Final answer:
To determine compensated demand functions, expenditure function, and indirect utility function, one must consider the utility function, budget constraint, total utility, and diminishing marginal utility. Roy's Identity is verified through derivatives of the indirect utility function.
Step-by-step explanation:
The student is seeking help in determining the compensated demand functions, the expenditure function, and the indirect utility function for a consumer with a utility function of U(x, y) = 0.5 √x + y, subject to a budget constraint due to a limited income I, where Px is the price of commodity x and Py is the price of commodity y. Furthermore, the student is asked to verify if Roy's Identity holds. When consumers face such decisions, economists use the concept of the budget constraint along with total utility and diminishing marginal utility to understand the choices made. Maximizing utility involves examining the ratios of marginal utility to price for each good and ensuring these ratios are equal at the optimal choice.
To answer the student's questions:
- Compensated demand functions would involve the use of Hicksian demand functions, which keep utility constant while prices and income change.
- The expenditure function indicates the minimum expenditure necessary to achieve a certain level of utility given prices.
- The indirect utility function reflects the maximum utility achievable with a given income and prices.
- Roy's Identity links the indirect utility function with Marshallian demand and can be assessed by taking the derivative of the indirect utility function with respect to the price of a good