12. General equilibrium



Contents
nassumptions of the model
nterm „efficiency“
nproduction possibility frontier
ngeneral equilibrium
ngeneral equilibrium formation and its change

Assumptions of the  model
nthere are only 2 consumers (A,B), with convex indifference curves
nthere are only 2 goods (X,Y)
nthere are only 2 firms – one produces X, the other produces Y, isoquants are convex
nthere are only 2 inputs (K,L)
nall  markets are perfect competition
nconsumers endeavour maximal TU, firms endeavour maximal economic profit
nthe economy is closed (without foreign trade)

Efficiency
nUpon general equilibrium there  must be fulfilled productive efficiency, exchange efficiency, and
productive-exchange efficiency
nProductive efficiency = such allocation of inputs when eventual reallocation would not lead to the
bigger total economy´s output
nExchange efficiency = such allocation of the goods, when eventual reallocation would not lead to
the bigger level of economy´s total utility
nProductive-exchange efficiency = such structure of production when its eventual change would not
lead to the bigger level of economy´s total utility
n Pareto efficiency

Production possibility frontier
nPPF = set of different combinations of goods possible to produce in the specific economy
nits position depends on:
n the volume of inputs (K,L)
n technological level (efficiency of use of K,L)
nits slope depends on the marginal productivity of labour (upon the given volume of capital and
technology)

PPF upon decreasing MPL
X
Y
PPF
E
A
B
L
TPL
QY
L
TPL
QX
Spot E represents productive efficient combination of X and Y, spot A is accessible but not
efficient, spot B is not accessible
PPF is concave – for each additional unit of X, we have to sacrifice more units of Y, because in
production of X the MPL is decreasing
slope of PPF: MRPT (marginal rate of product transformation) – ratio of substitution one good with
the other in the production – changing alongsied the PPF

PPF upon constant MPL
X
Y
PPF
PPF is linear – to an additional unit of X we sacrifice always the same volume of Y and vice versa,
because MPL is constant in production of both goods
MRPT is constant alongside the linear PPF
L
TPL
QY
L
TPL
QX

PPF upon constant but different MPL
X
Y
PPF
MPL(X) > MPL(Y)
X
Y
PPF
MPL(X) < MPL(Y)

PPF upon fixed proportion of production
X
Y
PPF
It is impossible to change the structure of production

How does the general equilibrium form?
ngeneral equilibrium forms, when it is not possible to rearrange the structure of production to
rise the total utility in the economy
nfor general equilibrium stands: MRSC(A)=MRSC(B)=PX/PY=MRPT=MRTS(X)=MRTS(Y)
n... if both consumers A and B find themselves in the equilibrium and also the firms producing
goods X and Y

General euqilibrium
Y
PPF
xA
x*
y*
yA
E
X
UA
UB
E'
Px/Py
Px/Py
xB
yB
...lies in spot E‘, upon the consumers´ equilibrium in spot E
 X* and Y* represent the total volume of X and Y produced upon the general equilibrium
Consumer A consumes XA and YA , consumer B consumes XB and YB
UA+UB

Formation of the general equilibrium
price mechanism assures the equilibrium stage
0A
0B
X*
Y*
E
XB
YB
XA
pX'/pY'
X*
Y*
YA
pX/pY
Initial relative price ratio: pX'/pY‚...
... but there is an overhang of demand on X market (XA+XB˃X*) and an overhang of supply on Y market
(YA+YB˂Y*)
On the X market the price increases, on the Y market the price decreases
Budget line rotates clock-wise because of the change of the relative price ratio – the new ratio of
prices: pX/pY. Consumers (and the entire economy) aims to the equilibrium in spot E
CC

Exchange equilibrium
0A
0B
X*
Y*
X*
Y*
ICA
ICB
E
CC
XB
YB
XA
Px/Py
YA
Consumers are heading to the CC (Contract Curve), that represents the set of Pareto effective
combinations of X and Y allocated between te consumers

How the general equilibrium rearranges?
nthe impulse to change is the change of consumers´ preferences
ni.e.: consumers wish to buy more Y and less X, that leads to the:
nincrease of the demand for Y and decrease of the demand for X
n↑D(Y) → ↑P(Y) → ↑D(LY) → ↑wY → ↑Y*
n↓D(X) → ↓P(X) → ↓D(LX) → ↓wX → ↓X*
nthe equilibrium shifts alongside the PPF to a different equilibrium spot

Initial and the new equilibrium
Y
PPF
xA
x*
y*
yA
E
X
UA
UB
E
Px/Py
Px/Py
xB
yB
Y
PPF
xA
x*
y*
yA
E'
X
UA
UB
E'
Px'/Py'
xB
yB