1) Given U (X, Y) = XaYfl, where a + fl = 1If X and Y have prices Px and Py and

1) Given U (X, Y) = XaYfl, where a + fl = 1If X and Y have prices Px and Py and consumers income is I:a) Set up the Lagrangian expressionb) Show the first order conditionsc) Show the optimum values of X and Yd) Derive the demand for goods X and Y2) Given specific values for the Cobb-Douglas function in Question 1above, where Px = 1, Py = 4 and 1 = 8 and if a = 13 = 0.5,a) Show the specific demand equations using the given values.b) Show the utility level at the optimal choices andc) Calculate the value for the Lagrangian multiplier (A) associatedwith the income allocation using the first order conditionsd) Interpret the meaning of the Lagrangian multiplier (A)e) What happens if the consumer’s income increases by onepercent?

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