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

1) Given U (X, Y) = XaYfl, where a + fl = 1

If X and Y have prices Px and Py and consumers income is I:

a) Set up the Lagrangian expression

b) Show the first order conditions

c) Show the optimum values of X and Y

d) Derive the demand for goods X and Y

2) Given specific values for the Cobb-Douglas function in Question 1

above, 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 and

c) Calculate the value for the Lagrangian multiplier (A) associated

with the income allocation using the first order conditions

d) Interpret the meaning of the Lagrangian multiplier (A)

e) What happens if the consumer's income increases by one

percent?