2. equlibrium and efficiency (均衡と効率性) - waseda ...2.1 introduction competition and...
Post on 27-Jan-2021
0 Views
Preview:
TRANSCRIPT
-
2. Equlibrium and Efficiency (均衡と効率性)
1
-
2.1 Introduction
competition and efficiency(競争と効率性) Smith’s invisible hand model of competitive economy(競争経済)
combine independent decision-making of consumers and firms into a complete model of the economy
existence of competitive equilibrium competitive equilibrium(競争均衡)=efficient coordinating role played by prices
2
-
2.2 Economic Models Why employ models to make predictions?
experiments(実験) --> difficult economic system is too large and too complex formal model = logical consistency(論理的整合性)
Many different models partial or general (部分と一般) trade-off between specified and general
3
-
2.3 Competitive Economies
competitive(競争的) individual agents do not consider their actions to
have any effect on prices prices(価格) = fixed or parametric negligible in size relative to the market
prices values --> relative values of different goods signals --> coordinating the decisions of agents
economic efficiency(経済的効率性)
4
-
secondary feature in the model symmetric information(対称的情報) uncertainty(不確実性) = all agents are equally
uninformed any agent has no informational advantage
two forms of competitive model exchange economy(交換経済) production economy(生産経済)
5
-
2.3.1 Exchange Economy trade of commodities between two parties for
mutual advantage(相互利益) two-consumer, two-good exchange economy → all results extend to large numbers endowment = initial stock of the goods (初期保有)↓ (constant) exchange (market prices = exchange rates ) ↓ competitive = price-taking(価格受容) behavior desirable consumption plans(消費計画)
6
-
consumer h endowment
: h’s initial stock of good i prices p1, p2
: h’s consumption plan budget constraint(予算制約)
preference(選好) = utility function(効用関数)
marginal utility(限界効用) is positive for both goods indifferent curve(無差別曲線) has convex(凸) shape
7
-
Edgeworth box
feasible plan(実行可能計画)
rectangle(長方形) length southwest corner: consumer 1’s origin(原点) northeast corner: consumer 2’s origin
8
-
2
1
9
-
Equilibrium budget constraints(予算制約)
consumer 1: relative to the southwest corner consumer 2: relative to the northeast corner same endowment point(初期保有点) gradient(傾き)
equilibrium prices(均衡価格) utility maximization for both consumers (効用最大化) supply = demand(供給=需要)
10
-
2
1
11
-
2
1
good 1: excess demand (超過需要) p1 goes up
good 2: excess supply (超過供給) p2 goes down
12
-
2
1
good 1: excess demand (超過供給) p1 goes down
good 2: excess supply (超過需要) p2 goes up
13
-
2
1
14
equilibrium (均衡)
-
consumers’ demand functions max of utility subject to budget constraint demand demand = supply (market clearing:市場清算)
equilibrium the prices lead to a budget line on which the
indifference curves has a point of common tangency(共通の接点)
number of prices, number of independent equations(独立の方程式)
15
-
only relative prices(相対価格) matter budget constraint always passes through the
endowment point(初期保有点) gradient(傾き) is determined by the price ratio demand and supply depend on the relative
pricebut not on the absolute values
homogeneous of degree 0(0次同次) any scaling up or down will also be equilibrium
prices price normalization(価格の正規化) numeraire(基準財) = unit of account
16
-
Walras’s law interdependence(相互依存) between the two
equilibrium equations excess demand (超過需要)
total value of excess demands, for any prices
17
-
Walras’s law (continued)(ワルラス法則) if Z1=0, then Z2=0 if Z2=0, then Z1=0 since p1Z1+p2Z2=0 equilibrium in one market implies equilibrium in
the other choose good 1 as the numeraire (p1=1) and plot
the excess demand for good 2 as a function of p2 if the ED of 2 is zero, then the ED of 1 is zero ---> equilibrium
extension of many consumers and goods number of equilibrium conditions
18
-
19
0
-
2.3.2 Production and Exchange addition of production to exchange economy
initial endowments (e.g. labor)(初期保有) consumption goods produced from ini. end. intermediates(中間財): produced from ini. end.
and input for another Arrow-Debreu economy
model of competitive economy(競争経済) producer (firm): production technology(生産技術) consumer: preference, initial endowments shareholdings(株式保有) of the firms
20
-
firm (producer) production set(生産集合)
available production technology = knowledge inputs ---> outputs (知識) Yj : firm j’s production set input: negative(負≦0) = subtraction from the
stock of that good available for consumption output: positive(正≧0) production plan: prices: profit:
21
-
-2
3
Good 2
Good 1
Yj
22
-
Process of profit maximization isoprofit curve(等利潤線) 0 inner product > 0 (acute angle) π
-
Process of profit maximization
profit maximization(利潤最大化) y* : tangency point between the highest
attainable isoprofit curve and production set the higher the isoprofit curve, the bigger the
profit (northeast shift gives more profit)
24
-
Good 2
Good 1
π > 0
π = 0
π < 0
p2
p1
25
-
economy with n goods
m firms(企業) production plan(生産計画)
chosen to maximize profits s.t. production set supply function (供給関数) level of profit
aggregate supply negative or positive
26
-
private ownership economy
H consumers(消費者): initial endowments(初期保有) ω h
shareholdings in firms (株式保有率) budget constraint(予算制約)
change in prices ---> endowment dividend income(配当所得)
27
-
demand function(需要関数) aggregate demand (集計された需要) equilibrium demand = supply (not fixed) excess demand=0
demand (supply) is determined by relative prices ---> Zi is homogeneous of degree zero
normalization, numeraire(正規化、基準財)
28
-
2.4 Efficiency of Competition efficiency(効率性)
if more cannot be achieved, then the outcome is efficient
-
2.4.1 Single Consumer individual preferences = social preferences best outcome = first-best
no constraint on policy choice single firm & single consumer diagram = Robinson Crusoe economy
Robinson acts as a firm carrying out production and as a consumer of the product of the firm
1) Robinson = social planner for coordination 2) profit maximization & utility maximization (利潤最大化) (効用最大化)
30
-
Good 2
Good 1
1
p1
π
good 2 =numeraire
31
-
Good 2
Good 1
1
p1
π
good 2 =numeraire
32
-
budget constraint(予算制約)
or where is net consumption(純消費) utility maximization ---> equilibrium for the economy --->
net consumption = supply profit maximization = utility maximization efficient(効率的)
33
-
Good 2
Good 1
1
p1
π
34
-
Good 2
Good 1
1
p1
π
35
-
Good 2
Good 1
1
p1
π
36
-
characterization of first-best allocation tangency point(接点) between the two
curves marginal rate of substitution(限界代替率)
MRS12=U1/U2 marginal rate of transformation(限界変形率)
MRT12(=MC1/MC2) MRS12=MRT12 marginal value(限界価値) = marginal cost(限界費用) at the first-best
37
-
the market achieves efficiency (市場は効率性を達成する)
utility maximization(効用最大化) ---> MRS12=p1/p2 profit maximization(利潤最大化) ---> MRT12=p1/p2 competitive equilibrium(競争均衡) MRS12=p1/p2 = MRT12
38
-
constant return to scale(規模に関して収穫一定) efficient production frontier(生産フロンティア) =straight line through the origin only equilibrium : zero profit(ゼロ利潤)
positive ---> infinitely large profit isoprofit curve with π =0 equal to efficient PF two further implications
equilibrium price ratio is determined by the zero-profit condition and is independent of demand
since the profit income of the consumer is zero, the budget constraint passes through the origin
39
-
Good 2
Good 1
1
p1
40
-
2.4.2 Pareto-Efficiency (パレート効率性) more than one consumer Pareto-efficiency
no unexploited economic gains consider whether it is possible to undertake a
reallocation of resources(資源の再配分) that can benefit at least one consumer without harming any other
if possible, there would exist unexploited gains if not, the initial position is Pareto-efficient efficient allocation of resources
41
-
feasibility(実行可能性): consumption, production, ini. endowment x = y + ω
Definition 1: A feasible consp. allocation is Pareto-efficient if there does not exist an alternative feasible allocation such that
i. Allocation gives all consumers at least as much utility as .
ii. Allocation gives at least one consumer more utility than . is Pareto-efficient if there is no that can make
someone better off without making anyone worse off
42
-
2.4.3 Efficiency in an Exchange Economy Two Theorems of Welfare Economics First Theorem(厚生経済学の第1定理)
a competitive equilibrium is Pareto efficient Second Theorem(厚生経済学の第2定理)
any Pareto-efficient allocation can be decentralized as a competitive equilibrium
encouragement of competition Edgeworth box diagram
a is not a Pareto-efficient allocation b is Pareto-preferred to a
43
-
2
1
44
-
Pareto-efficient allocation c beginning at c, any change in the allocation must
lower the utility of at least one of the consumers tangency between the two indifference curves MRS121=MRS122
Pareto-efficient allocation(パレート効率的配分) is not unique
---> contract curve(契約曲線)
45
-
2
1 contract curve (契約曲線)
46
-
competitive equilibrium(競争均衡) a price line through the initial endowment point ω
that is tangential to both indifference curves(無差別曲線) at the same point
competitive equilibrium = Pareto-efficient utility maximization ---> MRS12h=p1/p2 competitive equilibrium MRS121=p1/p2 = MRS122
Theorem 1 (First Theorem of Welfare Economics) The allocation of commodities at a competitive equilibrium is Pareto-efficient.
47
-
2
1
48
-
Second Theorem whether any chosen Pareto-efficient allocation can
be made into CE by choosing suitable location for the initial endowment
possible if indifference curves are convex(凸) a budget line through the Pareto-ef.allo. exists consumers’ potimal choice decentralization(分権化)
Theorem 2 (Second Theorem of Welfare Economics) With convex preferences, any Pareto-efficient allocation can be made a competitive equilibrium.
49
-
2.4.4 Extension to Production production ---> supply is variable consumer’s income differs Robinson Crusoe economy: same more than one consumer
utility maximization ---> MRSijh=pi/pj profit maximization ---> MRTijm=pi/pj competitive equilibrium efficiency in consumption MRSijh=pi/pj = MRSijh’ efficiency in production MRTijm=pi/pj = MRTijm’ MRSijh= MRTijm --->First Theorem
50
-
Second Theorem W: feasible output plans w=y+ω
Z: quantities for Pareto-improvement if both are convex, a common tangent exists total consumption
51
-
Price line
Feasible set
W Z
52
-
2.5 Lump-Sum Taxation decentralization mechanism Second Theorem lump-sum transfers(一括移転) (一括固定税、一括補助金) lump sum
no change in a consumer’s behavior can affect the size of the transfer
differentiated from income or commodity taxes(所得税、物品税)
redistributive instrument(再分配の手段)
53
-
2
1
54
-
initial endowment Pareto efficient e equilibrium prices income at the initial point budget constraint lump-sum taxes(一括(固定)税)
consumer 1 pays a tax consumer 2 pays a negative tax pair of taxes = transfer of endowment efficiency in achieving distributional objectives
55
top related