These notes were prepared based on the lectures and supplemented by information from textbooks and tutorials where parts of the lecture were unclear. Graphs, equations, and bullet-point explanations included. Prepared by a first class Economics and Management student for the FHS Microeconomics pape...
MT1 Microecons (General Equilibrium)
What would we like to know?
What is an equilibrium when there are multiple markets, and what does it look like?
How do goods markets interact with factor (input) markets?
Can we ensure that an equilibrium exists, that it's unique, and that there's a reasonable process
for getting there?
What are the welfare properties of an equilibrium?
We will look at
2-person exchange economies with two goods
Robinson Crusoe economies: one person, who both produces and consumes
Two issues in international trade: how changes in goods prices affect factor prices, and how
changes in resource endowments affect production patterns
How opening up an economy to international trade expands consumption possibilities and leads
to some specialization in production
How to find a general equilibrium, and some thoughts on existence and uniqueness
Lecture 1: General Equilibrium Introduction
Outline
The Edgeworth box
General equilibrium framework
Existence of competitive equilibrium in exchange economy
Extension to production economy with one input factor and one good
From partial to general equilibrium
How price change of one product affects demand and supply for all other products
An economy is in general equilibrium if every market in the economy is in partial equilibrium
(including goods and factor markets)
General Equilibrium Model components
Households: demand goods, supply inputs (including capital via investment like share
ownership) and own firms.
Firms: hire inputs, produce goods, and earn profits which are distributed to households.
Markets where goods and inputs are traded.
General Equilibrium is also called Competitive Equilibrium and Walrasian Equilibrium.
Assumptions
No frictions: no externalities or distortionary taxes
Price-taking: no market power
Exchange Economy
Exchange Economy: households/consumers endowed with consumption goods, which they
trade among themselves. There is no production.
Setting it up:
, o Two goods: x1 and x2
o Two agents: Alice and Bob
o Alice and Bob have endowments of goods
o Alice and Bob maximize utility subject to their budget constraints
o They can trade goods between themselves without any distortions, such as taxes or
external costs, taking prices as given
Notation
o
o Demand depends on prices and income (given by p*w)
o Bold represents vectors
Alice's problem
o
o Maximise utility subject to consumption value ≤ endowment value
o Dotted lines show initial endowment point
o The constraint is a line through the initial endowment point, with a slope equal to the
price ratio (sell endowment of one good and buy the other good)
o Note how vector notation is used above
Bob's problem
o
Plotting and solving an Edgeworth box
, Edgeworth box
o
o Oa (origin for Alice) and Ob (origin for Bob)
o The height of the box is the total endowment of w 2 (𝑤2𝑎 + 𝑤2𝑏), while the length of the
box is the total endowment of w 1.
o Hence, the Edgeworth box is constructed such that the endowment points for both Alice
and Bob are at the same point in the box
o The black line is the budget constraint for both Alice and Bob. It cuts through their
endowment point and has the slope of the price ratio
o Blue points show Alice and Bob's optimum consumption (tangency of utility function
and constraint)
Not an equilibrium: markets do not clear due to a mismatch between demand and endowment
o Good 1: demand exceeds endowment (sum of blue lines exceeds the length of the box)
o Good 2: endowment exceeds demand (sum of blue lines is below the height of the box)
To ensure markets clear and get to equilibrium, change the goods' relative prices to rotate the
budget line such that total demand = total supply
, o Adjust towards the equilibrium by increasing p1 relative to p2
This reduces demand for good 1 which currently has excess demand, and
increases demand for good 2 which currently has excess endowment
The budget line rotates around the endowment point
Notice the 2 optimal tangency points go closer together
o Markets clear where both Alice and Bob's demand point overlap (purple point)
Competitive equilibrium is (𝒙*,𝒑*) such that:
𝒙𝒂 (𝒑*, 𝒑* ⋅ 𝒘𝒂) + 𝒙𝒃 (𝒑*, 𝒑* ⋅ 𝒘𝒃) = 𝒘𝒂 + 𝒘𝒃
In words, at equilibrium, Demand = endowment for both goods
The competitive equilibrium vector x* has 4 values (2 for Alice, 2 for
Bob). Competitive equilibrium includes information on prices and
demands.
Slopes of both utility functions = slope of the budget line
General main result: Suppose that in an exchange economy, consumers’ preferences are
continuous, monotonic, and convex, and 𝒘> 𝟎 then competitive equilibrium exists!
Assumptions for nicely behaved preferences
Continuous preferences (“No jumps”)
o No break in utility function
o Differentiable (can compute MRS)
Monotonic preferences (“More is better”):
o Utility is strictly increasing in both goods
o Binding budget constraint
Convex preferences (“Combinations are better”)
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