Page 384 - DECO401_MICROECONOMIC_THEORY_ENGLISH

Unit-26: General Equilibrium Theory

a, b, c … n represents the product. Notes
p , p , p … n represents the relative price of product.
a b c
t, p, q … m represents the factors of production m for production of readymade product.
p , p , p … m represents the price of factors of production.
t p q
To get rid from the complexity of capital, Walras used a product a, which he called numeraire and the
price of all products are represented by this unit. The price of numeraire is p = 1.
a
The initial quantity (q , q , q …) of factor service on given price (P , P , P …), every consumer gets
q
q
p
t
p
t
maximum satisfaction when the quantity of factor services (O , O , O …) multiplied its price (p , p , p …)
q
p
t
q
t
p
equal to demanded quantity of product (d , d , d …) multiplied its price (p , p , p …). Thus the equation
a
c
b
c
b
a
comes as—
O p + O p + O p + … = d p + d p + d p + …
t t p p q q a a b b c c
This is budget equation.
Now we need m individual demand equation for consumer products which depend upon the price of
one product and all other products which he can buy and on that price which he sells to firms for his
services. This relation is represented by the following set of equation—
d = f (p , p , p , … p , p , p …)
a a t p q a b c
d = f (p , p , p , … p , p , p …)
a
t
b
b
b
q
c
p
Now we create n individual supply equation for factor services.
O = f (p , p , p , … p , p , p …)
t t t p q a b c
O = f (p , p , p , … p , p , p …)
p q t p q a b c
By addition the above equations, we get—
(1) The market demand equation for m product is—
D = Σd = F (p , p , p , … p , p , p …)
q
p
a
t
a
a
c
a
b
D = Σd = F (p , p , p , … p , p , p …)
b b b t p q a b c
(2) The market demand equation for n factor service is—
O = ΣO = F (p , p , p , … p , p , p …)
t t t t p q a b c
O = ΣO = F (p , p , p , … p , p , p …)
p p p t p q a b c
When market demand equation for product is equal to market supply equation of services then
Walrasian Market Equilibrium happens. Thus, from (1) and (2) we get—
D = O
a t
And D = O
b p
Then in Walrasian system, the factor services should be equal to its supply quantity and the price of
product should be equal to its average cost of production. These two conditions again give two sets—
1. The quantity of factor services should be equal to its quantity of supply for clearing the market
for n factor service—
O = a D + b D + c + D + …
t t a t b t c
O = a D + b D + c + D + …
p p a p b p c
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