Question

2.Optional Question on duality for those who welcome a challenge Consider the same utility function as given by: U(X, Y) = X-Y For the primal problem, find the Marshallian uncompensated demand functions, X(Px Ру and y(Rs Py, by maximizing utility subject to budget constraint Px. X + Ру.Y - I. After obtaining the optimal consumption choices, write down the indirect utility function. Give a simple diagrammatic and economic interpretation. Illustrate the use of the indirect utility function by plugging in the prices and income level, for example, when the money income level is I S3,600, the price of X is Px S9 and the price of Y is Py SI. b. Derive the expenditure function: e(P, Py, That is, find the Hicksian compensated demand functions, X c (Ps Py, рђ and yo (P& B, U), by minimizing expenditure subject to the utility constraint UX, Y) = U。. As an alternative approach to obtaining the expenditure function, you could take advantage of the short-cut approach in the light of duality. Give a simple diagrammatic and economic interpretation. Illustrate the use of the expenditure function by plugging in the prices and utility level, for example, when the price of X is P「$9, the price of Y Is Py = $1 and the utility level is the result obtained from part a. Your findings can now be used to perform applied welfare analysis a.k.a. cost-benefit analysis by obtaining the Hicksian Compensating Variation HCV and the Hicksian Equivalent Variation HEV when the price of X drops to Px S4 (due to, say, capacity expansion) and the price of Y remains. What is the change in Marshallian Consumer's Surplus AMCS? Provide an economic interpretation by solving the consumer's dual problem

Answer 1

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