Term 2 Lecture 9 Flashcards
(21 cards)
Summary: if we put consumers together and allow them to trade then we can
Ask whether prices will exist that lead all markets to clear, if so whether this provides a sensible or illuminating theory of price determination
- adding profit-maximising producers to the picture turns out not to complicate matters unmanageably
Suppose the economy consists of H households
- hth household has endowment wh and consumes a bundle qh
An allocation of goods is said to be feasible if the aggregate amount consumed of each good equals the aggregate endowment
SUM(qih) = SUM(wih), i = 1,2,…,H
A diagrammatic representation of exchange equilibrium for a two-person, two-good economy is the Edgeworth-Bowley Box
- shape
- initial endowment
- ICs?
- rectangular box where: the horizontal and vertical dimensions represent the total endowments of two goods
- each point in the box represents a possible allocation of goods between the two individuals
- initial endowment point is also inside the box, representing one possible allocation
- indifference curves can be inside the box, there are also some Pareto superior allocations within
Setting a price vector for the economy in Edgeworth-Bowley Box
Defines a common budget constraint passing through the endowment point, representing trading possibilities for the two
- as usual, allocation points will be at where IC are tangent to budget constraint
- if prices are set arbitrarily, rather than by market forces, then there will be excess supply or excess demand
Individual demand as a function of price
Each household has demands a certain amount of good i, denoted as:
- qih = fih(p0wh,p)
- p0wh is the value of the households endowment at initial prices
- p represents the vector of market prices for all goods
- fih is the demand function for good i from household h
So each households demand depends on both market prices and their initial wealth, so demand functions can differ
Market demand
Found by adding the demands across individuals:
Q(p’w1,p’w2,…,p) = SUMfih(p’wh,p)
- market demand depends on both prices and the entire distribution of endowments across households
- if two economies have the same total wealth but different distributions of endowments, their aggregate demand could still be different
Excess demand
Aggregate excess demand is given by the excess market demand over the sum of endowments
SUM(zih) = SUM[fih(p’wh,p) - wih]
If positive, excess demand
If negative, excess supply
General equilibrium/ Market equilibrium / Competitive equilibrium / Walrasian equilibrium
Set of prices such that aggregate excess demand is 0 on all markets
- Zi = SUM(zih) = 0
Walras’ Law
States the sum of the value of excess demands across all goods is always 0
- SUMpiZi(p) = 0
Proof:
- each household operates within a budget constraint, meaning the value of what they consume equals the value of their initial endowment
- so excess demand per household is 0
- when summing over all households, total market’s aggregates excess demand must also satisfy this equation, leading to Walras’ Law
Implications of Walras’ Law
- even though there are M goods lets say
- only M-1 excess demands are independent, as if all but one market clear, then the last must also clear systematically.
Why are only relative prices determined?
- if you multiply all prices by any positive number, the excess demands remain unchanged
- in a two-good economy, choosing the price of one good automatically determines the other
What guarantees the existence of Walrasian Equilbrium:
- two good case
- a key result in GE theory states that if AD functions change smoothly with prices, then an equilibrum must exist
- if price ratio p1/p2 is too low, good 1 cheap so ED, and vice versa, so as they vary continuously, there must be some intermediate price ratio where excess demand is exactly 0 - market clears.
- as prices change, individuals move along their offer curves, so equilibrium is where these offer curve cross.
Role of individual preferences in existence of WE
- if well-behaved, IC will be convex and downward-sloping
- demand functions will be continuous, as will excess demand functions, so as they are continuous, there must be existence of equilibrium
After guaranteeing existence of war, is it unique?
- multiple equilibria can arise when offer curves cross multiple times
- stale equilibrium requires a well-behaved price adjustment mechanism, as even if EQ exists, need to know whether economy will naturally move towards it when out of EQ
Introducing Production into the economy
K firms, price takers
- each firm chooses a production plan yk to max profits, given its tech
- Max piK = p’yk s.t. Yk technologically feasible, yk being outputs and inputs
- firms not assumed to have same technology
- firms rely on inputs to production from consumers and labour supply, transforming this into output.
Firms are owned by consumers
- new budget constraint for households
- profit distribution across all households
P’qh < p’wh + SUM(Thk.Pik)
- p’qh is the value of consumption for household h
- p’wh is the value of the households initial endowments
- summation is the profits received from firm ownership, Thk being the share owned of the kth firm
- it is assumed all firm profits are distributed among consumers
Redefine aggregate excess demand given firm production
Zi(p) = SUM( qih - wih ) - SUM ( yik )
- so (total consumption - total endowments) - (total production)
- even with production and firm ownership, Walras’ Law remains valid still
Robinson Crusoe Economy
- simplify economy to single agent who acts as both consumer and firm
- one person decides labour L supply, output Q to produce, how much to consume, c
- model considers two goods, Labour L and Output Q
Firm’s profit maximisation under a Robinson Crusoe Economy
Production function: Q = F(L)
- wage rate w, output price p
Profit function: pF(L) - wL
- maximised at F’(L) = w/p, so firm hires labour until the MPL equals the real wage
Consumer optimisation under RC economy
As a consumer, RC chooses labour and consumption to maximise utility
- optimal decision is when the MRS between leisure and consumption = real wage
Real world limitations of GE assumptions
- market power exists
- frictions may prevent market clearing
- non price interdependencies
- externalities/ public goods
