Question: The demand for widgets is given by P = 60 - Q . Widgets are competitively supplied according to the inverse supply curve (and marginal

The demand for widgets is given byP =60 -Q. Widgets are competitively supplied according to the inverse supply curve (and marginal private cost)PMC=5+Q. However, the production of widgets releases a toxic gas into the atmosphere, creating a marginal external cost ofEMC=Q.

(a)Calculate the equilibrium price and quantity of widgets when there is no correction for externality.

(b)Determine how much of the pollutant should the market supply at the social optimum.

(c)What is the deadweight loss from this externality?

(d)Suppose the government is considering imposing a tax of $Tper unit. Find the level of the tax,T, that ensures the socially optimal number of widgets will be produced in a competitive equilibrium.

(e)Suppose a breakthrough in widget technology lowers the marginal private cost,5+Q, by $3. How will this affect the optimal tax you found in part (d)?

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