General equilibrium Flashcards
What is GCE?
The set of prices (and associated quantities) that has households choosing consumption to maximise utility, firms maximising profits, and these profits distributed to households given their share (θ) of the firm.
What do we assume about a consumer’s utility function / preferences? [4]
- Complete - bundles can be ranked
- Transient - if A>B and B>C then A>C
- Convexity - averages are better than extremes
- Non-satiation - more is always better
Budget constraint: income must be greater than or equal to expenditure. Why can you replace ‘greater than or equal to’ with just ‘equal to’?
Since the utility functions satisfy local non-satiation - more of each good is better. Could in theory be beneath the budget constraint, but would always choose to be on it to maximise utility.
Due to Kuhn-Tucker - generalisation of the Lagrange multiplier method, which only allows equality constraints…
What do we mean by ‘the Kuhn-Tucker conditions’?
The first-order necessary conditions for a solution to be optimal, provided that some regularity conditions are satisfied.
The reason why you can set each partial derivative equal to zero.
What is λ in the Lagrangian?
The shadow price;
Marginal utility of income;
The rate of change of maximum (utility) as (income) changes / as the constraint is relaxed.
What are the steps in a maximisation problem? (Start with endowments and utility functions)
1) Budget constraint: expenditure < income/endowment
2) Replace < with =
3) Maximise utility subject to the budget constraint
4) Lagrangian, FOCs, solve for x1 and x2
5) Check it’s a maximum with SOCs
6) Market clears - so can solve FOCs for prices
7) Substitute in for allocations
When do you use the Envelope Theorem?
To find how the indirect objective function (maximum value function) changes as some exogenous variable changes.
At the optimum, as α varies, with x∗ and y∗ allowed to adjust optimally, gives the same result as if x∗ and y∗ were held constant.
Means that only the direct effects of a change in an exogenous variable need be considered, even though the exogenous variable may enter the maximum value function indirectly as part of the solution to the endogenous choice variables.
What is the difference between Marshallian and Hicksian demand?
Marshallian: keep budget fixed and maximise utility
Hicksian: set a target level of utility and minimise the cost associated with it
What is the offer curve?
How a consumer’s optimal bundle changes with the price of each good.
Walrasian equilibrium allocation is the intersection of the two offer curves in an Edgeworth box.
What is Walras’ Law?
The sum of the values of excess demands across all markets must equal zero, whether or not the economy is in a general equilibrium.
Excess demand function: demand - supply = E
Walras’ Law: p1E1 + p2E2 = 0
What does Walras’ Law imply?
That the sum of the values of excess demands across all markets must equal zero, whether or not the economy is in a general equilibrium.
So, if positive excess demand exists in one market, negative excess demand must exist in some other market.
Allows us to set one price as the numeraire since only relative prices matter.
What is the contract curve?
The set of points of tangency between the indifference curves of two people.
On contract curve, MRSa = MRSb, allocation is Pareto efficient.
Contract curve = connection of all places where offer curves intersect
What is the producer’s optimisation problem?
Maximise profits, π = pxs - wld, subject to the production function, xs=f(ld)
The production function is strictly concave. Its gradient is the MRT = w/p
If you have an individual firm and consumer, when is there efficient allocation?
When MRS = MRT
What is the consumer’s optimisation problem?
Endowment of labour, l0 (= 24 hours)
Choose demand of goods and supply of labour to maximise utility, u(xd, l0-ls)
Why, at competitive equilibrium, does MRS = price ratio?
L = u(x,y) + λ[m - pxx - pyy]
∂L/∂x = MUx - pxλ = 0
∂L/∂y = MUy - pyλ = 0
MUx/px = MUy/py
px/py = MUx/MUy = MRS
Explain comparative advantage
The ability of a firm or individual to produce goods and/or services at a lower opportunity cost than other firms or individuals.
A country has a comparative advantage in good 1 if that good is relatively cheaper under autarky than under free trade: p1/p2 < p1w/p2w
What is the advantage of trade?
It enlarges the consumption possibility set and enables the consumer to get on a higher indifference curve - they produce more of the good they have the comparative advantage in (p1), export it, and import the amount of good 2 they desire
What if a country has an absolute disadvantage in all goods (low factor productivity)?
It will still have a comparative advantage in things it is relatively not as bad at. It will gain from trade, and wages will adjust so that it becomes more competitive.
What does empirical evidence say about this Ricardian model of trade?
- The extreme specialisation it suggests doesn’t seem to occur
- No consideration of income distribution within each economy - some sectors benefit, others suffer
- Doesn’t look at the impact of resource endowments
- Doesn’t look at the role of economies of scale in explaining international trade
What is the Heckscher-Ohlin model?
Considers endowments: countries have different endowments of labour, land and capital inputs.
They will specialise in and export those products which use most intensively the factors which they are most endowed with.
What is the Specific Factors model?
A short-run specific version of the H-O model: only L is variable and can move between sectors; K and T are fixed - specific
