Find the price elasticity of demand of good, Microeconomics

Consider a consumer with the following Cobb-Douglass utility function:

U (x, y) = xαy1-α

a)  Find the Marshallian Demand for both goods.

b)  Find the Price Elasticity of Demand of good x, the Cross Price Elasticity, and the Income Elasticity of Demand.

c)  Find the Hicksian Demand.

d)  Find the Willingness to pay for a project that reduces the price of X by ½.

e)  Using the Marshallian Demand, find the Increment in Consumer Surplus induced by last project.

f)  Using the Hicksian Demand, find the increment in Consumer Surplus induced by last project.

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