Question: Consider the following utility function for two goods, x and z: 3. Decomposition Bundle. (10 points) Consider the following utility function for two goods, x

Consider the following utility function for two goods, x and z:

Consider the following utility function for two goods, x and z: 3.

3. Decomposition Bundle. (10 points) Consider the following utility function for two goods, x and z: = X0.520.5 (a) Using the tangency condition and budget line, derive the demand function for good x and demand function for good z. (b) Initial Bundle A. Let P.x = 5, Pz = 3, and I(income) = 30. Find the composition of Bundle A. (c) New Bundle B. Suppose price of good x increases to Px = 7.5, while the price of good z and income remain the same. Find the composition of Bundle B. (d) Calculate the decomposition bundle. (Hint: find another another bundle, say Bundle C, by using New Prices and Old Utility concept). (e) Find the Total Effect, Substitution Effect, and Income Effect . Does each of the effect make economic sense

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