# Derive demand functions for x and y for the general class of Cobb-Douglas preferences represented by the utility function u(x, y) = x α y β . As functions of px, py, I, α, and β, calculate price elasticities, cross-price elasticities, income elasticities, and expenditure shares for x and y.

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Derive demand functions for x and y for the general class of Cobb-Douglas preferences represented by the utility function u(x, y) = x α y β . As functions of px, py, I, α, and β, calculate price elasticities, cross-price elasticities, income elasticities, and expenditure shares for x and y.

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Step 1

The utility function of Cobb-Douglas preferences is given as,

Step 2

Derivation the demand functions for x and y

Maximize the given utility function subject to budget constraint using Lagrange method.

Step 3

First order conditions ...

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