Assume that a firm discharges waste into a river. As a result, the marginal social costs (MSC) are greater than the firm’s marginal (private) costs (MC). The following table shows how MC, MSC, AR and MR vary with output.

Output	1	2	3	4	5	6	7	8
MC	23	21	23	25	27	30	35	42
MSC	35	34	38	42	46	52	60	72
TR	60	102	138	168	195	219	238	252
AR	60	51	46	42	39	36.5	34	31.5
MR	60	42	36	30	27	24	19	14

(a)  How much will the firm produce if it seeks to maximise profits?

(b)  What is the socially efficient level of output (assuming no externalities on the demand side)?

(c)  How much is the marginal external cost at this level of output?

(d)  What size tax would be necessary for the firm to reduce its output to the socially efficient level?

(e)  Why is the tax less than the marginal externality?

(f)  Why might it be equitable to impose a lump-sum tax on this firm?

(g)  Why will a lump-sum tax not affect the firm’s output (assuming that in the long-run the firm can still make at least normal profit)?