Hi Welcome to The Hedonist
Today we will be discussing another important area in welfare economics
that is First Theorem of Welfare Economics
I have added a detailed note on First Theorem of Welfare Economics
at the end of this video for your reference
The First Theorem of Welfare Economics is also know as
the fundamental theorem of welfare economics
and also as
the invisible hand theorem of welfare economics
The First Theorem of Welfare Economics
is basically an explanation of
how the Pareto optimality conditions are working in a perfectly competitive market
So First Theorem of Welfare Economics
simply postulates general competitive equilibrium is Pareto optimal
The First Theorem of Welfare Economics
is showing how the three marginal conditions of
Pareto optimality are working in a perfectly competitive market
The three marginal conditions of Pareto optimality are
efficiency in exchange
efficiency in production
and allocation efficiency
so how these three conditions are fulfilled in perfectly competitive market
this what actually showing by
The First Theorem of Welfare Economics
Now let us check
how these three conditions are fulfilled
in a perfectly competitive market one by one
The first one
perfect competition and efficiency in exchange
According to Pareto optimality condition
the efficiency in exchange is attained
when marginal rate of substitution
for two consumers, consumer A and consumer B
for two goods, commodity X and commodity Y are same
A consumer maximises his satisfaction
when the marginal rate of substitution for commodity X and commodity Y
for that particular consumer is equal to the
price ratio of commodity X and commodity Y
That is the marginal rate of substitution
for  commodity X and commodity Y
for the consume A is equal to
the price of X divided by price of Y
it is at this point the consumer maximises his satisfaction
same way for consumer B
he will be also  maximising his satisfaction
at the point where marginal rate of substitution
for commodity X and commodity Y
is equal to the price ratios of two commodities
as we have studied the features of perfectly competitive market
the most important feature of a perfectly competitive market is that
the prices of goods are same
for all the consumers in the market
so in the above two equations
the price ratios, the price of X divided by price of Y
will be same
Therefor we can say that
Marginal Rate of Substitution for two commodities
by the consumer A
will be equal to the
Marginal Rate of Substitution by the consume B
for these two commodities
So we can say that
the first condition of Pareto optimality
the condition of efficiency in exchange
is perfectly working in a perfectly competitive market
Now moving to the second criteria of Pareto optimality
that is, efficiency in production
The efficiency in production criteria of Pareto optimality states that
MRTS, marginal rate of technical substitution
between any two inputs
for example, labour and capital
should be same for two firms
firm A and firm B
This condition can also be found fulfilled
in a perfectly competitive market
Being in a perfectly competitive market
the prices of factors of production are always constant
and firms are in equilibrium
at the point where
the highest possible isoquant tangents to the isocost line
There determines equilibrium of a producer
As you know the MRTS, Marginal Rate of Technical Substitution
which is nothing but the slope of a isoquant
and the slope of a isocost line or a budget line
is the price ratio between two factors
That is, at equilibrium point
the slope of isoquant, MRTS, will be equal to the
price ratio of factors of production
that is 'w' divided by 'r'
where 'w' is the wage, which is the payment for labour
and 'r' which is meant by rent
so the producer A will be in equilibrium
at the point where MRTS of labour and capital is equal to
'w' divided by 'r'
and in the same way, producer B will be also in equilibrium
at the point where
MRTS of L K, labour and capital will be equal to the 'w' divided by 'r'
so as I said under perfect competition
the prices of factors of production are same
that is in the both above equations
the price ratio of factors of production will be same
so we can say that
MRTS for labour and capital for producer A
will be equal to the
MRTS of labour and capital for producer B
which is simply the second condition of Pareto optimality
that is the condition of efficiency in production
Now let us move to the final criterion of Pareto optimality
that is the criterion of allocative efficiency
the allocative efficiency of Pareto optimality shows that
the MRS, the Marginal Rate of Substitution
of two commodities for two consumers
should be equal to the MRTS, the marginal rate of technical substitution
for labour and capital for two producers should be same
under perfect competition
a firm is in equilibrium when
marginal cost is equal to the price
that is for commodity X, the marginal cost of X
is equal to the price of X
where the firm will be in equilibrium
same way for commodity Y
marginal cost of Y is equal to the price of Y
so the firms in a perfectly competitive market
are reaching into equilibrium at the point where
marginal cost ratios are equal to the price ratios
here it is to be noted that
marginal cost ratios of two commodities
is nothing but the marginal rate of transformation between them
and under perfect competition
the consumer is reaching to the equilibrium
at the point where the highest possible indifference curve
tangents to his budget line
that is the MRS of X Y is equal to the price of X divided by price of Y
So when put these two cases of both the producer and consumer
we can write the equation as
MRS of X Y is equal to MRT of X Y
which is nothing but the allocative efficiency of Pareto optimality
so in this way we can say that
Pareto optimality conditions are holding in a
perfectly competitive market also
so this is how the Pareto conditions are fulfilled in a perfectly competitive market
this is what actually showing by the first theorem of welfare economics
hope you got some idea on the topic
Thank you for watching
have a nice day
