OPTIMAL PROVISION OF PUBLIC GOODS. Chapter 7: Public Goods. Optimal Provision of Private Goods
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1 Outlne hapter 7: Publc Goods Optmal provson of publc goods. Under-provson generally characterzes markets wth publc goods absent government nterventon. Prvate sector provson. rowd out Problems OPTIMAL PROVISION OF PUBLI GOODS Pure publc goods have two trats: They are non-rval n consumpton: The margnal cost of another person consumng the good s zero and does not affect your opportunty to consume the good. They are non-excludable: There s no way to deny someone the opportunty to consume the good. Table 1 gves some examples. If a good Ice cream s both s s rval also and because excludable Ths my able Some It s table excludable TV goods shows s non-rval are examples snce mpure because the of publc cable pure my consumpton Table because 1t I s can a of prvate smply t precludes good. not share you publc company goods from my consumpton goods because can mpure smply they of t publc refuse are n no non-rval way goods to hook consumng Yet For Other t example s non-excludable goods ce the cream a same are crowded wth mpure ce you. because cream. sdewalk publc Fnally It The t s dmnshes but Natonal s also they and pure non-excludable up are prvate defense publc the your (to system. some consumpton. goods. s a classc extent) because are both goods only rval clearly way because for very you dffcult they your to consume are enjoyment to rval prohbt but t example. once s s non-rval not to an area It s excludable. and s non-rval protected non-excludable. because everyone my pedestrans reduced make as from excludable. more usng pedestrans ce cream. the sdewalk. also consumpton consumes of that natonal protecton. defense use the same sdewalk. protecton does not dmnsh your consumpton of t. Defnng pure and mpure publc goods Is the good excludable? Yes No Is the good rval n consumpton? Yes Ice cream rowded cty sdewalk No able tv Natonal defense Optmal Provson of Prvate Goods onsder a prvate good lke ce cream. Fgure 1 shows the market for ce cream cones assumng that the alternatve use of the money s buyng cookes at $1 each. Ths makes cookes the numerare good. 1
2 Prce of ce cream $3 $2 Fgure 1 At a Addng prce Ben Addng of has up $3 up Ben s an nether Ben s ndvdual and and person erry s erry s S=SM demands ndvdual ndvdual demands demands at each erry downward-slopng also much has ce ndvdual cream. demand gve prce curve socety s gves for socety s ce demand cream. demand. downward-slopng demand at $3. curve At a prce for ce of Addng $2 cream. Leadng both up people to Ben s a compettve and erry s demand more equlbrum ndvdual ce cream. at demands $2. Ben gve & erry consume socety s dfferent demand There quanttes. at $2. s a market supply curve assocated wth producng ce cream. 0 Q ERRY Q BEN D ERRY Q TOTAL Demand for a prvate good D BEN SMB =D BEN+ERRY Quantty of ce cream Optmal Provson of Prvate Goods In ths fgure as prce adjusted each person changed hs quantty consumed. For a prvate good consumers demand dfferent quanttes at the same market prce. We can also represent ths relatonshp mathematcally. Ben has preferences over cookes () and ce cream (I): UB ( I) As does erry: U ( I) Optmal Provson of Prvate Goods Utlty maxmzaton requres that each of ther ndfference curves s tangent to the budget constrant. Moreover supplers set P=M. For Ben we have: For erry we have: B I B I I MRS B I P M P M = = = I I I MRS I P M P M = = = Optmal Provson of Prvate Goods The prvate market equlbrum n ths case s socally effcent. The MRS for any quantty of ce cream equals the SMB of that quantty the margnal value to socety equals the margnal value to any ndvdual n the perfectly compettve market. 2
3 Optmal Provson of Publc Goods Now consder the tradeoff between a publc good lke mssles and a prvate good lke cookes. Fgure 2 shows the market for mssles assumng that the alternatve use of the money s buyng cookes at $1 each. Prce of mssles $6 $4 $3 $2 $1 0 Fgure 2 Addng Addng up Ben s up Ben s and and erry s erry s wllngness to to pay pay gves for each socety s quantty demand gves socety s for 1 mssle. demand. As does erry. There s a market supply curve Leadng to a compettve Addng assocated up Ben s wth and producng erry s equlbrum at 5 mssles. wllngness Ben & to mssles pay gves socety s Ben has erry a downward consume slopng the same Q. demand Whle Ben s demand for the 5 Dcurve erry s wllngness S=SM ERRY for wllngness mssles. to pay for to pay the th mssle. for the frst frst mssle mssle $2. s $4. Whle Ben s erry s wllngness wllngness to pay for to pay the for the ffth ffth mssle mssle $1. s $2. 1 D BEN Demand for a publc good 5 SMB=D BEN+ERRY Quantty of mssles Optmal Provson of Publc Goods Unlke the case of prvate goods where aggregate demand s found by summng the ndvdual demands horzontally wth publc goods aggregate demand s found by summng vertcally. That s holdng quantty fxed what s each person s wllngness to pay? Optmal Provson of Publc Goods We can also represent ths relatonshp mathematcally. Ben has preferences over cookes () and mssles (M): UB To Ben the margnal mssle s worth B M B B = MRS M U ( M) erry s preferences are To erry the margnal mssle s worth ( M) M = MRS M 3
4 Optmal Provson of Publc Goods The socal margnal beneft (SMB) of the next mssle s the sum of Ben and erry s margnal rates of substtuton: MRS M where represents each person n socety. Effcency requres MRS M M = M M Optmal Provson of Publc Goods That s socal effcency s maxmzed when the margnal costs are set equal to the sum of the margnal rates of substtuton (rather than each ndvdual s MRS). Ths s because the good s non-rval. Snce a unt can be consumed by all consumers socety would lke the producer to take nto account all consumers preferences. PRIVATE PROVISION OF PUBLI GOODS: Prvate-sector Underprovson In general the prvate sector underprovdes publc goods because of the free rder problem. onsder two people Ben and erry and two consumpton goods ce cream and freworks. Set the prces of each good at $1 but freworks are a publc good. Assume that Ben and erry have dentcal preferences. Prvate-sector Underprovson Ben and erry beneft equally from a frework that s provded by ether of them. What matters s the total amount of freworks. Each person chooses combnatons of ce cream and freworks n whch hs own MRS equals the rato of prce. For both Ben and erry they set: MRS = 1 = FI I F Whereas optmal provson requres: MRS FI = 1 4
5 Prvate-sector Underprovson Wth dentcal preferences the optmal condton s: 2 F = 1 whch mples = F I 2 Recall that margnal utltes dmnsh wth ncreasng consumpton of a good. In ths example optmal provson would requre that freworks are consumed untl ther utlty equals half the margnal utlty of ce cream. Thus each ndvdually buys too much ce cream prvately. I The Free Rder Problem n Practce There are some nterestng examples of the freerder problem n practce. Only 7.5% of publc rado lsteners n New York contrbute to the statons that s there s a lot of freerdng. In the Unted Kngdom the BB charges an annual lcensng fee for all televson owners. Many users of fle sharng servces never contrbute uploaded fles; they only download fles. Some of these servces lke Kazaa gve download prorty to those who contrbute. When Is Prvate Provson Lkely to Overcome the Free Rder Problem? Under what crcumstances are prvate market forces lkely to solve the free rder problem? Intense preferences. Altrusm. Utlty from one s own contrbuton to the publc good. Some ndvduals care more than others When some ndvduals have especally hgh demand for a publc good prvate provson may emerge (but not necessarly provde effcently n partcular the publc good s stll lkely to be underprovded). The key ntuton s that the decson to provde a publc good s a functon of the enjoyment that the ndvdual gets from the total amount of the publc good net of cost. If a person gets a lot of enjoyment or has a lot of money he wll choose to purchase more of the publc good even though t benefts others. 5
6 Altrusm and Warm Glow A second reason s that there s evdence that many ndvduals are altrustc carng about the outcomes of others as well as themselves. A thrd reason s that that ndvduals may provde for a publc good s due to warm glow. The warm glow model s a model of publc good provson n whch ndvduals care about both the total amount of the publc good and ther partcular contrbutons as well. For example they may get some psychologcal beneft from knowng they helped a worthy cause. In ths case the publc good becomes more lke a prvate good though t also does not fully solve the underprovson problems. PUBLI PROVISION OF PUBLI GOODS In prncple the government could solve the optmal publc goods provson problem and then ether provde the good drectly or mandate ndvduals to provde the amount. In practce three problems emerge: rowd-out. Measurng costs and benefts. Determnng the publc s preferences. Prvate Responses to Publc Provson: The Problem of rowd-out In some cases the prvate market may already be provdng a socally neffcent level of the prvate good. In ths case publc provson may crowd-out some of the prvate provson as the government provdes more of the publc good the prvate sector provdes less. Prvate Responses to Publc Provson: The Problem of rowd-out For example n the freworks example wth Ben and erry f one assumes: Ben and erry care only about the total number of freworks provded. Government provson wll be fnanced by chargng equal amounts to each of them. And the government provdes no more freworks than were beng provded prvately beforehand. Then each dollar of publc provson wll crowd out prvate provson one-for-one. 6
7 Prvate Responses to Publc Provson: The Problem of rowd-out The full crowd-out n the freworks example s rare though partal crowd-out s much more common and can occur when: People who don t contrbute to the publc good are taxed to fnance ts provson. Or when ndvduals derve utlty from ther ndvdual contrbutons as well as the total amount of the publc good provded. Prvate Responses to Publc Provson: The Problem of rowd-out If noncontrbutors are forced to help pay for the good (but t s stll below the socal optmum) then the contrbutors effectve ncome levels are hgher than before. As a result of ths ncome effect contrbutors buy more f the publc good s a normal good offsettng the crowd-out to some extent. Prvate Responses to Publc Provson: The Problem of rowd-out Alternatvely as dscussed prevously there may not be full crowd-out f an ndvdual cares about hs own contrbutons (the warm glow model). In ths case an ncrease n government contrbutons wll not fully crowd out gvng. Publc Provson of Publc Goods: Measurng the costs and benefts of publc goods Another problem for government provson s measurng costs and benefts of the publc good. Ths entals the feld of cost-beneft analyss dscussed n the next lesson. For example mprovng a hghway nvolves valuatons of commutng tme saved as well reduced traffc fataltes. 7
8 How an We Measure Preferences for the Publc Good? Fnally our model of optmal publc good provson assumes the government knows each person s preferences over publc and prvate goods. In practce ths runs nto problems wth preference revelaton preference knowledge and preference aggregaton. These ssues are addressed n the feld of poltcal economy. Let me work two problems 8
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