Consider the following utility function: L= I' 0.4 (a) Derive the marginal rate of substitution. (b) Derive the demand functions for good z and good 2z as a function of income (), the price of x (p,) and the price of z (p.). () Assume Y = 100, p, = 5 and p, = 10. Find the equilibrium quantities (bundle A) for this consumer. (d) Let's now assmue good z goes on sale for $8 (p. = 8). If nothing else changes, what are the new equilibrium quantities (bundle B)? (e) Calculate the decomposition bundle. (Hint: find another another bundle, say Bundle C, by using New Prices and Old Utility concept). (f) Calculate the total, income and substitution effect for good z