Summary Oxford University FHS Microeconomics Revision Pack

Microeconomics- Takeaway Notes

General Equilibrium

Topic Takeaway Diagram
Competitive  No Frictions- no externalities, taxes, market failures, etc
Equilibrium  No market power- all are price takers
Assumptions
Edgeworth  X axis is total endowment of x1
Box  Y axis is total endowment of x2
 A maximises

 B maximises


 As we are dealing with relative prices, there is the same
budget constraint for both
 Graph shows excess demand for x1 and excess supply
for good 2 therefore should increase price of good 1
relative to good 2
Competitive  Partial equilibrium is supply=demand for only one
Equilibrium market whilst a general equilibrium looks at all markets
and whether they clear simultaneously
 For a consumer facing two goods: consumption ≤
endowment
 If consumer preferences are continuous, monotonic &
convex, and w>0, a competitive equilibrium exists
 The CE is where MRSa= MRSb = p1/p (Pareto efficiency
and where market clears)- the point where the IC curves
and budget line are all tangential

,  MRSa= - MUx/MUy
 CE is where the price of each good s.t total demand is
equal to total endowment (endowment is exhausted)
 A competitive equilibrium must specify an allocation
AND a price vector.
 NOTE: Ce is not simply where total demand= total
endowment because, if there is excess supply in one
market, there is excess demand in the other
 General Competitive Equilibrium: firms max profits,
profits distributed to households, households max utility
subject to budget constraint, all markets clear.
 Walras’s Law: if there is excess demand in one market,
then there is always excess supply in the other. If there
is equilibrium in one market, there is equilibrium in the
other. If there are n markets and n-1 are in equilibrium,
the nth will also be in equilibrium, since there is no
money from other markets to overspend or underspend
in the nth market
 NOTE: with quasi-linear utility, any efficient outcome
will entail the same allocation of the non-linear good
(provided initial wealth is high enough)
Calculating CE  The excess demand will be zero at the CE
 The CE can be calculated by setting p2=1 and dealing
with p1 as, if one market clears, both will clear
 When using a Lagrangian to solve, put the lambda as
positive and then subtract the spending from the
income (m-c) so that we can interpret lambda x m
economically if it is positive
 Lambda is the marginal cost of overspending & the
marginal utility of income

,  For a Cobb-Douglas consumer, always spends constant
faction of each good, given by the power on each good.
Production  In a model with one firm and one consumer CE exists if
Economy consumer demand & firm supply correspondences exist
and are continuous, production is irreversible and there
is free disposal of unnecessary output or inputs at no
cost
 Consumer owns the firm and its profits and has an
endowment- unit of leisure R with utility u(x,R) where
R=1-L
 Firm has production function F(L), pays wage w to the
consumer and produces good x at price p
 Consumer maximises


 Firm maximises

 The endowment E is where profit+ max labour income =
(1, profit) in diagram IRS
 For a CE:
o MRS = MRT – Allocative Efficiency
o MRS = w/p – Productive Efficiency
 If IRS, no CE as utility curve is non-convex so none of the
points are a CE
o Needs more sophisticated pricing structure
 Note: a tax on a wage income would place a wedge
between the consumer’s MRS and the producer’s MRT

, Multiple  2 producers with factors capital (K) and Labour (L)
Industries  Cost of K is r & cost of L is w
Model  Good X is labour intensive and the other is capital
intensive
 Assumes, CRS & competitive markets for both K&L (zero
profits)
 At optimum, MRTS= w/r
 Due to CRS assumption, the optimal K/L ratio does not
depend on the scale.
 For each firm, optimal choice of K,L minimises costs s.t
production constraints


 With Multiple industries, the optimal choice of K & L is
at the intersection of the two firms’ optimal choice
lines. Green and red line represent the firms’ optimal
K/L ratio given a certain w/r ratio. It is straight due to
CRS.
 Curved purple line is the contract curve
Rybczynski  If relative prices are constant and if both goods continue
Theorem to be produced, an increase in the supply of an input
(e.g. increase migration) will increase output of good
using this factor more intensively and a decrease in the
other one
 Optimal choices of industry Y just move to new origin,
slope will be the same
 If the supply of L increases, more of good X will be
produced and less of good Y