely functioning economy, market failure, alternative economic systems What form of organization will bring the economy near to the optimum?If it had all the information , a computer could in principle solve the problem we have passed. How would a freely functioning economy perform? Remarkably well if we make four sweeping assumption of perfect competition. The key one is that in every perfectly competitive market there are many buyers and sellers and underperfect competition all agents behave as price takers How a perfect competition economy can satisfy the three conditions for efficiency; 1- efficient consumption; Max ui=u(xi,yi) S.T. Pxxi + pyyi= Mii= individual i = 1,2,…,n CH 1 welfare

  21. freely functioning economy, market failure, alternative economic systems MRSi = Uix/Uiy = px/py = fixed (px , py are fixed for consumers) 2- efficient production ; For any commodity like x ; Min TCi = WiLxi+ WKKxi S.T. Xi0 = Xi (Ki , Li) i=1,2,3……n = number of firms RTSLKi= WL/WK = fixed under perfect competition . Since RTSLK is fixed for any commodity ,so efficiency is hold for each firm i. if firms exhibit constant return to scale , the RTS will hold in the economy for any two commodities. 3- efficient product-mix Under perfect competition for any commodity like x or y ; PK = XK Px = VMPKx , PL = XL Px = VMPLx PL fixed PK = YK Py = VMPKy , PL = YL Py = VMPLy PK fixed CH 1 welfare

  22. freely functioning economy, market failure, alternative economic systems ( Px/ Py)=(XKy)/(XKx) =( XL y)/(XLx) = (MPKy/MPK x) = (MPLy/MPLx)= ( Px/ Py) = MRSxy = (MCx/MCy) = MRTxy 1 , 2 , 3, concludes the efficient allocation of resources under perfectly competitive conditions. But it does not maximize social welfare function . As we will see it depends on the distribution of the ownership of factors of production . So there must be a distribution which maximizes the social welfare . This will be equitable (maximizing welfare ) as well as efficient. After finding the optimum allocation of factors and commodities, it is possible to find the relative prices . When (xA,yA) is known then UxA/UyA is known and Px/Py is known When Lx , Ly , Kx , Ky , is known , XL , XK , YL, YK , is known, then XL=WL/Px , YL=WL / Py , XK=WK/Px , YK=WK/Pyis known , Since (WL / WK ) = ( XL /XK ) , Relative factor prices will also be known. In order to be sure that social welfare is maximized , we have to be sure that each individual will consume the quantities of output which maximizes its welfare according to the social welfare function which is designed for him. CH 1 welfare

  23. Capitalism, market failure, alternative economic systems A’s (or B) consumption = A’s (or B) income (Px/Py)xA + yA = (WK/Py) KA +( WL /Py) LA (Px/Py)xB + yB = (WK/Py) KB +( WL/Py) LB xA , yA ,xB , yB , WK/Py ,WLPy are known , so KA , KB , LA , LB , should be chosen in such a way that the above relation be satisfied. In this way the smaller the labor power one has , the greater should be his capital stock in order to enable him to buy the consumption bundle necessary for welfare maximization . So , capital transfer may be necessary from one to the other . The initial labor and capital stock owned by individuals should be just and right in order to maximize the social welfare. If the distribution of factor ownership is right , a free market economy (competitive one , in the absence of market failure) can maxzimize the social welfare CH 1 welfare

  24. freely functioning economy, market failure, alternative economic systems Market failure This will provide the suitable framework for considering the proper role of state in a mixed economy. Four assumptions is necessary to hold for the market system to work properly and do not fail . These are as follows ; 1- No increasing return to scale with increasing return to scale , average cost falls as output rise. Large firms can always undercut small ones. Monopoles would emerge. MRx=MCx , MRx=Px [1 – 1 / |ex| ] → Px>MCx CH 1 welfare

  25. freely functioning economy, market failure, alternative economic systems In perfect competition →MRSx= Px/Py = MCx/MCy So , comparing to perfect competition , less X is produced than ought to. Solutions ; 1- State should regulate the price for optimal X to be produced. 2- Nationalize the industry. If Px should be equal to MCx and because in increasing return to scale , ACx>MCx → TC > TR , so subsidy is needed. So , for a free functioning economy to be efficient , increasing return to scale within the firm must be exhausted before equilibrium level of output reached. CH 1 welfare

  26. freely functioning economy, market failure, alternative economic systems No technological external effect Such effects arises if one agent decision directly affect the utility or output of other agents over and above any indirect effects they may have through their effects on relative prices . In these cases the decision maker is not charged for any possible cost his action may impose on other people nor reward for any benefits he may confer. Prices can not reflect the marginal opportunity cost, and they are irrelevant . UA = uA (xA , yA , xB ) , UB = uB (xB , yB ) All derivatives are positive except for dUA/dxB < 0 . CH 1 welfare

  27. freely functioning economy, market failure, alternative economic systems Consumption of x by consumer B cause negative effect on consumer’s A utility level. The optimum level of xB will be determined as follows ; Under free market and perfect competition ; MCx/MCy=Px/Py = MRSxyA=MRSxyB→ MCx/MCy = MRSBxByB Since MRSAxByA <0 , MCx/MCy ( MRTxy) should be lower than what it is in perfect competition. So in P.C. without taking externality into account MRTXY is higher than it should be . So under perfect competitiontoo much xB(X=XA + XB ) is consumed , more than what is necessary . In order for xB(equivalently X=XA + XB ) to be optimal under perfect competition , MRSxyB should be lowered by imposing a tax on the consumption of x by individual B .→ tax = MRSAxByA CH 1 welfare

  28. freely functioning economy, market failure, alternative economic systems For a free market be efficient , there must be no technological external effect , unless costless negotiation is possible between the parties concerned. 3- No market failure related to uncertainty . With uncertainty the conventional concept of unique price and quantity is not valid anymore , so perfect competition conditions may not result in pareto optimal situation. First optimality theorem Resource allocation is Pareto optimal if there is perfect competition ,no increasing return to scale, no technological externalities , and no market failure connected with uncertainty. CH 1 welfare

  29. freely functioning economy, market failure, alternative economic systems Second optimality Theorem ; Any specified Pareto optimal allocation that is technically feasible can be achieved by establishing free market operation (perfect competition) and an appropriate pattern of factor ownership, if there are no increasing return to scale , no technological externalities, and no market failure connected to uncertainty. To insure the second theorem we need to be sure that the ownership of the factors of production is right . In other words ,, the distribution of factor ownership must be such that each consumer can buy the consumption bundle which for a free market equilibrium to be socially optimal corresponds to the welfare maximizing configuration of the economy (social welfare function will define this according to the distributional criteria and value judgments of the policy makers). pursuit of distributional justice = state intervention . CH 1 welfare

  30. freely functioning economy, market failure, alternative economic systems Non market alternatives ; Oskare Lange claimed that decentralized socialismcould have the same formal properties of social optimum ; State would own all the capital and rent it out to the managers who are instructed to maximize the profit . There are freely functioning labor market . Wages are determined competitively . State would receive all the income of each enterprise net of wages and raw materials (including the managerial cost ) . If firms were constant return to scale , prices would left to be determined freely by the market forces but state will fix them on the base of signals received and observed from the market . CH 1 welfare

  31. freely functioning economy, market failure, alternative economic systems Even so the outcome is only necessarily optimal if the supply of capital is given . In fact the rate of saving would have to be determined by the state. In this mannersaving may not reflect the consumer preferences . The real deficiency of the Langeh analysis is that , the state should be responsible for the establishment of the enterprises and the appointment of the managers . A more decentralized system is Yugoslavian one in which there are workers managed firms operating in the economy , but workers can not still own the capital . Comparing the market system with centralized socialism , there are two obvious problem ; information and incentives CH 1 welfare

  32. freely functioning economy, market failure, alternative economic systems Information concerns ,taste , technology , endowments . Taste – income should be allocated in terms of purchasing power (cash income ) rather than in kind (commodities). In the market system cash income is the base of allocation , but in the centralized system coupons or vouchers are the base of allocation . Technology – centralized socialism assumes that the center of planning can know where and how each good is most efficiently produced. Endowments – centralized socialism assumes that the state have a detailed list of the talents , stock of machines , and natural resources. CH 1 welfare

  33. freely functioning economy, market failure, alternative economic systems Market system (price mechanism ) provides such an information which coordinates the action of different economic agents ; Good’s prices in the markettell producers that which one of the goods consumers want more, and guide the consumers what kind of sacrifice is needed for consuming different goods . Factor prices in the markettell producers the value of alternative uses of the factors of production they employ and ensure that they are not wasted . It may be claimed that the growing power of computers could possibly overcome the informational problem of the centralized socialism . But it is worth noting that the western countries were successful in wartime when they are subject to detailed controls . CH 1 welfare

  34. freely functioning economy, market failure, alternative economic systems Concerning the incentive problem of the centralized socialism , we may point that it is possible to have the pattern of wage differentials exist to ensure the reasonable utilization of the labor , but it is more difficult to devise incentives for the efficient use of capital when it is not privately owned. In choosing among alternative forms of social organization two important consideration should be taken in to account ; 1- the form of organization will itself influence people’s taste. 2- any plan to change system must be considered in a dynamic form , and take in to account the cost of change. CH 1 welfare

  35. Criteria for the welfare improvements We have so far discussed only the social optimum. But we often need to compare different economic states , none of which may be optimal. In these cases we have to undertake cost benefit analysis before and after the happening . The action of shifting from state 0 to state 1 is to be judged by its effects on the happiness of all those who have been affected two cases may be recognized ; 1- some one gains and no one loose (Pareto criteria ) , 2- some one gains but some others will loose . Pareto criteria ; A Pareto improvement is a social change which at least one person gains and nobody loose , that is ; ∆Ui >0 for some i , and ∆Ui ≥ 0 for all i . A Pareto situation is the one from which no Pareto improvement is possible . CH 1 welfare

  36. Criteria for the welfare improvements A general criteria in the real word most of the changes hurt someone , and Pareto criteria does not provide a complete ranking of all the states. To get a complete ranking of social states we have to invoke the welfare function , W = W( UA , UB ) . This function speedily tells us that whether a change is preferred or not . W = W( UA , UB ) ∆W =[ dW/dUA] ∆UA +[ dW/dUB ] ∆UB If ∆W >0 , there will be welfare improvement , vise versa . If enough points like p0 , and p1 , were compared and a move is made whenever ∆W >0 , we should ultimately reach to the optimum point or bliss point where no improvement is possible . p1 uB p0 w0 uA CH 1 welfare

  37. Criteria for the welfare improvements For practical purposes we need to measure changes in individual welfare and not in units of utility. In other words we need to measure changes in units of some numerate good, and then to attach social welfare to increments in the numerate good accruing to different members of the society; ∆w =( dw/duA )( uAy )(∆uA/ uAy ) + ( dw/duB)(uBy)(∆uB/uBy) (∆uA/ uAy ) = shows how many units of y would have produced the same change in utility as be actually been experienced . It also indicates approximately how many units of y might be willing to be paid to bring about the change from one state to the other . ( dw/duA )( uAy) = measures the social value of an extra unit of y accruing to A , or what one may call the weight attaching to a marginal units of y . CH 1 welfare

  38. Criteria for the welfare improvements The Caldor criteria Suppose that we have to decide whether to run a project or not. The result of the project is shown in the following table; ∆Yi weight=(wui )(uiy ) person A (rich) 200 1 person B (poor) -100 3 ∆w = (200)(1) + (-100)(3) = -100 <0 Why not pursue the above project and at the same time make A to give B 100 units . With the policy consisted of the project plus compensation , the above table will convert into the following ; ∆Yi weight=(wui )(uiy ) Person A 1001 Person B 0 3 ∆w = (1)(100) + (0)(3) = 100 >0 CH 1 welfare

  39. Criteria for the welfare improvements If compensation is not actually going to be paid , we can only claim that the project offer a potential Pareto improvement . It is of great importance to note that a great waste will result if productive projects have to be rejected on equity ground . Caldore improvement is a change from a given output mix distributed in a given way to another output mix which would enable the gainers to compensate the losers while continuing to gain themselves. Since the compensation need only be hypothetical , a Caldore improvement offers a potential pareto improvement . The argument is that we should think separately about production and distribution ; 1- production decisions would maximize the size of the cake, 2- distribution policies should ensure that it is divided equally. CH 1 welfare

  40. Criteria for the welfare improvements Critiques of the Caldore criteria The Caldore criteria could be criticized at least for three reasons ; 1- the concept of the cake is not clear if there is more than one type of the cake . In this way one may not be able to decide which of two output mixes is efficient unless one simultaneously settles the question of distribution . This can be shown by the concept of concept of community indifference curve A community indifference curve [CIC(uA0 , uB0 ) ] is a locus of all (x , y) which makes it just possible to achieve a given utility bundle (uA0 for uA, uB0 for uB ). The slope of the curve equals the marginal rate of substitution of y for x (which is the same for all the citizens ). By the help of CIC we will show that the output mix ( type of the cake) should de defined . CH 1 welfare

  41. CIC(uA0 , uB0) CIC(uA1 , uB1) y MRSxy = MRSAxy=MRSBxy Criteria for the welfare improvements OB0 y0 uB1 uA1 OB1 UA0 y1 T UB0 s s1 UB0 x OA x0 x1 CH 1 welfare

  42. Criteria for the welfare improvements y We have to know on which CIC curve we are. In other words we have to know whether we are at point T or S .since income distribution differs at points T and S . So separation of production and distribution fails . As it shown in the figure two CIC could pass from point OB0 . One relates to the utility bundle (UA0 , UB0 ) , and the other relates to the utility bundle ( UA1 , UB1 ) . In these cases there are no unambiguous ranking of social output independent of the income distribution ( utility levels of two persons in the figure) . So the Caldore criteria may yield the paradoxical result that a move from state 0 to state 1 may be an improvement , and so a move from state 1 to state 0 . 1 0 x CH 1 welfare

  43. Criteria for the welfare improvements How serious is this problem ? It would not rise if redistribution of a given output mix produce no change in the relative value of x and y . For this purpose MRSxy should not change when distribution of output mix will change . Consequently , marginal propensity to spend on x and y will not change as a result of redistribution of output mix . For this to happen we need to have homothetic utility function . As a result of this we need to have relative prices remain constant . So when income is transferred from one person to the other , there is no need for any change in relative prices to ensure that the total supply of x and y is demanded. The efficiency locus must be a straight line and MRSxy remains constant . CH 1 welfare

  44. CIC MRSxy= Px/Py Efficiency locus oB Y0 Q Criteria for the welfare improvements T S oA X0 The condition for unique set of community indifference curve is thatmarginal propensity to buy each good out of additional income should be the same for all individuals at any set of relative prices. For many limited problems such as cost benefit analysis of a motorway this may be a reasonable working assumption, though for the analysis of large tax changes and so on the problem may be more serious . CH 1 welfare

  45. Criteria for the welfare improvements This brings us to the second and more fundamental objection of the Caldore criteria . The reasoning is as following ; For pareto optimality we should have the following equity ; UAy(xA,yA) WUA (uA,uB) = UBy(xB ,yB) WUB(uA,uB) = α , and ∆w =( dw/duA )( uAy )(∆uA/ uAy ) + ( dw/duB)(uBy)(∆uB/uBy) , so ∆w/α = (∆uA/ uAy )+(∆uB/uBy) =∆YA + ∆YB = ∆Y this will hold only if the optimality condition holds first relation) . That is , ∆w >0 when ∆Y>0 , or Caldore criteria holds. In practice optimality can not hold for one overwhelming reason ;we can not redistribute (or it is very hard to redistribute) the ownership of the means of production in a manner to fulfill the following relations which is required for welfare maximization ; (Px/Py)xA + yA = (WK/Py) KA +( WL /Py) LA (Px/Py)xB + yB = (WK/Py) KB +( WL/Py) LB In order to redistribute L and K between A and B in such a way that fulfill the above relation ; CH 1 welfare

  46. Criteria for the welfare improvements 1- we should assume that labor power of each individual is known , so we can transfer capital between the individuals in order to fulfill the above equalities for each individual . But costless transfer of capital is not possible . If costless transfer is possible , then we will have lump-sump transfer. A lump-sum transfer is the one in which neither the loser nor the gainer can affect the size of the transfer by modifying their behavior . It should be noted that the original labor power which an individual posses can not be identified . Let us suppose that the tax collector can only observe an individual earnings. He then either tax it if it was high , or subsidize it if it was low . But we know that this will induce a substitution away from work and this will not be a lump-sum transfer. CH 1 welfare

  47. Criteria for the welfare improvements If lump-sum tax is impossible and social welfare is maximized only through an optimal income tax , then we can not have social bliss , and consequently the social value of each person’s dollar spending is not the same . So if we have a project which confers benefits in lump-sum form it might not be worth doing even if it benefits rich more than the poor . 3- the third case against Caldore approach would raise when the evaluator did not agree with the form of the welfare function implicit in the existing distribution of income . CH 1 welfare

  48. The measurement of welfare cost Despite he shortcoming of the Caldore criterion it is often useful to measure the effects of a change in the total value of output, independently of the distribution of output . There are two reasons for this approach ; 1-it is difficult to know exactly who are the gainers and who are the losers . 2 – even if we do , we can always think of our final choice as depending on the tradeoff between effects on total output and on inequality . Suppose that as result of a policy we move from P0 to P1 on the production possibility frontier . Further on , suppose that this would be done by a tax on Y ,which was used as a subsidy for x The question is how to measure the effect of this policy on the output level . CH 1 welfare

  49. (uA0 ,uB0 ) Y per x MRTxy (uA1, uB1 ) p0 The measurement of welfare cost Y0 p1 MRSxy x x0 x1 x1 x0 What is the net cost of moving from p1 to p0 . Naturally the question could be answered by one of the following questions; CH 1 welfare

  50. The measurement of welfare cost 1- if we start from P0 , what loss of y would have the same effect on utility as actual move to p1 . 2- if we start from P1 , what gain in y would have the same effect on utility as returning to P0 . We assume that the income elasticity of demand is equal to zero, which simplifies the matter and this means that the indifference curves are vertically parallel. MRSxy = MUx / MUy =value of x in terms of y = price of x . dMRSxy / dy =0 → price of x will remains constant as income increases . Y= income x x0 CH 1 welfare

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