Question

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

	output	1	2	3	4	5	6	7	8
	MPC	23	21	23	25	27	30	35	42
	4MSC	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

Assume that the marginal private benefit (MPB) is give by the price AR. Assume also that there are no externalities on the consumption side,and that therefore MSB=MPB.

1. How much will the firm produce if it seeks to maximize profits?
2. What is the socially efficient level of output (assuming no externalities on the demand side?
3. How much is the marginal external cost at this level of output?
4. What size of tax would be necessary for the firm to reduce its output to the socially efficient level?
5. Why is the tax less than the marginal externality?
6. Why might it be equitable to impose a lump-sum tax on this firm?

Answer 1

a) A profit maximizing firm will produce the output at the point where Marginal Revenue equals Marginal Private Cost. From the table it is clear that at the output level of 5 units both MR and MPC are equal to 27. So, a profit maximizing firm will produce 5 units of output.

b)Socially efficient level of output is the most efficient level of output because it equals to Marginal Social Benefit and Marginal Social Cost. Which in this case 42 and corresponding output level is 4 units.

c)Marginal external cost is the change in the total cost including social and private at that level of output which in our case is 4.

d) MR = MPC + t

and we want the output levelt to be equals to 4, so it is 42 = 30 + t, so t = 12