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A Note on ’Emissions Taxation in Durable Goods Oligopoly’

A Note on

’Emissions Taxation in Durable Goods Oligopoly’

Marco Runkel?

Department of Economics,University of Siegen,D-57068Siegen,Germany

email:runkel@wap-server.fb5.uni-siegen.de

Abstract:This note corrects an error in the analysis of Goering/Boyce(1999)and extends their results.In this way,it refutes the claim that the durability of rented products plays a decisive role for the second-best emission taxation under imperfect competition.

1.Introduction

Intuitively,one would expect that the second-best emission tax in an imperfectly com-petitive industry(the tax which maximizes the social welfare provided it is the only instrument available)falls short of the marginal environmental damage(underinternal-ization)since it has to account for two distortion simultaneously:the environmental externality and the market power of the?rms.However,in an interesting recent article Goering/Boyce(1999)(hereafter referred to as G&B)argue this to be not necessarily true in a durable good oligopoly in which the products are rented.They claim that the optimal emission tax exceeds the marginal damage(overinternalization)if a)the demand and the decay functions are linear,b)the emissions depend only on output and c)the production cost function exhibits increasing returns to durability(subsequently, the conditions a-c will be referred to as the GB-case).They explain this result by a third distortion only inherent in durable good markets,namely’...the misallocation due to producers choosing a durability which does not minimize the social cost of pro-viding a given service level.’(G&B,p.136)In their view,an increase in the emission tax has the additional bene?t of moving the?rms closer to the socially optimal durability, and consequently overinternalization may be welfare enhancing.

A closer look at previous results of the durability literature,however,raises doubt whether the reasoning of G&

B is correct:Under laissez-faire in a renting durable ?I would like to thank R¨u diger Pethig and Thomas Eichner for helpful comments.All remaining errors are my own responsibility.Support from the German Research Foundation(DFG)is gratefully acknowledged.04/10/1999

2M.Runkel

good industry without pollution,the product durability is independent of the market structure owing to Swan’s independence result(Swan(1970))and thus it is socially optimal not only under perfect competition but also under oligopoly(Goering(1992)). Hence,the misallocation of durability under laissez-faire in the renting durable good oligopoly with pollution can only rest on the environmental externality and doesn’t rep-resent a separate distortion.This implies that there are only the two above-mentioned distortions at work and that intuitively the second-best emission tax falls short of the marginal damage:If the emissions are taxed with a rate equal to the marginal damage then the?rst distortion,namely the environmental externality together with the misallocation of durability,is fully corrected whereas the second distortion,namely the market power of the?rms,tends to restrict the output and the stock of the durable below their socially optimal levels.According to the usual second-best argument,soci-ety can gain from lowering the emission tax since this reduction shifts the output and the stock closer to their e?cient levels.Thus the second-best tax underinternalizes the marginal damage.1

The present note supports this conclusion by identifying an error in the analysis of G&B.More speci?cly,their proof of overinternalization is incorrect since in the GB-case the individual?rm’s pro?t doesn’t attain a maximum owing to a non-concave pro?t function.As a consequence,in the GB-case there is no industry equilibrium and no second-best emission tax.Furthermore,it is shown that in the case of general demand, cost,emissions and decay functions the second-best tax turns out to be smaller than the marginal damage so long as the objective function of the individual?rm is concave and the emission function satis?es a mildly restrictive condition.This result turns out to be in line with previous results on nondurable goods.Hence,the claim of G&B that the durability of rented products plays a decisive role for the second-best emission taxation under imperfect competition is refuted.

2.The Analysis of G&B

For a renting durable good industry with n?rms G&B seek to determine the emission tax w which maximizes the long-run social welfare,i.e.which solves the problem

max w V(w):=

nˉQ(w)

f(g)dg?nc[ˉδ(w)]ˉq(w)?E[nε(ˉδ(w),ˉq(w))].(1)

1For a formal proof of these assertions see Runkel(1999)who employs a two-period model in which the durable causes pollution by the solid waste at the end of its life.

A Note on ’Emissions Taxation in Durable Goods Oligopoly’3

ˉδ,ˉq and ˉQ

denote the long-run equilibrium values for the individual ?rm’s product durability,output level and stock of the durable good,respectively.f is the demand

function satisfying f <0and f +ˉQf

<0.The unit production costs are c (δ)with c >0.ε(δ,q )with εq ,εqq >0and εδ≥0represents the ?rm’s emission function and E is the industry emission damage.Without loss of generality the marginal damage is normalized to unity,i.e.E (nε):=nεwith E =1.The ?rst-order condition for the welfare maximum reads

V =0and hence f d ˉQ dw ?(ˉq c +εδ)d ˉδdw ?(c +εq )d ˉq dw =0(2)

where it has been taken into account that ˉδ,ˉq and ˉQ

are functions of the emission tax w owing to the industry equilibrium conditions.

To derive these equilibrium conditions,a noncooperative integral game is used:Firm i chooses the time path for durability δi (t )and output q i (t ),t [τ,∞[,in order to maximize the present value of its rental pro?t

Πi = ∞τ f [Q i (t )+Q ?i (t )]Q i (t )?c [δi (t )]q i (t )?wε[δi (t ),q i (t )] e ?r (t ?τ)dt

s.t.Q j (t )=

t ?∞φ[t ?s,δj (s )]q j (s )ds,j =1,...,n (3)with Q ?i :=

j =i Q j .φwith φt ?s <0and φδ>0represents the decay function of

the durable good.Under an open-loop information structure,?rm i takes as given Q j ,j =i ,and hence the associated Hamiltonian is de?ned as 2

H [q i (t ),δi (t ),Q i (t ),μi (s ≥t )]:= ∞

t φ[s ?t,δi (t )]q i (t )μi (s )ds

+ f [Q i (t )+Q ?i (t )]Q i (t )?c [δi (t )]q i (t )?wε[δi (t ),q i (t )] e ?r (t ?τ)(4)

where the co-state μi >0may be interpreted as shadow price of ?rm i ’s stock Q i (see Kamien/Muller (1976)).Marking the pro?t-maximizing values by a superscript ’o ’and applying the maximum principle of Bakke (1974),the necessary conditions for a pro?t maximum of ?rm i reads

H Q i (t )= f [Q o i (t )+Q ?i (t )]+Q o i (t )f [Q o i (t )+Q ?i (t )] e ?r (t ?τ)=μi (t ),

(5)[q o i (t ),δo i (t )]=arg max q i (t ),δi (t )H [q i (t ),δi (t ),Q o i (t ),μi (s ≥t )],(6)

2The Hamiltonian in the anlysis of G&B also contains the restrictions for Q j ,j =i ,but under open-loop strategies the Hamiltonian (4)yields exactly the same results.

4M.Runkel

for all t [τ,∞[.In order to characterize the solution to(6),G&B use the?rst-order conditions(see also Kamien/Muller(1976))

H q

i(t)=Hδ

i(t)

=0,?t [τ,∞[.(6a)

In the symmetric long-run equilibrium,i.e.x o i(t)=x o(t)=ˉx for all i,t and x {Q,q,δ}, eqs.(5)and(6a)become

[f(nˉQ)+ˉQf (nˉQ)]ρ(ˉδ)?c(ˉδ)?wεq(ˉδ,ˉq)=0,(7)

[f(nˉQ)+ˉQf (nˉQ)]ρ (ˉδ)ˉq?c (ˉδ)ˉq?wεδ(ˉδ,ˉq)=0,(8)

withˉQ=ρ(ˉδ)ˉq from(3)andρ(ˉδ):= ∞

t

φ(s?t,ˉδ)e?r(s?t)ds.3(7)and(8)together

withˉQ=ρ(ˉδ)ˉq determine a long-run industry equilibrium which depends on the level of the emission tax w.

Now,G&B proceed as follows.They insert dˉQ/dw=ρ ˉq dˉδ/dw+ρdˉq/dw,(7)and (8)into(2).Solving the resulting expression with respect to w yields

w?=1+ˉQf ·

ρ ˉq

dˉδ

dw

dˉq

dw

εδ

dˉδ

dw

+εq

dˉq

dw

.(9)

as second-best emission tax.Totally di?erentiating(7),(8)andˉQ=ρ(ˉδ)ˉq yields dˉq/dw and dˉδ/dw.By inserting these derivatives into(9)G&B obtain the overinternalization result for the GB-case,i.e.the second-best tax exceeds the marginal damage(w?>1) if the demand and the decay functions are linear(f =φδδ=ρ =0),if the emissions depend only on output(εδ=0)and if the production costs exhibits increasing returns to durability(c <0)(see their proposition5).This conclusion will now be shown to be incorrect.

3.Erratum and Further Results

The error made by G&B is that they don’t realize the Hamiltonian(4)to be not concave in[q i(t),δi(t)]if f =φδδ=εδ=0and c <0:(4)is globally concave

in[q i(t),δi(t)]if its Jacobian is negative de?nite,i.e.if H q

i(t)q i(t),Hδ

i(t)δi(t)

<0and

H q

i(t)q i(t)Hδ

i(t)δi(t)

?H2q

i(t)δi(t)

>0or,respectively,

wεqq>0,(10)

3Actually,the correct expression isˉQ=ˉq ∞

t

φ(s?t,ˉδ)ds.But to obtain the correct derivatives

ofˉQ,the expressionˉQ=ρ(ˉδ)ˉq must be used.See fn.13in G&B.

A Note on ’Emissions Taxation in Durable Goods Oligopoly’5

c q i (t )+wεδδ?q i (t )

∞t φδδ[s ?t,δi (t )]e r (t ?τ)μi (s )ds >0,

(11)wεqq c q i (t )+wεδδ?q i (t ) ∞

t φδδ[s ?t,δi (t )]e r (t ?τ)μi (s )ds

? c +wεδq ? ∞t φδ[s ?t,δi (t )]e r (t ?τ)μi (s )ds 2>0.

(12)

For εδ=0we obtain εδδ=0which together with φδδ=0simpli?es the condition (11)to c q i (t )>0.Obviously,for c <0this condition is violated with the consequence that in the GB-case the Hamiltonian is globally concave in q i (t )but is globally convex in δi (t ).These properties of H in turn imply that in the GB-case the second-order conditions for the maximization problem (6)are not satis?ed.Hence,in the GB-case the ?rst-order conditions (6a)don’t characterize the solution to (6)and therefore G&B are not entitled to use (7)and (8)as long-run equilibrium conditions in order to determine d ˉQ/dw ,d ˉq /dw and d ˉδ/dw .Thus,(9)doesn’t represent the second-best tax in the GB-case and G&B’s proof of overinternalization fails to be correct.

This conclusion gives rise to the question how to determine the second-best tax in the GB-case.If there is no upper bound to durability 4then we obtain

PROPOSITION 1.Suppose there is no upper bound to durability,i.e.δi (t ) [δmin ,∞[with δmin >?∞for all t [τ,∞[.Then in the GB-case there doesn’t exist a second-best emission tax at all.

Proof:In the GB-case the condition H δi (t )=0simpli?es to c [δi (t )]= ∞

t ˉφ

δ[s ?t ]e r (t ?τ)μi (s )ds >0with ˉφδ[s ?t ]:=φδ[s ?t,δi (t )].The RHS of this equation is independent of δi (t )and hence the equation has exactly one solution for δi (t )due to the monotony of c .Consequently,this together with the global convexity of H with respect to δi (t )implies that for any given q i (t )the Hamiltonian is U-shaped with respect to δi (t ).Hence,in the GB-case there doesn’t exist a [q i (t ),δi (t )]which solves (6)since H can always be increased by increasing δi (t )owing to δi (t ) [δmin ,∞[.Because (6)is a necessary condition for the solution of (3)there doesn’t exist a pro?t maximum of the individual ?rm,neither a short-run nor a long-run industry equilibrium,no welfare function such as (1)and consequently no second-best tax.(Q.E.D.)

Owing to the nonexistence of the second-best emission tax proven in proposition 1it is impossible to say anything about the size of this tax rate,and hence G&B are wrong in claiming overinternalization to be second-best optimal in the GB-case.4For example,the exponential decay function φ[a,δi ]=e ?a/δi typically requires 1/δi [0,1]or,equivalently,δi [1,∞[.If δi represents the life-time of the product then δi [0,∞[.

6M.Runkel

Of course,the nonexistence of the industry equilibrium may be avoided by assuming the set of admissible values for durability to be compact,i.e.δi(t) [δmin,δmax]with ?∞<δmin<δmax<∞:For any given w the pro?t maximum of?rm i in the GB-case is then described by(5),H q

=0and a corner solution forδi(t),namely

i(t)

δi(t)=δmin orδi(t)=δmax depending on the relative size of H at these boundaries. The symmetric long-run industry equilibrium is then determined by(7),ˉQ=ρ(ˉδ)ˉq and ˉδequal toδmin orδmax.However,beside the somewhat ad hoc nature of the assumption δi(t) [δmin,δmax]there may arise an other technical problem:A marginal change in w may alter the relative size of H at the boundariesδi(t)=δmin andδi(t)=δmax and hence it may switch the equilibrium durability fromδmin toδmax or vice versa. Consequently,ˉδ(w),ˉq(w),ˉQ(w)and V(w)in(1)are discontinuous functions and the marginal analysis used in(2)may fail.5

To obtain more speci?c results,let us return to the question which G&B actually intended to answer:Their major aim is to compare the second-best emission tax in a renting durable good industry with that in a nondurable good industry previously investigated by e.g.Barnett(1980)or Ebert(1992).The latter authors,however, consider the case of general demand,cost and emission functions and assume a concave objective function of the individual?rm as well as an interior solution for all variables.

A suitable comparison thus requires to suppose analogous conditions for the durable good industry.Unfortunately,G&

B only consider the GB-case and don’t explictly in-vestigate second-best taxation in the case of general functions in which the Hamiltonian is concave and in which there is an interior solution.This gap is closed by

PROPOSITION2.Suppose H is globally concave in[q i(t),δi(t)],the maximization problem(6)has an interior solution for all t [τ,∞[and the emission function satis?es εδ/ˉq?εδq≥0.Then w?<1.

Proof:If H in(4)is globally concave in[q i(t),δi(t)]and if there is an interior solution to the maximization of H then the?rst-order conditions(6a)are suitable to characterize the solution to(6).Consequently,(7),(8)andˉQ=ρ(ˉδ)ˉq describe the long-run industry equilibrium and(9)represents the correct expression for the second-best emission tax. Hence,it remains to determine dˉq/dw and dˉδ/dw.First,note that in the long-run 5It is interesting to note that if a variation in w doesn’t change the relative size of H at its boundaries then dˉδ/dw=https://www.doczj.com/doc/8415981432.html,ing(7)andˉQ=ρ(ˉδ)ˉq in(2)then yields w?=1+ˉQf ρ/εq<1.This would refute the overinternalization result of G&B in the GB-case.As mentioned in the text,however, a jump in equilibrium durability can’t be ruled out,in general.

A Note on’Emissions Taxation in Durable Goods Oligopoly’7 equilibrium the concavity conditions(10)to(12)become

wεqq>0,c ˉq+wεδδ?ρ ˉq(f+ˉQf )>0,(13) wεqq[c ˉq+wεδδ?ρ ˉq(f+ˉQf )]?w2[εδ/ˉq?εδq]2>0,(14)

where(5)and(8)are employed.Totally di?erentiating(7),(8)andˉQ=ρ(ˉδ)ˉq and applying Cramer’s rule yields

dˉq dw =

1

|J|

[(n+1)f +nˉQf ][ρ 2ˉq2εq?ρρ ˉqεδ]

?εq[c ˉq+wεδδ?ρ ˉq(f+ˉQf )]?wεδ(εδ/ˉq?εδq)

,(15)

dˉδdw =

[(n+1)f +nˉQf ][ρ2εδ?ρρ ˉqεq]?wεδεqq?wεq(εδ/ˉq?εδq)

|J|,(16)

where the Jacobian determinant|J|is positive as is easily shown by employingεδ/ˉq?εδq≥0,(13)and(14).The size of the second-best emission tax is determined by inserting(15)and(16)in(9).After some tedious computations the two bracket terms in(9)become,respectively,

ρ ˉq dˉδ

dw

dˉq

dw

=?

1

|J|

ρεq[c ˉq+wεδδ?ρ ˉq(f+ˉQf )]+wρ ˉqεδεqq

+w(ρ ˉqεq+ρεδ)(εδ/ˉq?εδq)

<0,(17)

εδdˉδ

dw

+εq

dˉq

dw

=

1

|J|

[(n+1)f +nˉQf ][ρεδ?ρ ˉqεq]2?wε2δεqq

?2wεδεq(εδ/ˉq?εδq)?ε2q[c ˉq+wεδδ?ρ ˉq(f+ˉQf )]

<0.(18)

The signs of these expressions are obtained from|J|>0,(13)andεδ/ˉq?εδq≥https://www.doczj.com/doc/8415981432.html,ing (17),(18)and f <0in(9)proves w?<1.(Q.E.D.)

Proposition2shows that the conditions which render the second-best emission tax in the renting durable good industry smaller than the marginal damage are not very restrictive:Firstly,a concave objective function and an interior solution are typically assumed in all economic models which don’t explicitly focus on corner solutions or existence problems.Especially,they are used in the second-best taxation models sug-gested by Barnett(1980)or Ebert(1992)which serve as a standard of comparision for the present durable good model.Secondly,the conditionεδ/ˉq?εδq≥0is satis?ed by all separable emission functions(εδq=0)and by all those non-separable emission functions for which an increase in the output reduces the marginal damage of dura-bility(εδq<0)or increases the marginal damage of durability only relative slightly

8M.Runkel

(εδq≤εδ/ˉq).6Furthermore,note that the conditions for w?<1listed in proposition 2are su?cient.Hence,the second-best tax may be smaller than the marginal damage even ifεδ/ˉq?εδq<0.

Certainly,in case ofεδ/ˉq?εδq<0it can’t be ruled out that the second-best emission tax is greater than the marginal damage(w?>1).However,this case of overinternalization,if it exists,has counterintuitive implications:w?>1implies that one and only one of the two bracket terms in(9)has to be positive.However,the second bracket term equals the change of the?rm’s equilibrium emission due to a marginal change in the emission tax,dˉε/dw,and obviously there is a strong plausibility for this change to be negative.If the change in emission is negative then w?>1requires the ?rst bracket term in(9)to be positive.However,intuitively this term is also expected to be negative since it equals the change in the?rm’s equilibrium stock of the durable due to a marginal change in the emission tax,dˉQ/dw.Furthermore,the?rst bracket term to be positive implies that at least one of the equilibrium values,either that of durability or that of output,increases as the emission tax increases.This implication is counterintuitive since both variables are positively correlated with the?rm’s emission which in this scenario decreases.

Of course,plausibility arguments of this type are no good substitute for hard em-pirical evidence.Hence,although G&B are mistaken in the GB-case(which is their exclusive focus)they actually are correct in pointing out that overinternalization can’t be ruled out to be second-best optimal in a renting durable good industry,in general. Owing to proposition2a necessary condition for w?>1isεδq>0.However,this observation is not really a new insight since in a similar way it is already derived by Barnett(1980)and Ebert(1992)for nondurable goods:In a nondurable good model these authors assume cost and emission functions similar to those used in our model, namely C(δ,q)andε(δ,q)with Cδ>0butεδ<0sinceδis interpreted not as product durability but as pollution abatement e?ort of the individual?rm.In their model a necessary condition for overinternalization is Cδq+wεδq<0(see Barnett(1980),fn. 6,Ebert(1992),eq.(15))which in turn impliesεδq<0if constant returns to scale (i.e.C(δ,q)=c(δ)q and Cδq=c (δ)>0)are assumed,as in the present durable good model.Since the sign ofεδis reversed this necessary condition is analogous toεδq>0 in the durable good model.

6For example,ε(δ,q)=G(q)+(αq+β)δwithα,β,G ,G >0seems to be a reasonable emission function since a marginal increase in durability causes pollution by additional resources needed to make one unit of the good more durable(α)and by additional resources needed for R&D(β).For this function we obtainεδq=α>0butεδ/ˉq?εδq=β/ˉq>0.

A Note on’Emissions Taxation in Durable Goods Oligopoly’9

To sum up,the possibility of overinternalization to be second-best optimal in a renting durable good industry cannot be excluded,in general.If it occurs at all, however,overinternalization a)has counterintuitive implications,b)is not really a new insight but already derived in similar form by Barnett(1980)and Ebert(1992) for nondurable goods and thus c)is not due to a’third distortion’inherent in rental markets for durable goods but is due only to the special form of the emission function.

4.Concluding Remark

In contrast to the argumentation of G&B,the results of the present note deny a decisive role of the durability of rented products in the second-best emission taxation under imperfect competition.It should be also noted,however,that this?nding does not carry over to product durability in sales markets:As Bulow’s(1986)analysis of planned obsolescence shows there really is a misallocation of durability in sales markets even in the absence of environmental externalities.This distortion may render the second-best emission tax greater than the marginal environmental damage(see Runkel(1999)).

References

Barnett,A.H.(1980),’The Pigouvian Tax Rule under Monopoly’,American Economic Review70, 1037-41

Bakke,V.L.(1974),’A Maximum Principle for an Optimal Control Problem with Integral Constraints’, Journal of Optimization Theory and Application14,32-55

Bulow,J.(1986),’An Economic Theory of Planned Obsolescence’,Quarterly Journal of Economics 101,729-49

Ebert,U.(1992),’Pigouvian Tax and Market Structure:The Case of Oligopoly and Di?erent Abatement Technologies’,Finanzarchiv N.F.49,154-66

Goering,G.E.(1992),’Oligopolies and Product Durability’,International Journal of Industrial Organization10,55-63

Goering,G.E.and J.R.Boyce(1999),’Emissions Taxation in Durable Goods Oligopoly’,Journal of Industrial Economics47,125-43

Kamien,M.I.and E.Muller(1976),’Optimal Control with Integral State Equations’,Review of Economic Studies43,469-73

Runkel,M.(1999),’First-Best and Second-Best Regulation of Solid Waste under Imperfect Competi-tion in a Durable good Industry’,Discussion Paper81-99,University of Siegen

Swan,P.L.(1970),’Durability of Consumption Goods’,American Economic Review60,884-94

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介词(The Preposition)又叫做前置词,通常置于名词之前。它是一种虚词,不需要重读,在句中不单独作任何句子成分,只表示其后的名词或相当于名词的词语与其他句子成分的关系。中国学生在使用英语进行书面或口头表达时,往往会出现遗漏介词或误用介词的错误,因此各类考试语法的结构部分均有这方面的测试内容。 1. 介词的种类 英语中最常用的介词,按照不同的分类标准可分为以下几类: (1). 简单介词、复合介词和短语介词 ①.简单介词是指单一介词。如: at , in ,of ,by , about , for, from , except , since, near, with 等。②. 复合介词是指由两个简单介词组成的介词。如: Inside, outside , onto, into , throughout, without , as to as for , unpon, except for 等。 ③. 短语介词是指由短语构成的介词。如: In front of , by means o f, on behalf of, in spite of , by way of , in favor of , in regard to 等。 (2). 按词义分类 {1} 表地点(包括动向)的介词。如: About ,above, across, after, along , among, around , at, before, behind, below, beneath, beside, between , beyond ,by, down, from, in, into , near, off, on, over, through, throught, to, towards,, under, up, unpon, with, within , without 等。 {2} 表时间的介词。如: About, after, around , as , at, before , behind , between , by, during, for, from, in, into, of, on, over, past, since, through, throughout, till(until) , to, towards , within 等。 {3} 表除去的介词。如: beside , but, except等。 {4} 表比较的介词。如: As, like, above, over等。 {5} 表反对的介词。如: againt ,with 等。 {6} 表原因、目的的介词。如: for, with, from 等。 {7} 表结果的介词。如: to, with , without 等。 {8} 表手段、方式的介词。如: by, in ,with 等。 {9} 表所属的介词。如: of , with 等。 {10} 表条件的介词。如:

表示地点的介词

表示地点的介词 in、on、behind、next to、near、over、under (1) in在……里面:The pencil is in the desk. 铅笔在课桌里。 (2) on在……上面:There are some apple on the tree. 树上有些苹果。 (3) under在……下面/正下方:What's under your desk? 你书桌底下是什么? (4) over在……正上方:There is a shelf over the table. 桌子上方有一个书架。 (5) above 在……斜上方:Raise your arms above your head. (6) below 在……斜下方:Her skirt came below her knees. (7) behind在……之后:There is a bike behind the tree. 树后有一辆自行车。 (8) next to在……旁边:There is a shop next to the school. 理发店隔壁是一家咖啡馆。 (9) near在……附近:My bed is near the window. 我的床在窗户旁。 (10) by在……旁:He was sitting by the window. (11) beside 在旁边He sits down beside Jim. 一组:over, above和on的用法 1) over指在…的正上方,表示垂直在上。如 There is a lamp over the desk. 2) above指在上方,属于斜上方。如: Raise your arms above your head. 3) on指在上面,表示两物体接触。如: There is a cup on the table. 二组:under / below的用法: 1) under在……下面/正下方: What's under your desk? 2) below 在……斜下方: Her skirt came below her knees 三组:in 和on表示“在……上” 1)门/窗一类——镶嵌在墙里的,用in; 2)字画一类——挂/贴在墙面上的,用on ( ) 1 He put up a map ___ the back wall because there was a hole ______ it. A. on; on B. at; in C. on; in D. on; at ( ) 2 There is a door___ the wall. A. on B. to C. of D.in 3)人/鸟其他东西在树上,用in; 4)枝叶果实长在树上的,用on ( ) 1 There are some birds singing___ the trees. A. in B. on C. at D. from ( ) 2 There are so many apples___ that tree. A.in B, on C of D.from

浅析《诗经》中的方位词“南”及其文化内涵

龙源期刊网 https://www.doczj.com/doc/8415981432.html, 浅析《诗经》中的方位词“南”及其文化内涵作者:王春艳 来源:《汉字文化(教育科研卷)》2018年第07期 【提要】本文就《诗经》中出现频率较多的方位词“南”进行辨析,并对具有代表性的“南方”“南亩”“南山”进行具体分析,由此我们可知“南”这一方位词,有着温暖和煦、丰年祈福之愿,有着少妇思君、忧心忡忡之情。随着对“南”与长养、情思、尊愿等方面的分析,可见方位词“南”的文化内涵不断深化并影响深远。通过对方位词“南”的探析,我们可以加深对《诗经》的认识,从而揭开遥远先秦的神秘面纱。 【关键词】诗经方位词“南” 文化内涵 《诗经》作为先秦人民真实的生活写照,其所包含的先民思想、风俗习惯、地理方位等都是我们了解先秦人民生活风貌的重要载体。关于《诗经》中方位词“南”,此前已有学者对此进行研究,譬如张德鑫的《方位词的文化考察》,方经民的《汉语空间方位参照的认知结构经过统计》,金安辉的《诗经》中的“东、西、南、北”及其对后世诗歌的影响等,笔者在前人研究的基础上,旨在更加具体、深刻地分析方位词“南”及其文化内涵。据统计,《诗经》中“南”出现了81次,那么《诗经》中的“南”是仅指方向的方位词呢,还是有着特殊的文化内涵?文化内涵也可以说是文化义,周一农的《词汇的文化蕴涵》中指出“文化义,指的是词在特定文化背景下所获得的反映一个名族风俗习惯、文化背景、宗教信仰和思维方式等诸多文化因素的隐含义”。①因此方位词的文化内涵就是对这些文化因素的分析。下面我们将对《诗经》中的方位词“南”进行逐步探讨,从而还其完整面貌。 一、“南”与长养 万事万物皆有源头,那么方位词源于何处?先秦人民不像现代人一样可以用多种方式指认方向,他们最先感受到的是自身和空间的环境关系,“日出而作,日落而归”,四方就是根据太阳这一参照物来确定的。即太阳升起处定为东方,落下处定为西方,直照处定为南方,背阳处定为北方。这就是人们对方位最初的认识。而我们现在所说的方位词,更加术语化,其实还是指东、西、南、北等。 经统计,我们发现《诗经》中“南”多有表示南方的意思,《说文解字》:“南,木至南方而有枝任也”,即南方是夏天草木繁盛的象征。《诗经》中《周南·樛木》“南有樛木,葛藟累之”;《周南·漢广》“南有乔木,不可休思”;《召南·草虫》“陟彼南山,言采其蕨”这些例子不仅表明这些草木生长在南方,也进一步表明了南方的“樛木”“乔木”“蕨”是何其丰茂,这正如《白虎通·五行》中“南方主长养”的说法,又《黄帝内经·素问·异法方宜论》:“南方,天地所长养,阳之所盛处也”,所以南方是温暖和煦的,也是植物生长的好地方,是生命的象征。

初中英语考点 in_on_at_区别用法

in on at 区别用法 妙计口诀 1.早、午、晚要用in, at黎明、午夜、点与分。 年、月、年月、季节、周, 阳光、灯、影、衣、帽用in。 将来时态in...以后, 小处at大处in。 有形with无形by, 语言、单位、材料in。 特征、方面与方式, 心情成语惯用in。 介词at和to表方向, 攻击、位置、恶、善分。 2.日子、日期、年月日,星期加上早、午、晚, 收音、农场、值日on,关于、基础、靠、著论。 着、罢、出售、偷、公、假,故意、支付、相反,准。 特定时日和“一……就”,on后常接动名词。 年、月、日加早、午、晚,of之前on代in。 步行、驴、马、玩笑on,cab,carriage则用in。 at山脚、门口、在当前,速、温、日落、价、核心。 如大体掌握上面介词用法口诀,就不易出错。下面对该口诀分别举例帮助你理解消化。 <1.>关于时间 早、午、晚要用in in the evening 在晚上 in the day 在白天 例: in the afternoon 在下午 in the morning 在早上 at黎明、午、夜、点与分 例 at dawn /at daybreak 在黎明时候 at night 在夜间 at noon 在中午 at midnight 在午夜 (以上短语都不用冠词)

at nine o'clock 在9点钟 at half past ten 在10点半 at ten thirty a.m. 在上午10点30分 at the weekend 在周末 at a quarter to two 1点45分 <2.>关于年、月、年月、季节、周 即在“来年”,在“某月”,在“某年某月” 但在某年某月某日则用on ,在四季,在第几周等都要用in。 in 1927 在1927年 in March 在三月 in December 1986 在1986年12月 in July l984 在1984年7月 in the first week of this semester这学期的第一周 in the third week 在第三周 in spring 在春季 <3.>关于日子、日期、年月日,星期加上早午晚 以下皆用on on October the first 1949 1949年10月1日 on May the first 5月1日 on the sixteenth 16号 on the second of January /on January the second 1月2日 on a summer evening 在夏天的一个夜晚 on New Year's Day 在元旦 on my birthday 在我的生日 on winter day 在冬天 on December 12th 1950 l950年12月12日 on Sunday 在星期天 on Tuesday morning 星期二早晨 但last night 昨夜;in the evening 在晚上 on time准时,in time及时,等则不同。 【注】in the Christmas holidays在圣诞节假期 in the eighteenth century 在十八世纪 in ancient times 在古代 in earlier times 在早期 in modern times 在现代,则用in,at the present time 现在,at the present day当今则用at。 <4.>关于年月日,加早午晚,of之前on代in on the morning of 18th 18日早晨 On the eve of their departure在临行前夕 <5.>阳光、灯、影、衣、冒 in

介词in,on.at,for.with,by,of的基本用法

介词用法知多少 介词是英语中最活跃的词类之一。同一个汉语词汇在英语中可译成不同的英语介词。例如汉语中的“用”可译成:(1)用英语(in English);(2)用小刀(with a knife);(3)用手工(by hand);(4)用墨水(in ink)等。所以,千万不要以为记住介词的一两种意思就掌握了这个介词的用法,其实介词的用法非常广泛,搭配能力很强,越是常用的介词,其含义越多。下面就简单介绍几组近义介词的用法及其搭配方法。 一. in, to, on和off在方位名词前的区别 1. in表示A地在B地范围之内。如: Taiwan is in the southeast of China. 2. to表示A地在B地范围之外,即二者之间有距离间隔。如: Japan lies to the east of China. 3. on表示A地与B地接壤、毗邻。如: North Korea is on the east of China. 4. off表示“离……一些距离或离……不远的海上”。如: They arrived at a house off the main road. New Zealand lies off the eastern coast of Australia. 二. at, in, on, by和through在表示时间上的区别 1. at指时间表示: (1)时间的一点、时刻等。如: They came home at sunrise (at noon, at midnight, at ten o’clock, at daybreak, at dawn). (2)较短暂的一段时间。可指某个节日或被认为是一年中标志大事的日子。如: He went home at Christmas (at New Year, at the Spring Festival, at night). 2. in指时间表示: (1)在某个较长的时间(如世纪、朝代、年、月、季节以及泛指的上午、下午或傍晚等)内。如: in 2004, in March, in spring, in the morning, in the evening, etc (2)在一段时间之后。一般情况下,用于将来时,谓语动词为瞬间动词,意为“在……以后”。如: He will arrive in two hours. 谓语动词为延续性动词时,in意为“在……以内”。如: These products will be produced in a month. 注意:after用于将来时间也指一段时间之后,但其后的时间是“一点”,而不是“一段”。如: He will arrive after two o’clock. 3. on指时间表示: (1)具体的时日和一个特定的时间,如某日、某节日、星期几等。如: On Christmas Day(On May 4th), there will be a celebration. (2)在某个特定的早晨、下午或晚上。如: He arrived at 10 o’clock on the night of the 5th. (3)准时,按时。如: If the train should be on time, I should reach home before dark. 4. by指时间表示: (1)不迟于,在(某时)前。如:

介词的用法

(一)介词概述 介词是一种虚词,在句子中不单独作任何句子成分。它是一种表示名词和句中其他词之间关系的词。它常和名词、动词、形容词等搭配,构成固定短语,表示不同意思。介词还可以与名词构成介词短语,表示方位、方向、时间、地点、方式、原因等。这些介词短语在句中可充当定语、状语、补语等。2000—2005年的中考中主要考了形容词与介词的搭配:如:be famous for;表示时间的介词,如:at night;动词与介词的搭配,如:arrive in/have dinner with sb.;表示方式、手段的介词,如:by phone/in English. (二)基础知识梳理 1.名词与介词的搭配 a bit of有一点儿 a couple of两个、几个 a kind of一种、一类cover an area of占地面积 have pity on sb.怜悯某人huge amounts of大量的 make friends with与……交朋友make fun of拿……开玩笑 meet the needs of迎合……的需要one after another一个接一个;连续地 play a trick on捉弄the week after next下下周 2.动词与介词的搭配 agree with sb.同意某人的意见apologize to sb. for sth.为某事向某人道歉arrive at/in a place到达某地ask for请求、寻求 be covered with被……所覆盖be made of由……制成 be made up of由……组成belong to属于 break into破门而人、闯入 call on拜访 care for照顾、喜欢carry out执行 check in办理登机come across被理解;遇见 come from出生于、来自come on跟我来、走吧

地点和位置的介词

表示地点和位置的介词 1.at, in, on 1) at 表示较狭窄较小的地方(小村庄,小城镇),in 表示较大的地方(大城市,大的空间)。 I met her at the bus-stop. They arrived at the famous town in South Jiangsu. She is living in Nanjing. There are a great many islands in the Pacific. 2) 门牌号码前用at,road前面用on,street前用in或on。 in the street (BrE) on the street (AmE) at 103 Wall Street on the road 3) 把某个机构看成是机关或组织时用at,看成一个具体的地方时用in She is at Oxford. 她在牛津读书。She is in Oxford 她在牛津居住(工作或逗留) 4)at可以表示有意、有目的的行为。 She is at the table. 她在吃饭She is beside/ by the desk. 她坐在桌旁。 5) on 在---上面,表示上下两者紧贴在一起,in 表示在---里面。 She put the book on the desk. She put the book in the desk. She wore a smile on her face. (面部表情) She was wounded in the face. (伤有深度) 2.on 和underneath underneath 是on的反义词,表示某物紧贴在另一物的底下 There is a piece of paper underneath the dictionary. 3.under 和over under 和over 是一对反义词,表示正上方,正下方,没有接触的含义。 There are some chairs under the tree. The lamp hung over the table. under 和over 还可以表示上级、下级。 He is over us= We are under him. 4. above 和below 两者是一对反义词,表示高于、低于,既不表示接触,也不表示上下垂直。 The plane is flying above us. The sun has sunk below the horizon. 5. beneath 可以和underneath, under, below 互换。 6.at, by, beside at 表示有目的的接近、接触,by和beside 表示偶然的接近,不接触。 She will be waiting for you at the school gate at 7 tomorrow. The girl stood by/ beside her mother. To those who stand by me, I shall stand by my promise. 对那些支持我的人,我将恪守诺言。 7.near 和next to Near 表示在---附近,靠近;next to 表示紧挨着,紧靠着。 No birds or animals came near the lake. She went and sat next to him. 8. before, in front of, at the front of, ahead of before 用于某人前;in front of 用于建筑物前;in front of 和ahead of 用于空间可互换,用于时间只能用ahead of;in the front of 表示内部空间的前部;at the front of 表示外部空间

at,in与on的用法区别

at, in与on的用法区别 1. 表示时间,注意以下用法: ①表示时间的某一点、某一时刻或年龄等用at: I get up at six in the morning. 我早上六点钟起床。 He got married at the age of 25. 他25 岁结婚。 ②泛指一般意义的上午、下午或晚上以及月或年等较长的时间,一般用in:We watch TV in the evening. 我们晚上看电视。 He went to Japan in 1946. 他于1946 去了日本。 ③若表示星期几或某一特定的日期,则用on: He left here on the fifth of May. 他于5 月5 日离开这儿。 2. 表示地点、场所、位置等,注意以下用法: ①表示某一点位置,用at: We live at No 87 Beijing Road. 我们住在北京路87 号。 The hospital is at the end of the street. 医院在这条街的尽头。 与名词所有格连用表示地点,也用at。如: at my sister’s 在我姐姐家 at the doctor’s 在医务室 ②表示空间或范围,用in: What’s in the box? 这盒子里有什么? He lives in Paris with his wife. 他同他妻子住在巴黎。 但有时两者可换用:

The meeting was held at [in] the hotel. 会议在宾馆举行。 ③at与in的另一个区别是:at多用于指较小的地方,而in多用于指较大的地方:in Shanghai 在上海at the station 在车站 ④介词on 用于地点,主要指在某物的表面: What’s on the table? 桌上有什么? There’s a wallet lying on the ground. 地上有个钱包。 【注】在少数搭配中,也用介词on: He works on a farm. 他在农场工作。 3. 在某些搭配中,三者的区别与英国英语和美国英语有关: in the street (英) / on the street (美) 在街上 in the road (英) / on the road (美) 在路上 in the team (英) / on the team (美) 在这个队 at the weekend (英) / on the weekend (美) 在周末 at weekends (英) / on weekends (美) 在周末 4. 有时三者的差别与搭配习惯和用法有关: in bed / on the bed 在床上 in the tree (多指树外之物) / on the tree (多指树本身之物) 在树上

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