general Equilibrium Flashcards
Partial equilibrium
Studies a single market in isolation.
Général equilibrium
Takes into account all the interactions between all markets
Gross demand
Amount the person wants to consume
Net/excess demand
Amount the person wants to purchase
Pareto efficient allocation
If the 2 agents have the same MRS
First fundamental theorem of welfare eco
Compe equil allocation is Pareto efficient
proof p615最下
Compétitive equilibrium
A price pair st when each agent acts as a price taker and chooses his best bundle, both market clear
Contract curve
Line connecting Pareto efficient points ie where the MRS are equal
Stable equilibrium
Starting from some where (raise price when in excess demand and reduce price when in excess supply), the price will converge to an equilibrium
What is important about homogeneity of degree 0
Excess demands are unchanged if we multiply both prices by the same scalar
Hence Only relative prices matter
second theorem of welfare economics (exchange)
If all agents have convex preferences then there will always be a set of prices such that each Pareto efficient allocation is a market equilibrium for an appropriate assignment of endowments
What does contract curve tell given a particular utility level of B
The max u A can attain
PPS
What combinations of 2 goods can be feasibly produced
2 good 2 agent Pareto efficient allocation(FWT)
1 more condition
Production at the frontier, all produced goods are consumed, all consumers have the same MRS (on contract curve) and MRS=MRT
What is special about the production economy in terms of optimal and competitive equilibrium
The optimum and competitive equilibrium is the same
In a competitive equilibrium model when equilibrium is not reached the firm and consumers are choosing on the same line then why is this not Parato efficient
Because this is not feasible
Why does price have to be positive. explain in terms of the case when prices <0 or =0
When prize is negative from monotonic preferences Everyone will want it so nobody supplies it
If price equals zero then the goods will be in excess supply. Why excess supply? If excess demand, increase in p, so will not be in excess demand
If excess supply, then p falls, while 0 is the boundary
Condition for CRTS
0 profit, y intercept =0
Prod have infinite optimum, consumers have one, equilibrium chosen by consumer
Pareto efficient
Conditions for SWT in production
Convex preferences and convex production set, concave f( in addition to FWT
Lump sum tax feasible
Condition for FWT
No ext
Price takers
Equil exists- aggregate behaviour changes continuously as prices change
Non satiation
Why FWT holds for 2
MRS = price ratio : same as exchange: cons choose on budget line
MRT = price ratio
So everyone faces the same p ratio
MRT=
-MPLy/MPLx
Production externality
One firm’s cost/production function depends on other’s production
Consumption externalities
One agents utility function depends directly on another agents consumption
Quasilinear in coase
If preferences are quasi linear, the efficient amount of the good involved in the ext is independent of the distribution of property rights
Pollution permits
Gov solves social cost=0
And get the quantity out of this
Get this equal to the supply
The equilibrium must be equal to this quantity
So firms have to produce here
And evaluate MC
Market price will be determined and is equal to this
Pigou tax
Solve social cost=0
Get the quantity and evaluate external cost at this quantity
Set the tax
Firms will choose the quantity
Ways to do with externalities
The fundamental condition is that property rights should be well-defined however well-defined property rights not necessarily lead to markets. If Property rights are well defined to allow for negotiation between people then people may trade a right to produce externalities in the same way that the they trade a right to produce a good
Existence of a competitive equilibrium
Aggregate exist demand function is continuous
Each individual’s demand function is continuous- small changes in price will lead to only small changes in demand- convex preferences
Even if consumers themselves have discontinuous demand behaviour, as long as all consumers are small relative to the size of the market, agg demand function will be continuous
Obstacles to efficient bargaining
Difficulty of coordinating agents affected by the externality especially if they are large numbers of them
Lack of common information about the effects of the externality or costs of reducing it(Eg one agent might think his smoking does not poses a big problem towards others so he thinks his externality is small and yet others don’t think so
Public good
It has to be consumed in the same quantity by everyone-Consumption externalities
Non-rival if one persons consumption of it does not prevent other person consuming it
Nonexcludable if once the good is produced it is not possible to prevent anyone from consuming it
Ways to provide public goods and Pareto efficiency
Decentralised marketplace vision is unlikely to be p effi and the good pretend to be undersupplied
Collective provision of public it may also tend to be inefficient because of the free rider prob
Condition of pareto efficiency for a discrete public good
It is Parato efficient to supply a discrete public good if the sum of the consumers reservation values is a least as high as the cost of supplying it otherwise it inefficient to supply it
Pareto efficient condition for supplying continuous public good
Samuelson rule: the level of supply of the public good is Pareto effi if and if and only if the sum of the consumers marginal rate of substitution between the good and any other good is equal to the marginal rate of transformation between the public good and the other good
Why does decentralised provision fail
Each agent ignores the positive ext of contributing more :the extra utility for the other person
Set MRS=MRT Same as in the case of private good
What is special about public good in quasiliner pref
The level of G does not depend on endow- unique efficient level
comparison to priv goods
Assumption for private goods is that there is no consumption externalities. In a compe market each person optimising with respect to his own consumption was sufficient to achieve social optimum.
What does Private solution mean in coase
Role of gov is limited to establishing and enforcing property entitlement to resources and enforcing freely agreed to contracts
Price ratio in 2 good autacky
Prop to labour time
Competitive equilibrium in trade
Wage adjusts so that profits are zero in industry two countries choose to prod
This determines the Total output of each good via complete specialisation
The output price ratio adjusts so that market clears
Why does FWT hold in 2 output good economy
Given price ratio Px Py. Frim maximise profits by choosing the point on the PPF on the highest iso-profits line which has slope Px/ Py. Tangency condition MRT=Px/Py. Facing these prices, consumers choose the bundle such that the MRS= p ratio.
Hence MRSx=MRSy=MRT
Should one increase or decrease G if sum of MRS smaller than MRT
Reduce G
If A wants 1/3 unit of money instead of 1G, B wants 1/2 unit of money instead of 1G, but reducing G frees up 1 money
The explanation for Robinson-Friday economy condition for pareto efficient MRT=MRS
Suppose MRSr=MRSf=1 but MRT=2. Could reduce yam by 1u and get 2u of coconuts. At the same time Robinson reduces yam consumption by 1u and increases coconut consumption by 2u. Robinson strictly better and Friday unaffected
Comparative advantage
In a good: means the country has a lower opportunity cost of that good than the other country does. The principle of c/a says if Which specialises in the good in which it has a comparatively exports some of that good and imports the other one, both Can become better off
Trade introduces extra production possibilities
Absolute advantage
Means both goods are cheaper to produce in terms of labour requirement.
But it is not possible for one country to have a comparative advantage in both unless the PPF have the same slope
