General Equilibrium: Concept Guide
Cheat Sheet based on Varian’s Microeconomics
1. The Exchange Economy Intuition: Since every agent satisfies their budget con-
straint, the economy as a whole satisfies a budget con-
We analyze how two consumers (A, B) trade two goods straint. Implication: If there are k markets and k − 1
(1, 2) given initial endowments (ω). clear, the k-th market must also clear. We can discard
one market equation when solving.
The Edgeworth Box
4. Welfare Theorems
A graphical representation of all possible allocations.
• Dimensions: Width = Total Good 1 (ω̄1 ); Height = The theoretical link between markets and efficiency.
Total Good 2 (ω̄2 ).
First Fundamental Theorem
• Feasible Allocation: Any point inside the box
where xA + xB = ω̄. All competitive market equilibria are Pareto Efficient.
Pareto Efficiency • Assumes: No externalities, perfect competition.
An allocation is Pareto Efficient if it is impossible to make • Meaning: Decentralized markets lead to efficient out-
one person better off without making the other worse off. comes without central planning.
• Graphically: Where Indifference Curves are tangent. Second Fundamental Theorem
• Algebraically: Where slopes are equal.
Any Pareto Efficient allocation can be supported as a com-
petitive equilibrium with lump-sum transfers.
M RSA = M RSB
• Assumes: Convex preferences (diminishing MRS).
Contract Curve: The locus of all Pareto Efficient allo-
cations. Trade should always end here. • Meaning: Equity and efficiency can be separated. We
can redistribute wealth (change ω) and then let the
market achieve efficiency.
2. Market Equilibrium
Also called Walrasian Equilibrium. Prices adjust until 5. Production (Robinson Crusoe)
supply equals demand.
We add a firm. The firm produces Good 1 using Good 2
Conditions for Equilibrium (p∗1 , p∗2 ) (Labor).
1. Optimization: Each consumer maximizes utility Production Possibilities Frontier (PPF)
given prices (M RS = −p1 /p2 ). 2. Market Clearing:
Total demand equals total endowment for every good. The boundary of feasible production sets.
xA B A B
1 + x1 = ω1 + ω1
• Slope: Marginal Rate of Transformation (MRT).
xA
2 + xB
2 = ω2A + ω2B M C1
M RT =
M C2
Gross vs. Net Demand
Efficiency Condition
• Gross (x): What you consume.
For an economy to be efficient, the rate at which con-
• Net (e): What you trade (x − ω). sumers want to trade must equal the rate at which firms
can trade.
3. Walras’ Law
M RS = M RT
The value of aggregate excess demand is identically zero
In a competitive market, this happens because both equal
for any price vector p.
the price ratio:
p1 z1 (p) + p2 z2 (p) ≡ 0 p1
M RS = − = M RT
p2
1
Cheat Sheet based on Varian’s Microeconomics
1. The Exchange Economy Intuition: Since every agent satisfies their budget con-
straint, the economy as a whole satisfies a budget con-
We analyze how two consumers (A, B) trade two goods straint. Implication: If there are k markets and k − 1
(1, 2) given initial endowments (ω). clear, the k-th market must also clear. We can discard
one market equation when solving.
The Edgeworth Box
4. Welfare Theorems
A graphical representation of all possible allocations.
• Dimensions: Width = Total Good 1 (ω̄1 ); Height = The theoretical link between markets and efficiency.
Total Good 2 (ω̄2 ).
First Fundamental Theorem
• Feasible Allocation: Any point inside the box
where xA + xB = ω̄. All competitive market equilibria are Pareto Efficient.
Pareto Efficiency • Assumes: No externalities, perfect competition.
An allocation is Pareto Efficient if it is impossible to make • Meaning: Decentralized markets lead to efficient out-
one person better off without making the other worse off. comes without central planning.
• Graphically: Where Indifference Curves are tangent. Second Fundamental Theorem
• Algebraically: Where slopes are equal.
Any Pareto Efficient allocation can be supported as a com-
petitive equilibrium with lump-sum transfers.
M RSA = M RSB
• Assumes: Convex preferences (diminishing MRS).
Contract Curve: The locus of all Pareto Efficient allo-
cations. Trade should always end here. • Meaning: Equity and efficiency can be separated. We
can redistribute wealth (change ω) and then let the
market achieve efficiency.
2. Market Equilibrium
Also called Walrasian Equilibrium. Prices adjust until 5. Production (Robinson Crusoe)
supply equals demand.
We add a firm. The firm produces Good 1 using Good 2
Conditions for Equilibrium (p∗1 , p∗2 ) (Labor).
1. Optimization: Each consumer maximizes utility Production Possibilities Frontier (PPF)
given prices (M RS = −p1 /p2 ). 2. Market Clearing:
Total demand equals total endowment for every good. The boundary of feasible production sets.
xA B A B
1 + x1 = ω1 + ω1
• Slope: Marginal Rate of Transformation (MRT).
xA
2 + xB
2 = ω2A + ω2B M C1
M RT =
M C2
Gross vs. Net Demand
Efficiency Condition
• Gross (x): What you consume.
For an economy to be efficient, the rate at which con-
• Net (e): What you trade (x − ω). sumers want to trade must equal the rate at which firms
can trade.
3. Walras’ Law
M RS = M RT
The value of aggregate excess demand is identically zero
In a competitive market, this happens because both equal
for any price vector p.
the price ratio:
p1 z1 (p) + p2 z2 (p) ≡ 0 p1
M RS = − = M RT
p2
1
