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
