Problem 10 Easy Difficulty The development of optimal tax policy has been a major topic in public finance for centuries. 18Probably the most famous result in the theory of optimal taxation is due to the English economist Frank Ramsey, who conceptualized the problem as how to structure a tax system that would collect a given amount of revenues with the minimal deadweight loss. 19Specifically, suppose there are n goods (xi with prices pi) to be taxed with a scquence of ad valorem taxes (see Problem 12.9 ) whose rates are given by ti(i =1,n). Total tax revenue is therefore given by T=Afrin Ramsey's problem, then, is for a fixed T to choose tax rates that will minimize total deadweight loss DW = >_PW(ti). a. Use the Lagrangian multiplier method to show that the solution to Ramscy's problem requires ti= (1/es-1/ep), where > is the Lagrangian multiplier for the tax constraint. b. Interpret the Ramsey result intuitively. c. Describe some shortcomings of the Ramsey approach to optimal taxation