Free MEC 01 Microeconomics Analysis Assignment Solution
SECTION A
Answer the following questions in about 700 words each. The word limits do not apply in the case of numerical questions. Each question carries 20 marks.
Question No 1(B): Determine the conditions that need to be fulfilled by an allocation to be termed as Pareto efficient allocation.
Ans:
An allocation is considered Pareto efficient, or Pareto optimal, if it is not possible to make any individual better off without making at least one individual worse off. This means that the allocation is optimal in the sense that it is not possible to reallocate the resources in a way that would benefit one or more individuals without harming any other individual.
There are several conditions that need to be fulfilled for an allocation to be considered Pareto efficient:
- Completeness: All individuals in the economy must be able to express their preferences over all available goods and services. This means that there must be a well-defined set of goods and services that can be consumed, and all individuals must have preferences over these goods and services.
- Transitivity: Individual preferences must be transitive, meaning that if individual A prefers good X to good Y, and good Y to good Z, then they must also prefer good X to good Z. This condition is necessary to ensure that there is a clear and consistent ranking of goods and services according to individual preferences.
- Non-satiation: Individual preferences must be non-satiated, meaning that individuals always prefer more of a good or service to less, given the same level of utility. This condition is necessary to ensure that there is always room for improvement in terms of utility.
- Convexity: The utility function of each individual must be convex, meaning that the marginal utility of a good or service decreases as more of it is consumed. This condition is necessary to ensure that individuals are willing to trade some of a good or service for another good or service in order to achieve a higher level of utility.
- Feasibility: The allocation must be feasible, meaning that it must be possible to allocate the available resources in the way specified by the allocation. This means that the total quantity of each good or service consumed by all individuals must be less than or equal to the total quantity available.
- Pareto efficiency: The allocation must be Pareto efficient, meaning that it is not possible to make any individual better off without making at least one individual worse off. This condition is necessary to ensure that the allocation is optimal in the sense that it cannot be improved upon without harming someone else.
To illustrate the concept of Pareto efficiency, consider an economy with two individuals (A and B) and two goods (X and Y). Individual A has 5 units of good X and 3 units of good Y, while individual B has 3 units of good X and 4 units of good Y.
Suppose that the utility functions of the two individuals are given by UA=XA YA
2 and UB=XB
2 YB where Xi and Yi for i= {A, B} represent individual i’s consumption of good X and Y respectively.
An allocation that is not Pareto efficient might involve individual A consuming 4 units of good X and 2 units of good Y, and individual B consuming 1 unit of good X and 5 units of good Y. This allocation would give individual A a utility of 32 and individual B a utility of 25.
However, it is possible to reallocate the resources in a way that benefits both individuals without harming either of them. For example, we could give individual A 3 units of good X and 3 units of good Y, and give individual B 2 units of good X and 4 units of good Y. This allocation would give individual A a utility of 27 and individual B a utility of 32, which is higher than their utilities under the first allocation.
This example illustrates the concept of Pareto efficiency: it is not possible to improve the utility of one.
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