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# AMSB = 90 – 0.5Q MPC = 30

AMSB = 90 – 0.5Q MPC = 30 + 0.3QMEC = 0.2QFind the competitive equilibrium.Find the efficient equilibrium.Determine the dollar value of the Pigouvian tax that would ensure an efficient equilibrium.To add more rigor, consider a steel firm in a competitive market whose production causes a negative externality in the form of pollution. Its profit-maximization problem is:profit = p*q – c(q,x)whereis the price of steel,is output of steel, andis the cost function which includes output and external costs (x) as components. Take the first order conditions of the firm?s problem with respect to quantity and external costs and interpret your results. Particularly, how does the firm treat marginal external costs?Now suppose a per unit Pigouvian taxis imposed on the firm so its profit maximization problem takes the form_profit= p*q – c(q,x) -*qNow, take the first order condition with respect to quantity again and show that when, the efficient outcome is attained.