Micro 1: General Equilibrium Flashcards
What is general equilibrium, as opposed to partial equilibrium?
General equilibrium refers to equilibrium in all markets, as opposed to partial equilibrium, which is just concerned with equilibrium in particular markets.
What is an Edgeworth box? What does it illustrate?
An Edgeworth box illustrates all possible endowments in an exchange economy.
What does it mean to say that demand functions are ‘homogenous of degree zero’?
z(tp) = z(p) for any t: all demands and supplies stay the same when prices double.
What is Walras’ law?
Define aggregate excess demand as z(p). For any p, the dot product of p and z(p) = 0.
Why do we only need to find k –1 prices where markets clear, in a market with k goods?
This follows from Walras’ law.
What requirements do we need on preferences and endowments to ensure the existence of Walrasian equilibrium?
z must be a continuous function, so individual demand functions must be continuous and convex. All consumers must own at least a little of each good.
What assumptions are required for the First Theorem of Welfare Economics to hold?
- Price-taking agents
- Complete markets - ie no externalities
- Symmetric information
- Rational optimisation
- No distortionary taxation etc
- Locally non-satiated preferences
What does the First Theorem state?
All market equilibria are Pareto efficient - competitive markets will exhaust the gains from trade.
Sketch a proof of the First WT.
At any market equilibrium, both consumers operate where the budget line is tangent to an indifference curve. Since they must both choose the same point, their indifference curves must also be tangent to each other. Therefore, the set of Pareto improvements is empty.
Can the First WT still hold under intertemporal and risky markets?
Yes - this is the Arrow-Debreu theorem (1954).
What does the Second Theorem state? What additional assumptions does it require?
The Second Theorem states that any Pareto efficient allocation can be achieved by competitive markets given the correct redistribution of initial endowments.
What is a lump-sum tax, as opposed to a ‘distortionary’ tax?
When a tax is distortionary, agents can change the amount of tax they pay by changing their behaviour. For example, you can pay less income tax by working less. By contrast, lump-sum taxes (which may still change behaviour) cannot be avoided like this.
Can there be multiple Walrasian equilibria?
Yes. However, they are usually locally unique.
What is tâtonnement?
The ‘Walrasian auctioneer’ model of convergence to price equilibrium: p is announced in each period, demands are announced, and then prices are adjusted in proportion to excess aggregate demand.
What requirements do we need to impose on the nature of goods to ensure that tâtonnement always converges on the equilibrium price vector?
All goods must be gross substitutes.
