L19 - General Equilibrium Flashcards
Who contributed to general equilibrium theory from a mathematical perspective?
- Leon Walras (1834 - 1910) - French-Swiss Economist
- Started solving formally the general equilibrium assumption in a mathematical sense
- This was later solved by Kenneth Arrow (1921 -2017)
and Gerard Debreu (1921-2004).
What is Welfare economics?
- Welfare economics is the study of how the allocation of resources and goods affects social welfare. This relates directly to the study of economic efficiency and income distribution, as well as how they affect the overall well-being of people in the economy.
- In practical application, welfare economists seek to provide tools to guide public policy to achieve beneficial social and economic outcomes for all of society.
- However, welfare economics is a subjective study that depends heavily on chosen assumptions regarding how welfare can be defined, measured, and compared for individuals and society as a whole.
What does General Equilibrium refer to?
General Equilibrium refers to a situation where all markets clear simultaneously.
Clearly, what goes on in one market can affect other markets.
- demands for shoes can affect the demand for shoemakers, and hence for certain types of labour in general. This feeds back into the demand for shoes.
This is potentially a very complicated situation to model. However, on various simplifying assumptions, ARROW and DEBREU have produced some very powerful results about the properties of general equilibrium.
They have shown that under some circumstances a perfectly competitive free market general equilibrium will be PARETO OPTIMAL.
However, this is a definition of optimality which IGNORES DISTRIBUTION.
What does General Equilibrium theory also show?
it is also possible to show that if anyone market is missing or ‘distorted’ by tax, quantity constraints or imperfect competition, intervention in ANY other market MAY potentially improve welfare. –> a distortion in one market helps offset one in another market
This is the theorem of the SECOND BEST (Lipsey and Lancaster).
Working out which interventions are ‘good’ or ‘bad’ may require modelling the whole general equilibrium of the economy, if interactions between markets are strong.
What is a Pure Exchange Economy?
- A pure exchange economy is an economy in which there are no production opportunities. Consumer own initial stock or endowments of commodities. Economic activity is limited to trading and consumption. The simplest case involves only two consumers
- There is no money - the goods are just bartered
- Single Market
- Everything is written in terms of a numeraire:
- an item or commodity acting as a measure of value or as a standard for currency exchange.
- Example apple is a numeraire, and 1 banana sell for P apples –> two good 1 price
How do you represent the market’s clearing mathematically?
A market is said to clear when total demand equals total endowments:
The two goods are not produced, but available in fixed endowments ET1 and ET2.
These total endowments are the sums of the two individuals’ endowments:
- ET1 = EA1 + EB1
- ET2 = EA2 + EB2
The market for good 1 clears when
• DA1 + DB1 = EA1 + EB1
Similarly for good 2.
Trading doesn’t take place until the price has changed to clear all markets
- Walras’ Law –> the sum of excess demands in all markets equal zero
- therefore if all but one market clear then the alst market automatically clears.
- Walras’ Law –> the sum of excess demands in all markets equal zero
What is Walras’ Law?
- Walras’ Law –> the sum of excess demands in all markets equal zero
therefore if all but one market clear then the alst market automatically clears.
What does a consumer A’s indifference curve?
- Budget line is a negative gradient –> Marginal Rate of Transformation (MRT)–> Price ratio ( -1/P)
- It must go through the initial endowment point E
- the convexity of the indifference curves implies a diminishing rate of substitution –> the gradient of the indifference curve at any given point is the marginal rate of substitution
- Want to find the point where MRT =MRS (denoted as D -demand point) at where the indifference curve and budget curve are at a tangent
What is an Edgeworth Box?
A common tool in general equilibrium analysis is the Edgeworth box which allows the study of the interaction of two individuals trading two different commodities.
- E.g. that the horizontal length is equal to the total endowment for apples (ET1) and the vertical height is equal to the total endowment for bananas (ET2)–> this is the scale of the total economy
- Point E gives the initial endowment of resources –> it tells you how relatively equal or not equal the economy was to the initial endowment
- Point D gives the final demand point
- There is a line linking both points - is the budget line, the rate at which the two good are swapped
- at point D where both markets clear MRSA=MRSB
How can we define General Equilibrium?
We can define General Equilibrium as a set of prices P=(p1,p2….pn) which clear all n markets simultaneously.
- Where there are n commodities and n-1 prices (vector of prices) covering the markets
- If there are n goods, then we set the price of good 1 as the NUMERAIRE (i.e. we determine p1=1).
- All other prices are swap ratios (Pg many units of good g are swapped for 1 unit of good 1).
- by definition, at the final demand point D, both parties should feel like they are better off than at point E
What are the assumptions of Pure Exchange Economies?
- No money
- No production
- Good exist in fixed endowments (a quality or ability possessed or inherited by someone)
- Their ownership is determined by a set of well-established property rights
- Indifference curves are well-behaved and are convex
- All consumers are well-informed
What is the contract curve?
- By connecting the tangency point of the two consumers indifference curve (final demand point) for different initial endowment points we can create the contract curve
- This depicts all the possible market equilibrium
- BUT also links all Pareto efficient points –> all the Pareto optimal
- Every PO point is a market equilibrium depending on the initial distribution –> so important it’s the first fundamental theory of welfare economics
- Although the PO point has its flaws –> if we are at A - it is a PO point but also A has nothing - while libertarians might be happy with the most people wouldn’t think this is fair
- it does take account of the distribution
What did Arrow and Debreu say about Pareto Optimum?
- PO requires a complete set of contingent futures markets –> need to take account of all state of the future and their prices
- Otherwise, people will undervalue the future massively if there would not be any trade in the future
What is the The Core?
- Both consumers have an initial indifference curve going through E and will not accept any bundles less than the combination depicted on this curve (anything above is its boundary)
- The area in between the two initial indifference curves are all sets of possible trades
- The core is the area Bargained over by The consumers. If there is just one consumer On one side (say one B) but Lots on the other, then the Lone person is in a stronger bargaining position. If there was just one Consumer B, then D’ Would be the outcome.
- The width of a core shows you how much bargaining power one side has to exploit bargains to push the other down
- Perfectly competitive equilibrium falls right in the middle of the core
What did the Keynesian economists say about Pareto Optimum?
- Trading must not take place until the market clears
- People go away from the market with unfulfilled sales, this affects their budget and they start to trade to a false equilibrium
- Non-clearing markets were also called non-tatunnement (leijonhufvud)
