EC2A3 Exam Notes
EC2A3 Exam Notes
,EC2A3 Exam Notes
Market System: Week 1
System for producing, allocating goods with price signals: relative price, force trade offs
Decentralisation: people not coordinated explicitly on production/consumption
Self-Interest: people maximising own benefits, do not intrinsically care about others
Equilibriums:
→ Partial Eq. Analysis: study of equilibrium in 1 market isolation
→ General Eq. Analysis: demand, supply conditions interact in several markets to determine price of
goods and factor price of production (not solely market)
Good: broad definition, assume complete markets of all types of variants available - market (traded at
defined prices), non-market (home, gov. production, some non profits)
Role of Government: enforce property rights, enforce trades at agreed prices → fundamental for market,
no guarantee
Exchange Economy: 2 consumers (A, B), goods (X, Y), price takers, endowed (no production)
Edgeworth Box
Combine indifference of 2 consumers → fixed allocation (endowment E), total goods in economy X/Y axis
(→ When government redistribute: welfare (goods) loss)
Core: all allocations which makes A and B strictly better off (both
can increase UA, UB) through trading starting at E (constraint limit
on goods)
P: once reach tangency through mutually improving trade - pareto
efficient point (no one better without anyone worse)
→ MRSA = MRSB
Contract Curve
Locus of P (pareto efficient, tangency points), solution depends on
limit constraint E
𝑑𝑢/𝑑𝑥 1 𝑝1
EC1A3: [𝑀𝑅𝑆 = = ]
𝑑𝑢/𝑑𝑥 𝑝
2 2
,EC2A3 Exam Notes
Market Mechanism: competitive market, as if “auctioneer” presents price and agents decide
quantity to buy/sell (allows modelling of agents as price taker, end up on contact curve)
→ 2 agents realistically may bargain, have market power → if model extended to multiple A/B types:
small enough share of overall endowment to be price taker (solves problem)
General Equilibrium (Walrasian): unique vector of prices and consumption bundles (after trading) s.t
→ Every consumer max U given price → Market clears: total Demand = aggregate E
𝑝𝑥
Relative Price: (terms of trade) that clears market - set numeraire p = 1 and solve for p
𝑝 y x
𝑦
→ Changes with preferences/economy evolves
Walras’ Law: in n markets, if n-1 in equilibrium → so is the nth
→ GE: at point px/py = MRSA = MRSB, goes through endowment E
→ Not necessarily equitable: “Pareto optimal and still perfectly
disgusting” - Sen
→ Central Planners: do not know preferences
, EC2A3 Exam Notes
General Competitive Equilibrium: Week 2
GCE: vector of prices and consumption bundle for each consumer (allocations) (above)
Lagrangian Method: 𝑚𝑎𝑥 𝑈(𝑥, 𝑦) with constraint 𝑝 𝑋 + 𝑝 𝑌 ≤ 𝑀 (in E economy = pxEx + …)
𝑥 𝑦
Consumers (A/B) Demand: 𝑋 (𝑝 , 𝑝 ), 𝑌 (𝑝 , 𝑝 ) s.t 𝑋/𝑌 + 𝑋/𝑌 = 𝐸
𝐴/𝐵 𝑥 𝑦 𝐴/𝐵 𝑥 𝑦 𝐴 𝐵 𝑋/𝑌
→ Differentiate (for MRS), solve for one market (X/Y) to solve for GCE price (Walras), allocations, welfares
𝐿 = 𝑈(𝑋, 𝑌) − λ(𝑝 𝑋 + 𝑝 𝑌 − 𝑚) → maximise (partial derivatives)
𝑥 𝑦
⇒ 𝑑𝐿 : 𝑑𝑈 − λ𝑝 = 0 Remove λ by dividing through (dU/dx)/(dU/dy)
𝑑𝑋 𝑑𝑋
𝑥
⇒ 𝑑𝐿 : 𝑑𝑈 − λ𝑝 = 0 = MRS = px/py
𝑑𝑌 𝑑𝑌
𝑌
⇒ 𝑑𝐿 : 𝑝 𝑋 + 𝑝 𝑌 − 𝑚 = 0 : MU of income
𝑑λ 𝑥 𝑦
For GCE to exist need:
→ Convex demand preferences - if not can exist tangent
allocation ≠ max U
→ Many consumers in market - consumers may have discont.
demands but small relative to market
→ Continuous demand functions - no jumps (satisfied with
either of above conditions)
1st Fundamental Welfare Theorem: competitive market mechanisms result in Pareto-efficient allocations
(reach GCE from any endowment E),
Assumes:
→ Agents only care about own consumption - no externalities → Agents behave competitively
→ Antitrust, property rights → decentralised market function → Small market share (cont. AD)
Implies: Laissez faire, competitive market ensures efficient allocation, justifies competition,
environmental policy
→ Consumers need only know prices and own preferences to reach GCE from endowment (economy of
informational requirements)
2nd Fundamental Welfare Theorem: if preferences convex, then any PE allocation can be achieved (GCE)
→ Only depends on initial E → trade, manipulate
→ Arise discussions of which allocation more preferable
→ Government do not know individual preferences,
reallocation only deals with wealth
EC2A3 Exam Notes
,EC2A3 Exam Notes
Market System: Week 1
System for producing, allocating goods with price signals: relative price, force trade offs
Decentralisation: people not coordinated explicitly on production/consumption
Self-Interest: people maximising own benefits, do not intrinsically care about others
Equilibriums:
→ Partial Eq. Analysis: study of equilibrium in 1 market isolation
→ General Eq. Analysis: demand, supply conditions interact in several markets to determine price of
goods and factor price of production (not solely market)
Good: broad definition, assume complete markets of all types of variants available - market (traded at
defined prices), non-market (home, gov. production, some non profits)
Role of Government: enforce property rights, enforce trades at agreed prices → fundamental for market,
no guarantee
Exchange Economy: 2 consumers (A, B), goods (X, Y), price takers, endowed (no production)
Edgeworth Box
Combine indifference of 2 consumers → fixed allocation (endowment E), total goods in economy X/Y axis
(→ When government redistribute: welfare (goods) loss)
Core: all allocations which makes A and B strictly better off (both
can increase UA, UB) through trading starting at E (constraint limit
on goods)
P: once reach tangency through mutually improving trade - pareto
efficient point (no one better without anyone worse)
→ MRSA = MRSB
Contract Curve
Locus of P (pareto efficient, tangency points), solution depends on
limit constraint E
𝑑𝑢/𝑑𝑥 1 𝑝1
EC1A3: [𝑀𝑅𝑆 = = ]
𝑑𝑢/𝑑𝑥 𝑝
2 2
,EC2A3 Exam Notes
Market Mechanism: competitive market, as if “auctioneer” presents price and agents decide
quantity to buy/sell (allows modelling of agents as price taker, end up on contact curve)
→ 2 agents realistically may bargain, have market power → if model extended to multiple A/B types:
small enough share of overall endowment to be price taker (solves problem)
General Equilibrium (Walrasian): unique vector of prices and consumption bundles (after trading) s.t
→ Every consumer max U given price → Market clears: total Demand = aggregate E
𝑝𝑥
Relative Price: (terms of trade) that clears market - set numeraire p = 1 and solve for p
𝑝 y x
𝑦
→ Changes with preferences/economy evolves
Walras’ Law: in n markets, if n-1 in equilibrium → so is the nth
→ GE: at point px/py = MRSA = MRSB, goes through endowment E
→ Not necessarily equitable: “Pareto optimal and still perfectly
disgusting” - Sen
→ Central Planners: do not know preferences
, EC2A3 Exam Notes
General Competitive Equilibrium: Week 2
GCE: vector of prices and consumption bundle for each consumer (allocations) (above)
Lagrangian Method: 𝑚𝑎𝑥 𝑈(𝑥, 𝑦) with constraint 𝑝 𝑋 + 𝑝 𝑌 ≤ 𝑀 (in E economy = pxEx + …)
𝑥 𝑦
Consumers (A/B) Demand: 𝑋 (𝑝 , 𝑝 ), 𝑌 (𝑝 , 𝑝 ) s.t 𝑋/𝑌 + 𝑋/𝑌 = 𝐸
𝐴/𝐵 𝑥 𝑦 𝐴/𝐵 𝑥 𝑦 𝐴 𝐵 𝑋/𝑌
→ Differentiate (for MRS), solve for one market (X/Y) to solve for GCE price (Walras), allocations, welfares
𝐿 = 𝑈(𝑋, 𝑌) − λ(𝑝 𝑋 + 𝑝 𝑌 − 𝑚) → maximise (partial derivatives)
𝑥 𝑦
⇒ 𝑑𝐿 : 𝑑𝑈 − λ𝑝 = 0 Remove λ by dividing through (dU/dx)/(dU/dy)
𝑑𝑋 𝑑𝑋
𝑥
⇒ 𝑑𝐿 : 𝑑𝑈 − λ𝑝 = 0 = MRS = px/py
𝑑𝑌 𝑑𝑌
𝑌
⇒ 𝑑𝐿 : 𝑝 𝑋 + 𝑝 𝑌 − 𝑚 = 0 : MU of income
𝑑λ 𝑥 𝑦
For GCE to exist need:
→ Convex demand preferences - if not can exist tangent
allocation ≠ max U
→ Many consumers in market - consumers may have discont.
demands but small relative to market
→ Continuous demand functions - no jumps (satisfied with
either of above conditions)
1st Fundamental Welfare Theorem: competitive market mechanisms result in Pareto-efficient allocations
(reach GCE from any endowment E),
Assumes:
→ Agents only care about own consumption - no externalities → Agents behave competitively
→ Antitrust, property rights → decentralised market function → Small market share (cont. AD)
Implies: Laissez faire, competitive market ensures efficient allocation, justifies competition,
environmental policy
→ Consumers need only know prices and own preferences to reach GCE from endowment (economy of
informational requirements)
2nd Fundamental Welfare Theorem: if preferences convex, then any PE allocation can be achieved (GCE)
→ Only depends on initial E → trade, manipulate
→ Arise discussions of which allocation more preferable
→ Government do not know individual preferences,
reallocation only deals with wealth
