The demand for widgets is given by P = 60 - Q. Widgets are competitively supplied according to the inverse supply curve (and marginal private cost) MPC = c. However, the production of widgets releases a toxic gas into the atmosphere, creating a marginal external cost of MEC = Q.
a) Suppose the government is considering imposing a tax of $T per unit. Find the level of the tax, T, that ensures the socially optimal amount of widgets will be produced in a competitive equilibrium.
b) Suppose a breakthrough in widget technology lowers the marginal private cost, c, by $1. How will this affect the optimal tax you found in part (a)?