Differentiate between a Hicksian and a Walrasian demand function? Do they ever intersect? Explain.

(b) Consider a Cobb-Douglas utility function

U (X,Y)= X^1/5 Y^4/5

where X and Y are the two goods that a consumer has an option to consume at per unit prices of PX and PY, respectively. Assume income of the consumer to be Rs M. Determine (a) Uncompensated demand functions for goods X and Y

(b) Compensated demand functions for goods X and Y

The Hicksian and Walrasian demand functions are two distinct approaches in microeconomic analysis, focusing on consumer behavior and choices. Below is their differentiation and an analysis of their intersection possibilities, followed by solving the Cobb-Douglas utility function problem.

### Hicksian vs. Walrasian Demand Function:

1. Definition:
   - Hicksian Demand Function (Compensated Demand): It represents the quantity of goods a consumer demands while maintaining a constant utility level, adjusting for price changes by compensating income. It focuses on minimizing expenditure to achieve a given utility.
   - Walrasian Demand Function (Uncompensated Demand): It represents the quantity of goods a consumer demands given their income and prices, maximizing utility subject to a budget constraint.

2. Utility and Expenditure:
   - Hicksian demand is derived from the expenditure minimization problem, ensuring the consumer attains a specified utility level \( U \).
   - Walrasian demand is derived from the utility maximization problem, constrained by the consumer's budget \( M \).

3. Price Effects:
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