Choosing Policies Op/mally Efficiency and Redistribu/on. Economics 525

Transcription

1 Choosing Policies Op/mally Efficiency and Redistribu/on Economics 525

2 Choosing best policy When should policymakers intervene in markets? Need norma/ve criteria for judging whether to intervene and which policy to use. Simple example: We could have a policy rule that says Implement any policy that is a Pareto improvement. Few could argue against a policy that makes no one worse off and makes some beoer off But this might be a bit restric/ve as a general rule 1

3 Use Poten/al Pareto Improvements Instead Cost Benefit Analysis allows us to iden/fy efficient policies. Take status quo and ask if poten/ally the winners of the policy change could compensate the losers. No actual compensa/on. 2

4 Distribu/on of wealth Perhaps the biggest cri/cism of using CBA to select policies is that a transfer of 1 dollar from a poor person to a rich person leaves net benefits unchanged Yet most people would consider that to be making society worse off, because it worsens the distribu/on of income without increasing the size of the economic pie. 3

5 Distribu/on of Wealth vs. Efficiency For economists concerned only with efficiency, implemen/ng the biggest poten/al Pareto improvements is a useful rule for assessing policy But society is o\en concerned with more than just efficiency. People worry about highly unequal distribu/ons of income Some efficient policies will exacerbate the unequal distribu/on of income (e.g., shi\ing from a progressive income tax to a flat consump/on tax) 4

6 Second Welfare Theorem Second Welfare Theorem is kind of a crock. There s no way (in the real world) to lump sum redistribute income Even if the government could arbitrarily seize wealth and redistribute it, it wouldn t be lump sum because people would think it might happen again. This would likely distort behaviour that affects wealth accumula/on 5

7 Social Welfare Func/ons Can economists say anything analy/cally about distribu/on? Many people certainly have an intui/on that some alloca/ons are preferable to others, due to a more equal distribu/on of outcomes Perhaps we can construct a no/on of social welfare that takes into account both efficiency and distribu/on 6

8 Coming up with a policy rule that accounts for efficiency and equity The goal of policymakers should be to maximize the public interest or social welfare Ideally, we d like our defini/on of social welfare to reflect the individual preferences of people living in our society This approach would be consistent with liberal democracy government is meant to act in the interest of individuals 7

9 Social welfare and individual preferences If there was only one individual in society, maximizing social welfare would be easy Just choose the policy (or resource alloca/on) favoured by that individual Models that use a representa/ve agent effec/vely do that Maximizing social welfare <=> maximizing individual u/lity Sadly (happily?) there s a diversity of individuals So maximizing social welfare is much trickier 8

10 Social Preferences If we could aggregate individual preferences into social preferences we could determine whether a resource realloca/on e.g., a policy makes social welfare rise or fall. Unfortunately, it is impossible to sa/sfy all of Arrow s axioms Hence the op/mis/cally- named Impossibility Theorem of Kenneth Arrow (1950) 9

11 Impossibility of aggrega/ng preferences Essen/ally, without making interpersonal comparisons of u/lity (or happiness or any other human feeling), and no maoer what the preferences of people might be, we will not always be able to judge sa/sfactorily which policy maximizes overall happiness (or u/lity or any other measure of well- being). Not clear that cardinality doesn t exist. It is, however, very challenging to measure cardinal preferences. We also use cardinal u/lity in expected u/lity theory and we have some experimental evidence that people are risk averse which is equivalent to sta/ng that their u/lity is concave in income. However, expected u/lity theory does not rely on interpersonal comparison to analyze people s choice under uncertainty. 10

12 Using Social Welfare Func/ons If u/lity was cardinal and observable, then we could implement policies that maximize the sum of u/li/es across individuals (as u/litarian philosophers suggested) or use some other func/on that assigns social welfare to any given vector of people s u/li/es. Welfarism or U/litarianism has been around for a long /me Predates Social Choice (preference aggrega/on when u/lity is ordinal) Goes back to Jeremy Bentham and John Stewart Mill 11

13 Meet Mr. Bentham Embalmed and stored in a glass case in the halls of UCL To this day aoends occasional faculty mee/ngs as a non- vo/ng member Movie about him on course web page 12

14 Diminishing Marginal U/lity of Wealth Of two people having unequal fortunes, he who has most wealth must by a legislator be regarded as having most happiness. But the quan;ty of happiness will not go on increasing in anything near the same propor;on as the quan;ty of wealth: ten thousand ;mes the quan;ty of wealth will not bring with it ten thousand ;mes the quan;ty of happiness. It will even be ma?er of doubt, whether ten thousand ;mes the wealth will in general bring with it twice the happiness. The effect of wealth in the produc;on of happiness goes on diminishing, as the quan;ty by which the wealth of one man exceeds that of another goes on increasing: In other words, the quan;ty of happiness produced by a par;cle of wealth (each par;cle being of the same magnitude) will be less at every par;cle; the second will produce less than the first, the third than the second, and so on. - - Jeremy Bentham 13

15 Meet John Stewart Mill Said that progressive taxa/on penalized those who worked harder and saved more and was therefore a mild form of robbery but advocated for an inheritance tax Became advocate of socialist policies later in life. Introduced merit goods. For example, only people who have experienced educa/on know the value of educa/on. 14

16 Conceptual Issues in Redistribu/on Can think about redistribu/on using tools similar to our modeling of individual choice Individual Choice Social Choice Define Opportunity Set Define Preferences Choose preferred point in opportunity set Budget constraint Individual indiff. curves Tangency btwn indiv indiff curve and budget const. Utility possibilities frontier Social indiff. curves Tangency btwn social indiff curve and UPF 15

17 Defining Social Preferences Social Indifference Curves Set of combina/ons of u/lity of different individuals that yields equal levels of social welfare to society What does social indifference curve look like? Depends how society weights individual u/li/es of each member Philosophers differ on this point Bentham and Mill: Social welfare is equal to the sum of individual welfare NashSWF: Social welfare is equal to the product of individual welfare Rawls SWF: Social welfare is equal to the welfare of the least well off individual 16

18 U/litarianism Assuming 1) Diminishing marginal u/lity of income 2) Everyone has same u/lity func/on 3) Total income in society is fixed (i.e., no distor/ons) Then u/litarianism implies that SW will be maximized when incomes are equalized. Assuming 1) Constant marginal u/lity of income 2) Everyone has same u/lity func/on 3) Total income in society is fixed (i.e., no distor/ons) Then u/litarianism implies that SW will be maximized at any income distribu/on no maoer whether it is egalitarian or very unequal. 17

19 Total income in society isn t fixed People make decisions about whether to work, invest on basis of returns to doing so That s OK, because a u/litarian SWF will account for u/lity losses due to Okun s leaky bucket. In the face of distor/ons, it will not be socially op/mal to redistribute as completely as we would want to in the absence of distor/ons 18

20 Op/mal Redistribu/on Using SWF When faced with taxes on labour people can change their tax liability by changing their labour supply. This creates a distor/on. Leave most to the market; choosing tax to transfer is the only policy instrument W (u 1,u 2 ) = 2 u i i =1 u i (y i,l i ) = y i l i ; y 1 = (1 τ)w 1 (T l 1 ) y 2 = w 2 (T l 2 ) + S 2 S 2 = τw 1 (T l 1 ) 19

21 Simple Example Person 1 has different skills than person 2. Suppose consump/on good y is produced with CRS produc/on technology of the form y= (z 1 ) 3/4 (z 2 ) 1/4 z 1, z 2 is the amount of /me from each individual devoted to the produc/on of good y. Government maximizes sum of u/li/es subject to its balanced budget and takes the firm s behaviour and consumers behaviour as given. Consumers max u/lity, firm profit. However CRS leads to zero profit. 20

22 Market Firm min z1,z 2 w 1 z 1 + w 2 z 2 + µ(y z 1 3 / 4 z 2 1/ 4 ) FOCs w 1 3y 4z 1 = 0 w 2 y 4z 2 = 0 c(w 1,w 2, y) = 4 w w2 ( ) 1 4 y Set price of y =1 then P = MC yields 1 = 4 w w2 w 1 w 2 = 3z 2 z 1 z 1 = 3z 2w 2 w 1 3w y = z 2 2 ( ) 1 4 w 1 3 / 4 w z 2 = y 1 3w 2 3 / 4,z 1 = y 3w 2 w 1 Consumer I C- D u/lity func/on; 1/ 4 Set price of y =1. y 1 = l 1 = T 2. T ( 1 τ )w 1 2, y 2 = w 2 T 2 + S 2 2, l 2 = T 2 + S 2 2w 2. 21

23 Clear goods market, one skill market 22 1 = 4 w w2 ( ) 1 4 w 2 = w 1 3 ( 1 τ ( )w 1 + w 2 ) T 2 + S 2 2 = y z 1 = y 3w 2 w 1 1/ 4 T 2 = w 1 3 w 1 1/ 4 (1 τ)w w 1 3 T 2 + S 2 2 T 2 = 3 4w 1 (1 τ)w w 1 3 T 2 + S 2 2

24 Market Equilibrium Without tax and subsidy scheme 4 5 w 4 1 = 3( 4 4 w ) w 1 = 3 4 w 2 = 1 4 ; y = T 2, y 1 = 3 4 l 1 = l 2 = T 2 T 2,y 2 = 1 4 T 2 v 1 = T 4 3,v 2 = T 4 W = v 1 + v 2 = T 4 ( 3 +1) = 0.683T 23

25 Compe//ve Eqm does not maximize Social Welfare Note that we can solve for the highest possible social welfare by maximizing W subject to resource and technological constraints. This is not what the government can actually do, but we can always ask the ques/on what it would like to do if it had full control over all agents ac/ons. Plugging in eqm values into FOCs here, we find that the compe//ve equilibrium does not maximize social welfare. max y1,l 1,l 2,λ l 1 y 1 + l 2 ((T l 1 ) 3 / 4 (T l 2 ) 1/ 4 y 1 ) FOCs u 1 2y 1 u 2 2y 2 = 0 u 1 2l 1 u 2 2y 2 u 2 2l 2 u 2 2y 2 3y 4(T l 1 ) = 0 y 4(T l 2 ) = 0 y eqm = T 2,y eqm 1 = 3 T 4 2, y2eqm = 1 T 4 2 l 1 eqm = l 2 eqm = T 2 v eqm 1 = T 4 3,v eqm 2 = T 4 W eqm = v 1 eqm + v 2 eqm = T 4 ( 3 +1) 24

26 Solving for Socially Op/mal Alloca/on y 1 l 1 = y 2 l 2 y 1 l 1 = y 2 l 2 = 3y 4(T l 1 ) y 4(T l 2 ) l 2 = 3 4 T,l 1 = 1 4 v 1 = 33 / 8 T, y = 33 / 4 8 T,v 2 = 311/ 8 l 1 = 3l 2 2T ( y 1 = 3l 2T 2 )3 3 / 4 (T l 2 ) (4l 2 2T) l 2 = 3 4 T 4 T,y 1 = 33 / 4 8 T;W = 33 / / T,y 2 = 37 / 4 16 T T =

27 Compe//ve eqm is not socially op/mal Compe//ve Eqm W=0.683T Person with higher skills has higher u/lity Person with lower skills has lower u/lity Both work the same amount Efficient Social Op/mum W=0.755T Person with higher skills has lower u/lity Person with lower skills has higher u/lity Person with higher skills works more Efficient 26

28 Constrained Social Op/mum Use indirect u/lity func/ons as govt does not interfere in the market beyond taxing the higher skilled worker and transferring good y to lower skilled worker We have seen that higher skilled worker would always supply T/2 labour. In socially op/mal alloca/on high skilled worker needs to supply more than T/2. Low skilled worker reduces labour supply as desired, but high skilled worker cannot be induced to work more with income tax than he does in comp. eqm. 27

29 Constrained Social Op/mum W = T 2 (1 τ)w 1 + T 4 W τ = + T 4 w 1 1 τ at τ = 0, W τ > 0. ( ) dw 1 4 (1 τ)w 1 2w 2 + τw 1 w 2 dτ T 2 dw 2 dτ + τ dw 1 dτ + w 1 w 2 w 2 1 dw 2 ( 2 w 2 dτ 2w + τw 2 1) Note that this is not a trivial deriva/on and actually solving for the expression is not part of the lecture. 28

30 Conclusion Redistribu/on via income tax is inefficient: less is produced than in the compe//ve equilibrium, but it increases social welfare. 29