Econ 551 Government Finance: Revenues Winter, 2018

Transcription

1 Econ 551 Government Finance: Revenues Winter, 2018 Given by Kevin Milligan Vancouver Scool of Economics University of Britis Columbia Lecture 4b: Optimal Commodity Taxation, Part II ECON 551: Lecture 4b 1 of 35

2 Agenda: 1. Commodity taxation wit many ouseolds 2. Commodity taxation and production efficiency 3. Application: Soft drink taxation, Fletcer, Frisvold, and Tefft (2010). ECON 551: Lecture 4b 2 of 35

3 Diamond and Mirrlees 1971 AER: Tis paper eralded te resurgence of interest in optimal taxation trougout te 1970s. See Myles (p ); Atkinson-Stiglitz (p ). Take a planner s perspective: intro is about using taxes to control te economy. o Tis empasizes a key point of tis literature: we are simply coosing a set of prices tat is optimal. Tis is an important way to tink about taxes for reasons tat will become clearer in a few minutes. Study bot te production and consumption sides of te economy. In general equilibrium. Used contemporary micro tools. Duality, etc. Tey start wit production, ten move on to te consumer side. We ll do it in backwards order, toug. ECON 551: Lecture 4b 3 of 35

4 Te setup: H ouseolds. {1,, H} Linear commodity taxation available; no lump sum taxes, no income taxes. No direct revelation problems; everyone reports te trut. (Tis will be different for income taxation.) Labour is te untaxed numeraire good. Individual utility evaluated using indirect utility function (prices, wages, exogenous income). V = V (q, w I ) Welfare is aggregated using a Bergson-Samuelson SWF. Ψ(V) ECON 551: Lecture 4b 4 of 35

5 Today s lemmata and notation: λ = V I Ψ = Ψ V β = Ψ λ Marginal utility of income. Weigt put on ouseold in te SWF. Social weigt on ouseold s marginal income. x i = e q ik x x i Slutsky equation, were e k k I ik is derivative of expenditure function wit respect to i and k. X i = E q ik x x i k Slutsky aggregated over ouseolds. (Capital letters for k I aggregate quantities; lower-case for ouseold level.) x k = V q k V I Roy s identity ECON 551: Lecture 4b 5 of 35

6 Start wit te optimization problem: max q k Ψ(V) s. t. t i X i R i Set up a Lagrangian: L = Ψ(V) + μ ( t i X i i R) First order conditions: L = 0 = Ψ V t k V t k + μ (X k + t i X i q k i ) ECON 551: Lecture 4b 6 of 35

7 Manipulate te results using Roy s identity and Slutsky equation: Plug in Roy s identity to get: Ψ V V I x k = β x k = μ (X k + t i X i q k i ) Now plug in Slutsky equation to derivative on te far rigt, and rearrange: t i i E ki = β μ x k + t i i x x i k I X k Now just divide bot sides by X k and we ll ave someting to interpret. i t i X k E ki = β μ x k X k + t i i x k x i X k I 1 ECON 551: Lecture 4b 7 of 35

8 Interpretation of te result: i t i X k E ki = β μ x k X k + t i i x k x i X k I 1 1) Te LHS is similar to wat we saw for te Mirrlees index of discouragement. 2) On RHS, last part (-1) is a constant. Middle part represents extra tax revenue received wen gets one more dollar. First part is wat we want to interpret. 3) β μ is te marginal benefit to society of giving a dollar to, divided by te cost of giving a dollar to. Say we get 15 utils for tis for an extra dollar, but te extra dollar costs us 1.5. Ten tis ratio comes out as 10 dollars-wort of social benefit. 4) x k X k is te proportion of good k consumed by tis ouseold. ECON 551: Lecture 4b 8 of 35

9 continued i t i X k E ki = β μ x k X k + t i i x k x i X k I 1 5) β is terefore like a correlation of welfare weigt wit proportion consumed. μ x k X k 6) Te LHS is negative, so a larger value for te first term on te RHS means tat te taxes must be smaller so tat proportionate demand cange is smaller. 7) Te RHS becomes more positive wen te first term is larger. So, lower tax rates. Summarized, tis means tat good consumed more by tose wo ave ig social weigt sould be taxed less. ECON 551: Lecture 4b 9 of 35

10 Comparing tis result to one-consumer case: 1) If social marginal utility of income is te same for everyone (β = β ), ten te correlation will be zero and tere is no gain from attempts to redistribute. Tings reduce to te one-person case. 2) If all individuals demand goods in te same proportions, ten tere will be no variation in te proportion across ouseolds leading to a zero correlation and again it reduced to te one-ouseold case. Tink of tis as a signaling problem. Te state is trying to infer wom to tax by looking at wo disproportionately consumes wic goods. If tere is no signal, it can t do anyting about equity. ECON 551: Lecture 4b 10 of 35

11 Agenda: 1. Commodity taxation wit many ouseolds 2. Commodity taxation and production efficiency 3. Application: Soft drink taxation, Fletcer, Frisvold, and Tefft (2010). ECON 551: Lecture 4b 11 of 35

12 Breaktime! Hungarian Matematician Paul Erdős ( ) traveled te world coucsurfing and coautoring. Wrote 1525 publised papers. Had 511 coautors. People like to calculate teir Erdős number, wic counts te collaboration distance to Erdős. Peter Diamond as Erdős number of 3. o Peter Diamond-Eric Maskin-Peter Fisburn-Paul Erdős. Mine is 5: Milligan---Courtney Coile---Peter Diamond---Maskin--- Fisburn--- Erdős. IIRC, some oter entry points for economists to Erdős come from econometricians. ECON 551: Lecture 4b 12 of 35

13 Now we allow for a production side of te economy Recall, tis is te first part of Diamond Mirrlees (1971). Te question being posed ere is weter we sould tax intermediate inputs or not. Diamond and Mirrlees sow tat, in general, it is not optimal to tax inputs. Instead, only final goods sould be taxed. Tis is referred to as te Production Efficiency Lemma. We re going to look at a diagram rater tan go troug all of te mat ECON 551: Lecture 4b 13 of 35

14 Production efficiency and taxation U0 E0 Offer Curve Distortionary tax troug origin E1 U1 Input Production Possibility Frontier Lumpsum tax budget line, not troug origin. Taken from Myles (p. 128) ECON 551: Lecture 4b 14 of 35

15 Walking troug te result Two goods; one input one output. Houseolds supply input and consume output. Production possibility set defined for some convex tecnology. Ignoring taxes, we would be at a place like E 0 were te MRTS =MRS. However, tax revenue requirements sifts te set out to te left from te origin. Wit lumpsum taxes, we can still get to E 0. How? Adjust endowment along te input axis until we are at te tangent point to E 0. Tis is sown wit dark black lumpsum tax budget line. Wit distortionary taxes, price line must go troug te origin. Offer curve represents te locus of tangencies for ICs and price lines troug te origin. Optimal coice is at E 1. Wy? o Want to get te most output possible for te least input. o At interior point below E 1, could ave increased output witout more input. o At interior point to te left of E 1, could ave ad same output wit less input. ECON 551: Lecture 4b 15 of 35

16 Te lemma and its implications Stating it formally: If an optimum exists, ten te optimum as production on te frontier of te production possibilities set. Implications: 1) Input taxes sould not be differentiated among firms; all sould face te same post-tax input prices. (Wy is tis te case? If you are taxing inputs, you re not going to be on te efficient production frontier. Don t tax inputs.) 2) We can mimic any set of input taxes using a tax on final goods, so wy don t we just tax final goods instead? If we do tat, we re not distorting production decisions. Tat is, do not tax intermediate goods. Tis is a major motivation for value-added taxation. Tax final consumption; not intermediate goods. 3) Since capital is an input, we souldn t tax te return to capital. Tis is a conjecture; we ll see ow it olds up. ECON 551: Lecture 4b 16 of 35

17 Some caveats 1) In general, only olds wit CRTS. However, later autors sowed tat wit DRTS you could still get te result if you taxed away 100% of te economic profit. In reality, tis is ard to do owever, since distinguising between economic profit and return to capital is difficult. 2) In imperfect competition settings, intermediate good taxation can be optimal. ECON 551: Lecture 4b 17 of 35

18 Summary of optimal commodity taxation: 1. Can t tax all goods uniformly or else no revenue raised. 2. Wen one good not taxed, Ramsey sowed tat uniform taxation is not generally desirable for te taxed goods. 3. Ramsey-Mirrlees index of discouragement: taxation sould affect goods demand equiproportionately. 4. Wit redistribution concerns, goods eavily consumed by poorer people sould be taxed less. 5. If CRTS (or more precisely zero profits), ten tax only final goods not intermediate goods. ECON 551: Lecture 4b 18 of 35

19 Agenda: 1. Commodity taxation wit many ouseolds 2. Commodity taxation and production efficiency 3. Application: Soft drink taxation, Fletcer, Frisvold, and Tefft (2010). ECON 551: Lecture 4b 19 of 35

20 Start wit Musgrave Merit goods One of te concepts introduced in Musgrave s 1959 book was te merit good. Here is Musgrave s definition. A different type of intervention occurs were public policy aims at an allocation of resources wic deviates from tat reflected by consumer sovereignty. In oter words, wants are satisfied tat could be serviced troug te market but are not, since consumers coose to spend teir money on oter tings. Te reason, ten, for budgetary action is to correct individual coice. Wants satisfied under tese conditions constitute a second type of public wants, and will be referred to as merit wants. Q: Can you tink of any examples? Q: Wat is te difference between tis and a public good? ECON 551: Lecture 4b 20 of 35

21 Now, wat about te opposite--demerit goods Musgrave (1959) also talked about demerit goods. Te concept is te same, except tat instead of underconsuming tem, we tend to overconsume tem. Musgrave specifically mentioned liquor. Q: Wat oter wants migt be demerit wants. Q: Does te idea of aving your wants labeled as good and bad boter you? Is paternalism OK? ECON 551: Lecture 4b 21 of 35

22 Modern take: libertarian paternalism Sunstein and Taler ave pused te idea of libertarian paternalism. Key features of tis approac: Allow people to make coices, but restrict in some way te range or presentation of tose coices. Embraces recent researc on beavioural economics; ow people actually make decisions. Critic: Glaeser (2006 UofC Law Review) Quis custodiet ipsos custodies Wo gets to be te one wo sets te default? Are we flawed voters going to pick good default-pickers? ECON 551: Lecture 4b 22 of 35

23 Fletcer, Frisvold and Tefft: JPubE 2010 Te effects of soft drink taxes on cild and adolescent consumption and weigt outcomes Soda facts: Consumption grown 500% over 50 years. 7% of total calories consumed. One sugary drink per day more 60% increase in obesity odds $70.1 B in sales in US/year, getting close to tobacco. Price elasticity around -0.8 to Delicious on a ot day; goes well wit salty snacks. Question of tis paper: Wat appens wen tax on soda goes up? ECON 551: Lecture 4b 23 of 35

24 Wat kind of responses migt consumers ave to soda tax? Evidence from cigarette literature o Does tat only apply to addictive goods? (Is soda addictive?) Substitutes? ECON 551: Lecture 4b 24 of 35

25 Data and measurement How do tey measure taxes? How to tey measure soda intake? Wat data source do tey use? ECON 551: Lecture 4b 25 of 35

26 Empirical Approac Wat is teir empirical approac? Y istq = β 1 X istq + β 2 T stq + μ s + δ t + γ q + ε istq Wat assumptions underlie tis approac? Wat treats do you see for tis approac? ECON 551: Lecture 4b 26 of 35

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34 Points for discussion: Instead of taxing soda o Sould we tax sugar? Trans-fat or oter bad ingredients? o Sould we tax a broader set of drinks? If you were at a dinner party wit a medical doctor wo advocated a soda tax, ow migt you try to argue against er point? o Witout sounding like a jerk. (Occupational azard for an economist.) Are any lessons from optimal commodity taxation relevant ere? ECON 551: Lecture 4b 34 of 35

35 Next time: Optimal Income taxation Mirrlees, J.A. (1971), An Exploration in te Teory of Optimum Income Taxation, Review of Economic Studies, Vol. 38, No. 2, pp ECON 551: Lecture 4b 35 of 35