General Equilibrium & Welfare Flashcards
What are the two components of efficiency and what do they imply?
- Supply side: x,y is ON PPF (Technically efficient)
- Demand side: of all points on PPF, x,y provides greatest utility
- Slope of PPF (OC of goods in production) = Slope of U curve (rate at which people are willing to trade goods)
- First Theorem Of Welfare Economics
- Under certain conditions, competitive markets can achieve an efficient allocation of resources
- First Theorem Of Welfare Economics
What is the form of a PPF?
PPF = x2 + y2 = 100, X ≥ 0, Y ≥0
What is the working to find the slope of a PPF?
- To find slope of PPF, need the total differential of PPF: z = x2 + y2 = 100
- dz = ∂z/∂x .∆x + ∂z/∂y .∆y = 0
- ∂z/∂x .∆x = -( ∂z/∂y .∆y)
- Slope of PPF: ∆y/∆x = (∂z/∂x)/(∂z/∂y) = 2x/2y = -(x/y)
What is the price relation when there preferences are x = y and how is this different from other models?
- Perfect Substitutes
- Sub preferences into PPF:
- x2 + y2 = 100
- x2 + x2 = 100
- 2x2 = 100
- x = sqr(50) = y
- slope of price is -1
- Unlike consumption model, doesn’t mean the economy only produces one of the goods
What is the price relation when there preferences are x = 2y?
- Sub preferences into PPF:
- x2 + y2 = 100
- (2y)2 + y2 = 100
- 4y2+ y2 = 100
- 5y2 = 100
- y = sqr(20)
- x = 2(sqr(20))
- Slope of price is -2/1
What is the price relation when there preferences are x = 3y?
- Px/Py = 1/3
- Set equal to slope of PPF
- -x/y = 1/3, 3x = y
- Plug 3x = y into PPF
What is the Edgeworth Box model?
- Equity
What are the specifications of an Edgeworth Box?
- Box contains all possible allocations of goods
- Production is fixed at ‘size’ of box
- All goods are fully allocated - D = S
- As we move away from an individuals origin the level of utility increases
How can consumption efficiency be determined in the Edgeworth Box model?
- Given an endowment we need to determine if consumption efficiency is achieved for the two consumers
- To do this, need to find a set of prices such that:
- Given this set of prices our 2 consumers maximise their utility
- Quantity supplied = quantity demanded for both goods
What is the importance of the price change mechanism in Edgeworth Box analysis?
- At initial point e, the MRS of the two indifference curves are not equal, not tangent
- This means there is room for trade to improve at least one of the consumers
- i.e. room for pareto improvement
What is a trading lens?
- Anywhere within will bring pareto improvement
- The point in the middle is equal improvement and pareto efficient
What is a contract curve and what does it imply about pareto eqm?
- All points on curve have MRS’s equal to each other and to the given price ratio
- i.e. the contract curve shows all the pareto efficient points
- From e, consumers will trade within themselves and move to a pareto efficient point on the contract curve between the two indifference curves
- The pareto equilibrium we arrive at depends on the starting point
What is the First Fundamental Theorem Of Welfare Economics?
- Any competitive equilibrium is going to be a Pareto Equilibrium
- When there is price taking behaviour on both sides, allocation of resources is perfect: consumption efficient, production efficient and allocative efficient
What is pareto eqm?
- Pareto - have exhausted all possible voluntary trades that allow one consumer to be better off without hurting another one
- Can’t move from this point without hurting one consumer
What are the components of the First Fundamental Theorem of Welfare Economics?
- Consumption Efficient
- Given price takers and face same prices
- MRSsmith = MRSjones = Px/Py
- Consumption Efficient
- Production Efficiency
- Given prices takers and face same input costs
- MRTSx = w/v = MRTSy
- Production Efficiency
- Allocative efficiency
- Px = MCx
- Py = MCy
- MCx/MCy = Px/Py = MRTSy,x = MRSy,x
- Allocative efficiency
What is the major implication of Welfare Economics analysis?
- We can’t necessarily choose a particular pareto efficient outcome
- The competitive equilibrium that we end up at depends on initial endowment
What is the Second Fundamental Theorem of Welfare Economics?
Any pareto efficient equilibrium can be obtained by competition, given an appropriate initial endowment
What is important in PPF eqm questions?
Px/Py - assign axis properly!
How is the PPF related to the price line in PPF eqm?
Slope of PPF = X/Y
Price ratio = Px/Py
Therefore the ratio to plug into the PPF to find the eqm point is simply the price ratio
What does excess S/D lead to?
Excess S leads to decrease in price
Excess D leads to increase in price
How is indifference integrated into a PPF eqm question?
Tangent to the PPF at the correct ratio (i.e. plug in MRS ratio into PPF ratio)
Cost curve and therefore PPF location will move towards this point
What does excess supply of Y and excess demand of X cause to happen to the price ratio in PPF eqm?
Py decrease
Px increase
What are the steps to a PPF eqm question?
- Draw PPF, intercepts
- Find point where Px/Py = PPF by plugging in and draw
- Find point where MRS = PPF by plugging in and draw
- Describe change to price ratio to reach eqm
What are the steps to an Edgeworth Box question (perfect complements)?
- Draw Grid
- Make POINTS from preferences (i.e. 1,2 - 2,4 - 3,6 etc)
- Draw U curves (POINTS are corners)
- Identify U curves that intersect Endowment
- Identify CORNER POINTS where pareto improvements are possible
