1. A ( (I just need D and E) Assume that the US market for some inorganic chemic

Question

1.A( (I just need D and E)Assume that the US market for some inorganic chemical is modeled as follows, where Q is in thousands of kilograms, P is the price per kilogram, and there are no externalities, positive or negative, on the consumption side of the market:

MSB = 90 - 0.5Q MPC = 30 + 0.3Q

MEC = 0.2Q

A.Find the competitive equilibrium.

B.Find the efficient equilibrium.

C.Determine the dollar value of the Pigouvian tax that would ensure an efficient equilibrium.

D.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 = ps*q - c(q,x)

where ps is the price of steel, q is output of steel, and c(q,x) is the cost function which includes output and external costs (x) as components. Take the first order conditions of the firms problem with respect to quantity and external costs and interpret your results. Particularly, how does the firm treat marginal external costs?

E.Now suppose a per unit Pigouvian tax t is imposed on the firm so its profit maximization problem takes the form:

profit= ps*q - c(q,x) - t*q

Now, take the first order condition with respect to quantity again and show that when t = ?c(q,x)/?x, the efficient outcome is attained.

Explanation / Answer

D. First order condtions for the steel firm: d(profit)/dq = 0

=> ps - d(c(q,x))/dq = 0 => ps = d(c(q,x))/dq

This states that the steel firm should produce the output level of steel for which price = marginal production cost.

and d(profit)/dx = 0 => d(c(q,x))/dx=0

d(c(q,x))/dx is the rate at which the firm

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