Question

How do you use MRT and MRS to find the efficient production and consumption point? What happens if the equilibrium conditions are not met? What is the economic intuition behind this MRT=MRS requirement. Try to be as through as possible. Use of calculus is recommended.

Answer 1

Efficient production and consumption is determined by the Pareto Optimal solution and this makes the use of both MRS and MRT. Now, pareto optimality under perfect competition requires that the Marginal rate of substitution (MRS) between two goods is equal to the marginal rate of transformation (MRT) between them. It indicates to the point of simultaneous efficiency in both consumption and production.

So the price ratios of two products, suppose goods A and B, will be PA/PB  and this will be the same to consumers and firms under perfect competition. The MRS of all the individual consumers will be equal to the MRT of all the firms as MRS = MRT is equal to the price ratio. So, the two goods will be produced and exchanged in an efficient manner.

MRSAB = PA/PB and MRTAB = PA/PB, therefore, MRSAB = MRTAB

Take a look at the figure 1 which showcases pareto optimality. The transformation curve or the PPF for the two goods is shown by PPT. Any point on this curve gives the MRT between A and B which also gives the relative opportunity cost of producing A and B i,e. MCA/MCB , Curves I-0 and I-1 represent the indifference curves which show the consumer yastes for goods A and B.

The slope of an IC at any point will give thee MRS between A and B. Pareto optimality is attained at the point where the slope of the transformation curve PPT and the indifference curve I-1 intersect. This equality in theirr slopes is pointed out by the price line 'pp' which implies that at the equlibrium point E, the MRSAB = MRTAB = PA/PB,

Or, MUA/MUB = MCA/MCB = PA/PB,

Given this PPF PPT, there is no other IC which will satisfy pareto optimality. Point X shows inefficient production as it below the PPF curve and point Y is on the PPF but it is on a lower IC I-0, where the consumer is not satisfied to the maximum level. Hence, pareto optimality exclusively exists at point E where there is both efficiency in consumption as well as in production. This happens when the economy consumes and produces OA1 of good A and OB1 of good B.

If the conditions of pareto optimality are not met, then changes to the allocation of resources in an economy is possible. It can be done in such a way that at least one person gains without any other individual losing because of the change. So, it is possible to increase the production level of some good without reducing that of any other good. These changes are considered to be moves toward attainment of pareto efficiency and are known as pareto improvement.

Now, coming to the economic idea between the MRS = MRT :

MRS is considered to be the demand side of the equation while MRT is considered to be the supply side. MRS tells us how much a comsumer is ready to give up of good A in order to keep an additional unit of good B on the same utility level. It is represented by an indifference curve and is given by MRSAB = PA/PB

Now, MRT is how much amount a supplier is willing to give up of good A for producing one additional unit of good B, given the same level of resources. It is represented by the production possibility frontier and is given by MRTAB = MCA/MCB.

In a perfectly competitive economy, equilibrium will be attained only when all the opposite parties are better off by executing the trade. If consumer is ready to give up 3 tops for 1 pant while the supplier is willing to give up 2 tops for producing 1 more pant, the economy wont be in equilibrium. The supplier will be better off by giving up 3 tops as it further reduces the cost and the consumer is better off by giving up 2 tops for a pant, as he will be left with 1 top along with the pant. So, it creates a better trade and outcome for both the consumer and the supplier. In equilibrium, neither of the parties will switch as it is favourable for them.