GEW Flashcards
(32 cards)
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
Tangency condition for profit-maximising firm (2-good case) - why is the allocation Pareto-efficient?
MRT = -(py/pc)
Consumers also choose consumption so that MRS between yams and coconuts = -(py/pc)
Hence in competitive equilibrium - MRT = MRSa = MRSb, so the allocation is Pareto efficient and FWT applies as before
Ricardian model - under autarky, what are the equilibrium prices in a competitive equilibrium?
The inverse of labour productivity e.g. pcR = 1/acR
Limitations of Ricardian Model
- Cannot be used to analyse changes in income distribution between owners of different factors (vs. Heckscher-Ohlin model - two factors, labour and capital - could be that with trade, workers worse off and capitalists better off (or vice versa) vs autarky) whereas in Ricardo model, opening up to trade has no distributional consequences within a country since everyone in the country is the same.
In developing countries, trade quotas and tariffs have sometimes been justified on distributional grounds e.g. rich people may import a lot of luxury consumer goods, using up scarce foreign exchange.
In response to this, could be argued (invoking SWT) that it would be better to have free trade, maximising the total ‘pie’ available via comparative advantage, then deal with inequality via lump sum taxation and redistribution - Doesn’t take into account dynamic effects.
Suppose developing country has a comparative advantage in primary products e.g. cocoa. But suppose that commodities such as cocoa are expected to decline in price relative to manufactures. If the country were to specialise in cocoa, it would benefit in SR but become impoverished in the LR.
Argument: under free trade, entrepreneurs will invest in industries which are most profitable in the LR (i.e. those in which the country has a LR comparative advantage).
So if this does not happen, may be because, say, they are unable to borrow to invest (imperfect capital markets).
But in this case, would be better to tackle market failure directly (credit market imperfection) than to restrict trade (reason for failure is not really a failure of trade).
What is the idea of the Pigou tax?
The tax is set in such a way that the decision-maker is faced with the full social marginal consequences of his actions
Criticism of Pigou tax
(in case of steel firm and fishery)
Pollution tax is equal to the marginal damage that the pollution causes (increasing the fishery’s costs.)
However, to set the tax, the government needs to know the Pareto efficient level of pollution - so why not just cap the steel firm at this level of pollution?
Emissions permit market - how does it work?
Given the fixed amount of permits, this should induce production efficiency. Each firm sets the marginal cost of abatement equal to the permit price.
Hence all firms have equal marginal costs of abatement.
This is efficient - if one firm (i) had lower marginal costs of abatement cost than another (j) then i could reduce emissions by δ and j could increase by δ. Emissions would be the same but costs lower.
What is the Tragedy of the Commons?
The idea that a common resource will be over-used (and even destroyed) if it belongs to nobody and people follow their own private interests.
Examples of common goods: Common grazing land, ocean fisheries, global atmosphere.
Coase Theorem with quasilinear preferences
If preferences are quasilinear, the efficient amount of the good involved in the externality is independent of the distribution of property rights
Coase Theorem - actual argument
(i) if there are no transaction costs, bargaining will lead to an efficient solution of an externality
(ii) in practice, there are transaction costs associated with bargaining, but
(iii) there are also costs associated with government solutions of externalities and it’s essential to study these different kinds of costs in any given case.
