The market demand for gadgets is given by Pd = 120 - Q, where Q is the quantity consumers demand when the price that consumers pay is Pd. Gadgets are competitively supplied according to the inverse supply curve (and marginal private cost) MPC = 2Q, where Q is the amount suppliers will produce when they receive a price equal to MPC. The production of gadgets releases a toxic effluent into the water supply, creating a marginal external cost of MEC = Q. The government wants to impose a sales tax on gadgets to correct for the externality. When producers receive a price equal to MPC, the amount consumers must pay is (1 + t)MPC, where t is the sales tax rate. Find the level of the tax rate that ensures the socially optimal amount of gadgets will be produced in a competitive equilibrium.