Week 1

Question 1

What are Barter Economies?

Answer 1

An economy where people don’t trade with money but with goods.

Question 2

What is e^i?

Answer 2

The consumers initial endowment of goods before barter

Question 3

What is x^i

Answer 3

The consumption after barter

Question 4

What is E?

Answer 4

The set of feasible allocations

Question 5

What is e^(bar)?

Answer 5

The positive vector of total initial endowments

Question 6

What is an Edgeworth box?

Answer 6

A box with two consumers and two goods, where each point represents a combination for any feasible combination

Question 7

What is the definition of a Pareto improvement?

Answer 7

Feasible addition x^hat = (x^{hat, A}, x^{hat, B}) ∈ E is a Pareto improvement with respect to feasible allocation x = (x^A, x^B) ∈ E if u_i(x^{hat, i}) ≥ u_i(xⁱ) for all i ∈ {A, B} and there’s a player j ∈ {A, B} for whom u_j(x^{hat, j}) > u_j(x^j)

Question 8

When is something Pareto efficient?

Answer 8

Feasible allocation x = (x^A, x^B) ∈ E is Pareto efficient if no Pareto improvement x^hat = (x^{hat, A}, x^{hat, B}) ∈ E exists

Question 9

What is w_i?

Answer 9

The weight of player i, the sum of all weights must be 1

Question 10

What is the weighed utility function?

Answer 10

𝝨_i∈Nw_iu_i

Question 11

What is X(w)?

Answer 11

arg max_x∈E𝝨w_iu_i(xⁱ) is the set of maximizers in E of the weighed utility function with vector of weights w

Question 12

When is every Feasible allocation Pareto efficient?

Answer 12

If u_A and u_B are continuous utility functions and w = (w_A, w_B) > 0 then X(w) != ⦰ and every feasible allocation x ∈ X(w) is Pareto efficient

Question 13

When is something Pareto inefficient?

Answer 13

If an Pareto improvement is available

Question 14

How to calculate Pareto efficient allocations?

Answer 14

1. Set the weights (𝛾, 1 -𝛾) with 𝛾 ∈ (0, 1)
2. Derive on x_k
3. Equate to 0
4. Solve for x_k(𝛾)

Question 15

When does x maximize the weighed utility function?

Answer 15

If MU₁^A(x^A)/MU₂^A(x^A) = MU₁^B(x^B)/MU₂^B(x^B​) > 0

Question 16

What is a market?

Answer 16

An institution with estabilished property rights, commercial law and merchants

Question 17

How do you calculate the general equilibrium price and the general equilibrium allocation?

Answer 17

1. Calculate/Get the demand vector d^A(p, e^A), and d^B(p, e^B)
2. Solve d^A(p, e^A) + d^B(p, e^B) = e^(bar)

Question 18

How to get the demand function?

Answer 18

1. Just use from last period d^A(.., ..) using MU/MU, however p₁x₁ + p₂x₂ = e^A p

Note e^A and p are vectors

Question 19

How is value determined?

Answer 19

Value is always defined in comparison to some something else, so price ratios matter, rather then price levels

Question 20

What is Walras’ Law?

Answer 20

For all p ∈ R₊^m: p * z(p) = 0

This holds for all p, both equilibrium as out-of-equilibrium prices.

Question 21

What is the First Fundemental Theorem of Welfare Economics?

Answer 21

If each utility function uⁱ, i ∈ N, is increasing and (p, x) forms a general equilibrium, then allocation x is Pareto efficient.

Question 22

What is the Second Fundemental Theorem of Welfare Economics?

Answer 22

If uⁱ is an icreasing and strictly quasi-concave utility function, then every feasible allocation x^(hat) on the contract curve is supportable as a general equilibrium with lumpsum wealth redistribution.

Question 23

When does a general equilibrium price vector exists with p*> 0?

Answer 23

If all utility function uⁱ, i in N, are increasing, strictly quasi concave and continuous, then p* in P is a general equilibrium price vector iff. f(p*) = p*. Moreover, any fixed point p*>0. Most importantly, there exists a general equilibrium price vector p*.