Question: Consider an individual that consumes two goods (X and Y) and has a Cobb-Douglass Utility Function of the form: U = 8 X.6 Y.4 The

Consider an individual that consumes two goods (X and Y) and has a Cobb-Douglass Utility Function of the form: U = 8 X.6 Y.4 The individual has income of 100, the price of Good X is 20 and the Price of Good Y is 15.

a) Find the Marginal Rate of Substitution as a function of the quantities consumed of Good X and Good Y [note: you should not use the budget constraint for this]

b) Write out the Lagrangian for this problem

c) Solve to find the demand for Good X, the demand for Good Y, and the highest level of utility for this individual. You must take the derivative and solve to get full credit.

d) What are the demand for Good X, the demand for Good Y, and the highest level of utility for this individual if the price of Good Y changes to 20?r

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