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# MEC-001/101:Microeconomic Analysis Assignment Solution

Course Code: MEC-001/101
Assignment Code: Asst /TMA /2022-23
Total Marks: 100

## SECTION

#### 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(A): Consider a pure-exchange economy of two individuals (A and B) and two goods (X and Y) Individual A is endowed with 5 units of good X and 3 units of good Y, while individual B with 3 and 4 units of goods X and Y respectively. Assuming utility functions of individuals A and B to be 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, what will be the set of Pareto optimal allocation in this economy?

Ans: A Pareto optimal allocation is an allocation of resources in which it is not possible to make any individual better off without making at least one individual worse off. In this economy, there are a total of 5 units of good X and 7 units of good Y available.

One possible Pareto optimal allocation is for individual A to consume 3 units of good X and 3 units of good Y, and for individual B to consume 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.

Another possible Pareto optimal allocation is for individual A to consume 4 units of good X and 2 units of good Y, and for individual B to consume 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.

There may be other Pareto optimal allocations as well, depending on the exact utility functions of the individuals. In general, any allocation that allows both individuals to consume a mix of both goods and achieves the highest possible utility for both individuals would be Pareto optimal.

The utility functions of individuals A and B are both increasing in both goods, which means that more of either good will always lead to a higher utility. However, the marginal utility of each good will likely decline as more of that good is consumed.

Since individual A has more units of good X and individual B has more units of good Y, a Pareto optimal allocation would likely involve some trade between the two individuals. This would allow both individuals to consume a mix of both goods and achieve a higher utility than if they were restricted to consuming only the goods that they are initially endowed with.

To find a Pareto optimal allocation, we can use the concept of an Edgeworth box, which is a graphical representation of the endowments of the two individuals and the feasible set of consumption bundles (i.e., the set of combinations of goods that can be consumed given the available endowments). The Pareto optimal allocations will correspond to the points on the Edgeworth box that are on or inside the contract curve, which is the curve that represents the set of Pareto efficient allocations.

In this economy, the contract curve would likely be a straight line connecting the two endowment points (5 units of good X and 3 units of good Y for individual A, and 3 units of good X and 4 units of good Y for individual B). Any point on or inside this curve would correspond to a Pareto optimal allocation.

I hope this helps! Let me know if you have any other questions.