The economics of climate change
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1 The Economcs of Clmate Change C 175 The economcs of clmate change C 175 Chrstan Traeger Part 2: Effcency, Publc Goods, Externaltes Suggested background readng for emergng questons: olstad, Charles D. (2000), Envronmental Economcs, Oxford Unversty Press, New ork. Varan, Hal R. (any edton...), Intermedate Mcroeconomcs a modern aroach, W. W. Norton & Comany, New ork. Srng 09 UC erkeley Traeger 2 Effcency 1
2 The Economcs of Clmate Change C 175 ref Mcro Revew: From Preferences to Effcency Srng 09 UC erkeley Traeger 2 Effcency 2
3 The Economcs of Clmate Change C 175 Preferences Preferences, Indfference Curves, udget Constrants, and Choce (lackboard) Srng 09 UC erkeley Traeger 2 Effcency 3
4 The Economcs of Clmate Change C 175 Utlty From (well behaved) references we can buld Mountans of Pleasure (lackboard? No, you have seen me drawng ntarctca and England ) Srng 09 UC erkeley Traeger 2 Effcency 4
5 The Economcs of Clmate Change C 175 Srng 09 UC erkeley Traeger 2 Effcency 5
6 The Economcs of Clmate Change C 175 Srng 09 UC erkeley Traeger 2 Effcency 6
7 The Economcs of Clmate Change C 175 Utlty Each bundle s assocated wth a utlty level U(x,y) ou can thnk of utlty as a measure of leasure, or haness, or smly as reresentng references More utlty = referred Indfference curves are the too lnes or contour lnes of the utlty mountan Whle of a lot of the analyss that we wll do could be done rght away wth h references, utlty functons are a very convenent tool to make thngs easer Srng 09 UC erkeley Traeger 2 Effcency 7
8 The Economcs of Clmate Change C 175 Utlty Margnal utlty (MU) of good x: Change n utlty (ΔU) assocated wth a small change n the amount of good x (Δx). (Note that t good y s ket constant, t MU deends d on x level) l) Dscrete change: MU x U x U ( x x, y) U ( x, y) x Infntesmal change: MU x U U ( x x, y) U ( x, y) lm x 0 x Change n utlty caused by a change Δx s then (aroxmately) ΔU = MU x Δx Srng 09 UC erkeley Traeger 2 Effcency 8
9 The Economcs of Clmate Change C 175 Utlty More recsely margnal utlty s tself a functon of x and y: MU x = MU x (x,y) Frequently met assumton: Dmnshng Margnal Utlty: The leasure of an addtonal unt of consumton of good x decreases the more of good x I consume. Srng 09 UC erkeley Traeger 2 Effcency 9
10 The Economcs of Clmate Change C 175 sde on Cardnal vs Ordnal Utlty: n ordnal measure/ n ordnal utlty functon: (only) ranks alternatves the value means nothng n absolute terms e.g. grades, fnshng oston n race cardnal measure / cardnal utlty functon: bsolute measure allowng rankng and absolute comarson e.g. tons of carbon, ncome For descrbng market outcomes we only need ordnal utlty To aggregate utlty over dfferent ndvdual we need cardnal utlty (necessary for most normatve comarsons of market outcomes) Srng 09 UC erkeley Traeger 2 Effcency 10
11 The Economcs of Clmate Change C 175 Margnal Rate of Substtuton Margnal rate of substtuton (MRS) = Rate at whch a consumer s just wllng to substtute one good for the other = Rate at whch the consumer s just on the margn of beng wllng to ay some of good x n order to buy some more of good y = Sloe of ndfference curve (Note: Generally negatve, what does that mean?) Formally: MRS MU MU U U Ths sde s all about the consumer Here he hts the market Derve ths from ΔU = MU x Δx+ MU y Δy=0 (meanng U s constant)! Srng 09 UC erkeley Traeger 2 Effcency 11
12 The Economcs of Clmate Change C 175 Margnal Rate of Substtuton Remark: Whle MU s a cardnal measure, MRS s an ordnal measure! Frequently made assumton: Dmnshng margnal rate of substtuton s resonsble for convex ndfference curves Dfferent ersectve on convex ndfference curves: verages are referred max U feasble bundles, M better bundles Srng 09 UC erkeley Traeger 2 Effcency 12
13 The Economcs of Clmate Change C 175 Effcency n consumton: vs For some Indvdual : The necessary condton for Indvdual utlty utlty maxmzng maxmsaton: max U, M Max U(,) better bundles subject to: x + y =M feasble bundles gven rces and ncome M are MRS U U and yeld the generally effcent choces * and * Srng 09 UC erkeley Traeger 2 Effcency 13
14 The Economcs of Clmate Change C 175 Pareto Effcency One of the most mortant t economc concets named after the Italan economst Vlfredo Pareto ( ). Defnton n allocaton s Pareto otmal or Pareto effcent, f t s not ossble to reallocate the resources of the economy n a way such that at least one erson s better off wthout makng any other erson worse off. n allocaton s neffcent f t s ossble to make one member of the socety better off wthout makng any other member worse off. Such a movement s called Pareto mrovement. Srng 09 UC erkeley Traeger 2 Effcency 14
15 The Economcs of Clmate Change C 175 Effcency n consumton: vs Take a second consumer oth consumers face same market rces and take them as gven Then effcency requres MRS U U U U MRS What about the effcency of onts a and b? Edgeworth ox: Consumer s orgn s the uer rght corner and hs utlty ncreases movng to the lower left (blue ndfference curve) Srng 09 UC erkeley Traeger 2 Effcency 15
16 The Economcs of Clmate Change C 175 Effcency n consumton: vs Take a second consumer oth consumers face same market rces and take them as gven Then effcency requres MRS U U U U MRS Pont a not Pareto effcent; ont b s Pareto effcent Edgeworth ox: Consumer s orgn s the uer rght corner and hs utlty ncreases movng to the lower left (blue ndfference curve) Srng 09 UC erkeley Traeger 2 Effcency 16
17 The Economcs of Clmate Change C 175 Effcency n consumton: versus Note that there are nfntely many Pareto effcent allocatons Whch one wll occur deends on ntal allocaton of resources Srng 09 UC erkeley Traeger 2 Effcency 17
18 The Economcs of Clmate Change C 175 Producton (lease revew these sldes n more detal at home) Frm roduces and maxmzes rofts: max, Where (, ) s the roducton functon. It uses the nuts catal and labor. Smlarly some frms j roduce and maxmze: max j, j j j j j Srng 09 UC erkeley Traeger 2 Effcency 18
19 The Economcs of Clmate Change C 175 smlar reasonng holds for roducton Margnal Rate of Techncal Substtuton (MRTS) or Techncal Rate of Substtuton = how much more of an nut factor nto roducton do we need f we gve u a lttle bt of the other nut factor whle keeng the outut constant nalogy: MRS Isoquant = set of all ossble nut combnatons that are just suffcent to roduce a gven amount of the outut nalogy: Indfference curve Margnal Rate of Transformaton (MRT) = rate at whch we can techncally transform one outut good nto the other nalogy: lso MRS (Note: we do not actually transform one outut nto the other, but swtch nuts from one roducton to the other) Srng 09 UC erkeley Traeger 2 Effcency 19
20 The Economcs of Clmate Change C 175 Effcency n roducton: Catal versus abor (nuts) ll frms face the same factor rces and take them as gven, say two roducers (frst lne) and two roducer (second lne) Then effcency requres: MRTS MRTS MRTS MRTS2 Pont a not Pareto effcent; ont b s Pareto effcent Srng 09 UC erkeley Traeger 2 Effcency 20
21 Effcent roduct mx: outut goods versus ( a tough one ) The Economcs of Clmate Change C 175 Proft maxmzaton: 0 0, max d 0 0 MRT d d 1, max MRT d d 1 Srng 09 UC erkeley Traeger 2 Effcency 21
22 The Economcs of Clmate Change C 175 Effcency n consumton and roduct mx Utlty maxmzaton: MRS U U U U MRS If not equal, then consumton mx should be changed. Proft maxmzaton: MRT MRT If not equal, then roduct mx should be changed. Effcency of consumton and of roduct mx requres MRS =MRS =MRT =MRT Srng 09 UC erkeley Traeger 2 Effcency 22
23 The Economcs of Clmate Change C 175 Cometetve Equlbrum n allocaton of goods and a set of rces consttute a comettve (or Walrasan) equlbrum f: all frms maxmze ther rofts, all ndvduals maxmze ther utlty (gven the budget constrant), and all markets clear (no leftovers). Remark: The assumtons on slde 32 can also be consdered as art of the defnton of a (more narrowly defned) comettve equlbrum. Srng 09 UC erkeley Traeger 2 Effcency 23
24 The Economcs of Clmate Change C 175 Theorems of Welfare Economcs Frst theorem of welfare economcs: In a comettve economy, a market equlbrum s Pareto otmal Second theorem of welfare economcs: In a comettve economy, any Pareto otmum can be acheved as a market equlbrum, rovded the resources of the economy are arorately dstrbuted before the market s allowed to oerate. ut: Only hold under secfc assumtons Srng 09 UC erkeley Traeger 2 Effcency 24
25 The Economcs of Clmate Change C 175 ssumtons: Comlete roerty rghts: well defned, transferable, and secure set of roerty rghts must exst for all goods and bads n the economy so that these commodtes can be freely exchanged. ll the benefts or costs must accrue to the agent holdng the roerty rght for the good or bad. tomstc agents: Producers and consumers are small relatve to the market and thus cannot nfluence rces. Instead, they maxmze rofts or utlty takng the rces as gven. Comlete Informaton: Consumers and roducers have full knowledge of current and future rces. No transacton costs Techncal assumton on references/utlty and roducton (n artcular for the second welfare theorem) The comlete roerty rghts assumton ncludes: Comlete markets (all goods are traded) Prvate goods (no ublc goods, to aear soon...) No externaltes (to aear soon...) Srng 09 UC erkeley Traeger 2 Effcency 25
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