Consider identical farmers, Farmer A and Farmer B, who share a common grazing field. The two farmers face Hardin's Tragedy of the Commons. The utility functions for the farmers, u A and u B, are given below with h representing the hours each farmer allows their cattle to graze. In addition, assume a social welfare function given as W = u A + u B. u A = h A [ 0.5(h A + h B )] 1 2 (h A ) 2 u B = h B [ 0.5(h A + h B )] 1 2 (h B ) 2 1. Concerned about the Tragedy of the Commons facing the farmers, the government decides to intervene by imposing a tax on grazing hours. Mathematically solve for the joint utility maximising Nash Equilibrium tax. Show all your workings. [12 marks]