l) Given the below functions for supply and demand: Supply: P = In (Q? 3) Demand: P = 22e-arctan a) Find the total welfare using the market equilibrium condition (to find the equilibrium point you need to use Newton's method at some point): b) Find the equilibrium price using the welfare optimization method directly; verify whether the results from part A & B are consistence. 2) Consider the following function. z . = (xy) D2z c) Find axay d) Find the second-order Taylor expansion of the function. 02 z e) How large is the residual of using the second-order Taylor expansion Dray at point (2,3)? ap+qz f) Derive the general form of [show your work]. axPDyq