3 - General Equilibrium

Question 1

What’s a 2x2 pure exchange economy?

Answer 1

E = ({R², uₐ, R², uᵦ}, {ω₁ₐ, ω₂ₐ, ω₁ᵦ, ω₂ᵦ})

• two consumers, two goods
• no production, no firms
• only endowments!

Question 2

What’s the Edgeworthbox?

Answer 2

the Edgeworth box allows the study of the interaction of two individuals trading two different commodities: this “box” is formed using two sets of typical indifference maps, which in this case represent the indifference curves of agents A (green) and B (red), who must choose quantities of goods x and y. When the indifference map of agent B is rotated, and put on top of the map of agent A, the box is formed.

Question 3

What’s the contract curve?

Answer 3

In Edgeworth box:

• When indifference curves are tangent to each other, a contract curve (blue) can be drawn using these tangency points.
• It is the curve of all pareto optimal allocation. Shape depends on the preferences and the box.
• (Price line determines feasible/possible trade)

Question 4

What are limitations of the General Equilibrium?

Answer 4

 Non-convexities in production (Fixed costs, increasing returns to scale)
 Externalities
 Imperfect competition
 Asymmetric information
 Bounded rational agents

Question 5

What is the budget line in a 2x2 exchange economy?

Answer 5

Rate at which you can exchange goods (-p₁/p₂)

Question 6

What is general equilibrium analysis?

Answer 6

Extension of partial equilibrium analysis: how demand and supply conditions interact in several markets to determine the price of many goods

Question 7

What’s the negotiation space in the Edgeworth box?

Answer 7

The space between two indifference curves: the set of all pareto-superior outcomes resulting in pareto improvements

Question 8

What is local nonsatiation?

Answer 8

The property of local nonsatiation of consumer preferences states that for any bundle of goods there is always another bundle of goods arbitrarily close that is preferred to it.[1] What this means is that a consumer always either prefers more of an item or less of an item, never a particular amount of a good. An additional requirement is that there is some good that consumer does prefer more of.

Question 9

How can you derive the demand function for each consumer in a 2x2 exchange economy?

Answer 9

1) maximize each consumer’s utility function uᵢ, subject to the budget constraint Σ pₗ xₗᵢ = ωᵢ
2) plug result back into budget constraint and utility function

Question 10

How do you calculate all pareto optimal allocations in a 2x2 exchange economy?

Answer 10

all pareto optimal allocations:

1) find where the indifference curves are tangent i.e. the slopes (MRS) are equal
- > slopes: marg. utility from good 1 / marg. utility from good 2 = [ ∂ u / ∂ x1i ] / [∂ u / ∂ x2i]
2) use the budget constraint (all endowments = all available goods)
3) plug in the solutions for the goods from the budget constraints to get the solutions for which allocations will be pareto optimal

Question 11

How do you calculate the MRS (marginal rate of substitution)?

Answer 11

marginal utility of good 1 / marginal utility of good 2

Question 12

How do you calculate aggregate demand in a competitive market?

Answer 12

You maximize the individual consumer’s preferences and then sum them up.

Question 13

How does the market equilibrium “demand = supply” translate to in the competitive market?

Answer 13

Final consumption = endowment + production