General Equilibrium and Welfare Economics Flashcards
Partial Equilibrium
Looks at one market at a time in isolation
General Equilbrium
Looks at all markets together, and how they are interconnected. Everything is endogenous
Market clearing
demand=supply
Solving a simple general equilibrium model
- Define the allocation
- Feasible allocation to be pareto optimal iff there is does not exist another feasible allocation
- Form the social planner problem (max utility s.t. the constraints)
- Form the Lagrangian
- Derive the first order conditions.
Marginal Product of Labour
δG/δL
Marginal Product of Capital
δH/δK
Marginal Technical Rate of Substitution
δG/La / δG/δKa
Slope of isoquant of production
Production Efficiency
MTRSa=MTRSb
Marginal Utility of A1 for person 1
δU1/δA1
Marginal Utility of A2 for person 2
δU2/δA2
Marginal Utility of B1 for person 1
δU1/δB1
Marginal Utility of B2 for person 2
δU2/δB2
Marginal rate of Substitution for person 1
Marginal Utility of A1/Marginal Utility of B1
Consumption efficiency
MRS1=MRS2
Overal efficiency
Brings together the production side and consumer side.
MRS = MRT
Marginal rate of transformation
Slope of the PPF curve
δH/δLb /δG/La = δH/δKb / δG/δKa
Working through a general competitive equilibrium
Worked out as a vector of prices and utility. Also have the market clearing functions.
- work out the first order conditions wrt to the consumers. my maximising their utility and forming a lagrangian
- The do the same for the producers by maximising their profit function and finding the first order conditions.
- Work through to see if they satisfy consumption, production and overall efficiency
First theorem of welfare economics
A general competitive equilibrium allocation is Pareto Optimal. i.e. all three of the criteria (overall, production and consumption) are satisfied.
Second Theorem of Welfare economics
Any pareto optimal allocation can be obtained via a general competitive equilibrium provided the government is able to implement the required system of lump sum (non distortionary) taxes and transfers.
Failure of welfare theorems lies in…
Distortionary taxation
Example of distortionary taxation
where the government places a tax on labour income of t in sector A so firm A has to pay (1+t)pL for labour whilst consumers/workers receive only pL. Tax revenue of tpL goes to the government. This then affects the production efficiency of the market.
Another example where the welfare economics fails…
Externalities
Negative consumption externality
When consumption of some goods by some consumers adversely affects the welfare of other consumers. eg smoking or loud music
What effect does an negative consumption externality have
It changes the first order conditions
Overall efficiency with externality
MRS1>MRS2=MRT
when negative externality A1 hurts person 2
Another failure of welfare economics
public goods
What is a public good?
A good x is said to be a public good if consumption of x by one person does not preclude consumption of x by another person, and no one can be excluded from consuming x
non rival and non exclusive
How does the fact that good A may be a public good affect the set up of the constrained optimisation problem?
As total supply of A is the same as A1 or A2 there is no need to split the consumption as such A=A1=A2. This then means we have less FOCs
What conditions are satisfied if there is a public good present?
Overall and production
Stopler-Samuelson Theorem
An increase in pa/pb increases the real wage rate and decreases the real rental rate
Rybeynski Theorem
1) An increase in K results in an increase in production of the capital intensive commodity B and a decrease in the production of the labour intensive commodity A.
2) An increase in L results in a decrease in the capital intensive commodity B and an increase in the labour intensive commodity A.
Assumptions of the 2x2 model
1) G(.) and H(.) exhibit constant returns to scale
2) Sector B is capital intensive and Sector A is labour intensive
