General Equilibrium

Question 1

What is a walrasian equilibrium?

Answer 1

a competitive equilibrium in an exchange economy

Question 2

What is the general main result in an exchange economy?

Answer 2

Suppose that in an exchange economy, consumers’ preferences are continuous,
monotonic, and convex, and each consumer is endowed with a positive amount of each good (𝒘 > 𝟎).
Competitive equilibrium exists

Question 3

What is Walras’ law

Answer 3

𝒑 ∙ 𝒛(𝒑) = 𝑝1𝑧1 + 𝑝2𝑧2 = 0

(also by Walras’ law if one market clears, both will clear)

Question 4

What is the general main result in a production economy?

Answer 4

Suppose that in a production economy, consumers’ demands correspondences and firms’ net supply correspondences exist and are continuous, production is irreversible and there is free disposal, then… competitive equilibrium exists

Question 5

How much profit is there when there are multiple industries?

Answer 5

zero because CRS + competition: 𝑝𝑖 = 𝐴𝐶𝑖 = 𝑀𝐶𝑖

Question 6

What are general assumptions made in the multiple industries model?

Answer 6

• constant returns to scale
• Decreasing marginal returns to each factor
• Factors are perfectly mobile across sectors (same 𝑤 and 𝑟)
• Perfectly competitive markets for 𝐾 and 𝐿

Question 6

What is the maximization problem of consumers in an exchange economy?

Answer 6

max 𝑢𝑎(𝑥𝑎1, 𝑥𝑎2) subject to 𝑝1𝑥𝑎1 + 𝑝2𝑥𝑎2 ≤ 𝑝1𝑤𝑎1 + 𝑝2𝑤𝑎

Question 7

What is competitive equilibrium in an exchange economy?

Answer 7

Competitive equilibrium is (𝒙∗, 𝒑∗) such that
𝒙𝒂 (𝒑∗, 𝒑∗ ⋅ 𝒘𝒂) + 𝒙𝒃 (𝒑∗, 𝒑∗ ⋅ 𝒘𝒃) = 𝒘𝒂 + 𝒘𝒃

(In a competitive equilibrium MRSa = MRSb = p1/p2)

at equilibrium excess demands of all goods are zero so total demand = total amount of resources

Question 8

Define aggregate excess demand for good 1 as?

Answer 8

z1(p)=(x1a(p)-w1a) + (x1b(p)-w1b)

Question 9

what is a firms optimal choice when there are multiple industries

Answer 9

A firm’s optimal choice of 𝐾𝑖, 𝐿𝑖 minimizes costs subject to a
production constraint:
min𝐾𝑖,𝐿𝑖 {𝑤𝐿𝑖 + 𝑟𝐾𝑖} s. t. 𝐹𝑖 (𝐾𝑖, 𝐿𝑖) = 𝑌

Question 10

For firms what is the marginal rate of technical substitution equal to at the optimum?

Answer 10

The Marginal Rate of Technical Substitution (MRTS) is equal to the relative factor price

Question 11

What is the Rybczynski Theorem?

Answer 11

If relative prices are constant and if both goods continue to be produced, an increase in the supply of a factor will lead to an increase in the output of the good using this factor more intensively and a decrease in the output of the
other good.

Question 12

What is the Stolper-Samuelson Theorem?

Answer 12

If there are constant returns to scale and if both goods continue to be produced, an increase in the relative price of a good will increase the real return to the factor used intensively in that industry and reduce the real return to the other factor.

Question 13

What is the autarky budget?

Answer 13

consumer expenditure = firms’ sales = consumer budget

under autarky
production of each good = consumption of each good
MRS = MRT = Px/Py

Question 13

Key points about trade

Answer 13

-The ability of the country to trade at any world prices other than autarkic prices makes the consumer better off.
-Direction of trade is irrelevant for improving consumer’s utility.
-Specialization is not necessary for improvement