GEW Flashcards
3 important themes of GE Theory
- Decentralisation - no central planner telling agents what to do, everyone acts in their own self-interest
- Prices as signals
- The Invisible Hand - ensure efficiency
Model of Competitive Equilibrium (5 + 1)
- Large number of distinct goods. Each good has a market and a market price.
- Large number of households/consumers. Each household has an endowment of goods (maybe including labour). Each consumer also has preferences over consumption bundles, represented by a utility function.
- Large number of firms. Each firm has a production technology, describing what combinations of inputs of various goods can be turned into outputs of other goods (feasible production plans).
- Each firm takes prices of inputs and outputs as given and chooses a profit-maximising production plan given those prices.
- Each consumer takes prices as given and chooses what to sell and what to buy on the markets at those prices i.e. chooses a utility-maximising consumption bundle within the budget set.
If prices are such that ALL markets clear, we have an equilibrium.
Will an equilibrium price pair necessarily exist?
Yes, if optimal bundle for each agent changes in a continuous way as price changes
How to get Walras’ Law? What does Walras’ Law tell us?
Rearrange budget constraints and add.
Tells us that the VALUE of aggregate excess demands, summed over all goods, is 0.
Implies that if n-1 markets clear, then n markets must clear.
Also implies that if one market is in excess demand, then the other must be in excess supply (assuming both prices are strictly positive).
TRUE FOR ALL PRICES, not just equilibrium.
What does the First Fundamental Theorem of Welfare Economics state? (assumption? - 1 + 3)
A competitive equilibrium allocation is Pareto efficient (assuming that preferences satisfy the NON-SATIATION property - indifference curves are infinitely thin / there always exists another bundle in a very small Euclidean space which is strictly preferred so rankings are strict).
Also assumes:
- No externalities - agents care only about their final consumption bundle (nothing else enters the utility function)
- Agents act as price-takers
- An equilibrium exists - perhaps because agents’ aggregate behaviour changes continuously as prices change
What does the Second Fundamental Theorem of Welfare Economics state? (assumption?)
For any Pareto-efficient allocation, one can find initial endowments such that this allocation is a competitive equilibrium (assumes that preferences are convex)
Also same assumptions as FWT (No externalities, price takers, existence of equilibrium) AND that a lump sum tax is feasible
What is the key implication of the Second Welfare Theorem?
The best way to deal with inequitable allocations is not to interfere with free, decentralised markets, but to re-allocate endowments (using lump-sum taxes) and then let the market decide (via competitive equilibrium) on prices and final consumption bundles
Why does the tax have to be lump sum?
Suppose that agent’s endowment includes labour as one of the goods. Suppose that the government imposes a 10% tax on labour supplied (proportional labour income tax).
Then buyers of labour (firms) will face a different price of labour relative to other goods than sellers (workers) do - this will cause inefficient allocation of labour (too little supplied - MRS for labour vs other goods will differ across individuals.
So tax has to be lump sum i.e. dependent only on endowment, not choices e.g. tax on potential labour, not actual labour supplied.
But this is difficult because labour comes in different qualities, which should be taxed differently (e.g. more intelligent people taxed more).
On the other hand, the amount of inefficiency caused by distortionary taxes, as opposed to lump sum taxes, may not be that large, so the message of the SWT may be broadly correct.
Robinson Crusoe Economy - competitive equilibrium
Each firm produces in such a way that marginal product of labour = price ratio (w/p)
Each individual consumes in such a way that |MRS| between consumption and leisure equals price ratio
Hence MPL = |MRS| - this is the condition for Pareto efficiency
e.g. if MPL > |MRS|, you could make one individual better off by marginally increasing their labour supply and giving them the resulting extra product - no other individual affected
HENCE - FWT APPLIES
Robinson Crusoe Economy - how to get Walras’ Law
Add profit equation to budget constraint
Robinson Crusoe Economy - what if returns to labour are constant?
Suppose production function f(L) = aL (- 1/a is number of hours needed to produce 1 coconut)
Profit = pc - wL = pf(L) - wL = (pa-w)L
If pa < w (iso-profit line steeper than production function) then optimal to set L = 0
But in equilibrium, cannot be that L = 0 (at least for reasonable utility function e.g. Cobb-Douglas - zero consumption must be suboptimal)
If pa > w, there is no optimal L - increasing L always increases profit (iso-profit line less steep than production function)
So it must be that w/p = a i.e. iso-profit lines are parallel to the production function and the highest feasible one is the same as the production function, giving zero profit
Do consumer preferences matter for equilibrium prices IN THE CASE OF CONSTANT RETURNS TO SCALE?
NO - we can deduce solely from technology (since slope of production function is w/p)
Robinson Crusoe - Increasing Returns to Scale
Tangency of production function and indifference curve gives the optimum choice (L*, c*)
However, there is no competitive equilibrium - whatever the prices (hence slope of iso-profit lines), the firm can always get more profit by increasing production
Increasing returns is a form of non-convexity (production set is not convex)
What is MRT in constant returns case?
-(a2/a1)
-(ay/ax)
The slope of the frontier
(for non-constant returns -dT/dX1 / dT/dX2)
When is an allocation Pareto-efficient in a production economy?
As long as production is at the frontier, all produced goods are consumed, and for any pair of goods, all consumers have same MRS AND this common MRS = MRT
