This question refers to the first fundamental theorem of welfare economics. (a) State and intuitively explain the three conditions for Pareto efficiency in an economy with no public goods (b) State and explain the importance of the first fundamental theorem of welfare economics. (c) State and explain the Samuelson condition

A. An economy is in a Pareto Optimal state when no further changes in the economy can make one person better off without at the same time making another worse off.
This can be examined more formally in terms of three criteria that have to be met for a market equilibrium to result in Pareto Optimality. These are that there should be: exchange efficiency, production efficiency and output efficiency.

Exchange efficiency
Exchange efficiency occurs when, for any given bundle of goods, it is not possible to redistribute them such that the utility (welfare) of one consumer is raised without reducing the utility (welfare) of another consumer.
A simple example of this is where there are two individuals, one with a loaf of bread, the other with a block of cheese. Both can be made better off by exchanging bread for cheese. An efficient exchange system will allow exchange of bread and cheese to take place until neither party can be made better off without one of them becoming worse off.
In a multi-product, multi-consumer economy, exchange is far more complex and involves the use of money to facilitate exchange. However, the principle is the same. So long as products can be reallocated to make one person better off without making another worse off, the economy is operating sub-optimally from the point of view of exchange efficiency. In a perfectly competitive market, exchange will occur until this criterion is met.
Exchange efficiency alone does not necessarily result in Pareto Optimality. This is because it relates only to a specific bundle of goods. It may be possible to make one or more individuals even better off – without making any one else worse off – by altering the bundle of goods produced in the economy. This could involve raising the total volume of goods produced, as well as altering the combination of goods produced.

Production efficiency
Production efficiency occurs when the available factors of production are allocated between products in such a way that it is not possible to reallocate the production factors so as to raise the output of one product without reducing the output of another product.
This is analogous to technical or production efficiency at the level of the firm. What is being said here is that there are many situations in which it is possible to raise the total output in an economy by simply reallocating factors of production at no additional cost. This is because factors of production are more productive in some uses than they are in others. In a competitive economy, producers bid for factors of production until they are reallocated to their most productive use.
For example, if there is a lot of unproductive, low-wage labor employed in the agricultural sector and labor shortages in the industrial sector where labor productivity is potentially high, factory owners will bid up the price of labor and draw labor from the agricultural sector into the industrial sector. This could significantly raise output in the industrial sector without having a negative impact on output in the agricultural sector. So long as factors of production can be redistributed in a way that increases the output of one product without reducing the output of others, the economy is operating sub-optimally in terms of production efficiency.

Output efficiency
Output efficiency occurs where the combination of products actually produced is such that there is no alternative combination of products that would raise the welfare of one consumer without reducing the welfare of another.
Both the exchange efficiency and the production efficiency criteria must hold in order for this criterion to be met. The combination of outputs produced according to this criterion is distributed between consumers according to the exchange efficiency criterion, and the economy is operating with production efficiency.
Pareto Optimality is the result of rational economic behavior on the part of producers, consumers and owners of factors of production in a perfectly competitive economy. Although we don’t have the scope to examine the underlying theory here it can be shown that Pareto Optimality will be achieved if all markets are perfectly competitive and in equilibrium.
It is important to realize that, whilst Pareto Optimality is the outcome in an economy that meets each of the three efficiency criteria listed earlier, this does not mean that there is only one ‘optimal’ allocation of resources. A Pareto efficient economy results in the maximization of aggregate economic welfare for a given distribution of income and a specific set of consumer preferences. A shift in income distribution changes the incomes of individual consumers. As their incomes change, so too will their preferences, as their demand curves for various products shift to the left or right. This will result in a different equilibrium point in the various markets that make up the economy. Every alternative distribution of income or set of preferences is characterized by a different Pareto Optimum. Thus, since there is an infinite number of different ways in which income can be distributed, there is also an infinite number of different Pareto Optimal equilibrium.

B.First fundamental theorem of welfare economics (also known as the “Invisible Hand Theorem”):

any competitive equilibrium leads to a Pareto efficient allocation of resources.

The main idea here is that markets lead to social optimum. Thus, no intervention of the government is required, and it should adopt only “laissez faire” policies. However, those who support government intervention say that the assumptions needed in order for this theorem to work, are rarely seen in real life.

C.Samuelson condition:

For an economy with n consumers the conditions reads as follows:

MRSi=MRTi

MBi=MC

MRSi is individual i’s marginal rate of substitution and MRT is the economy’s marginal rate of transformation between the public good and an arbitrarily chosen private good.

If the private good is a numeraire good then the Samuelson condition can be re-written as:

MBi=MC

where MBi is the marginal benefit to each person of consuming one more unit of the public good, and MC is the marginal cost of providing that good. In other words, the public good should be provided as long as the overall benefits to consumers from that good are at least as great as the cost of providing it. (Remember that public goods are non-rival, so can be enjoyed by many consumers simultaneously).