Subsidies_vs_taxes_Notes - Ill. FEES VERSUS SUBSIDIES The...

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Unformatted text preview: Ill. FEES VERSUS SUBSIDIES The Coase Theorem suggests that it makes no difference whether the polluter must com— pensate the victim of the pollution or the victim must pay the polluter not to pollute. There is an analogous issue in the context of Pigovian fees. Is it possible to obtain the same out- come by subsidizing firms to reduce pollution? In the “real” world, is there any danger in providing tax breaks and other subsidies for pollution control, rather than making pol- luters pay for the pollution they generate? Is it possible to obtain efficiency using a sub- 3 sidy instead of a fee? This is an important question since subsidies are usually much more ‘ politically popular than taxes or fees. The answer to this is that these two approaches yield different outcomes.4 The 1 tax is efficient, whereas the subsidy can result in too many firms in the industry and thus an inefficient amount of both pollution and the good associated with the pollu- tion. We will consider two cases. The first is for the short run—there is no time for new firms to enter the industry. The second is for the long run—there is time for en— try and exit (although exit in the sense of shut—down is always possible, even in the short run). FEES VERSUS SUBSIDIES 125 A. The Short Run Let us consider a competitive industry, producing some good in conjunction with pollu- tion. Initially, assume all of the firms in the industry are identical. Under a pollution tax (t), the production costs of a typical firm would be CT(y,e) = V(y,e) + te + FC (7.6) where y is the amount of the good being produced, 6 is emissions, V(y,e) represents vari- able production costs for producing e and y, and F C is the fixed cost of production. To simplify things, suppose there is a fixed relation between output and emissions—the more you produce, the more you pollute. In particular, suppose emissions are related to output by e = ay where a is a constant. We can rewrite Eq. (7.6) as CT(y,ay) = V(y,ay) + my + FC (7.7a) Recognizing that V and CT are now functions of y only, we let TC(y) = CT(y,ay) and VC(y) = V(y,ay) and rewrite Eq. (7.7a) as TC(y) = VC(y) + tay + FC (7.7b) This means that marginal production costs are MC(y) = MVC(y) + at (7.8) So basically, marginal costs are increased by at. Now consider what happens with a subsidy, s. With no attention to pollution con- trol, a firm might pollute at the level 6. With a subsidy, the firm will be paid to reduce emissions. If the firm reduces emissions to e, the subsidy payment will be s(é — e)./;l' his means that costs will be glance e :: or TC(y) = VC(y) + FC —— s(é — e) (7.9) = VC(y) + say + {FC — sé} Note that the term in braces is a fixed cost, consisting of the standard fixed cost plus a lump-sum transfer of sé that is independent of the firm’s choice of y or e. Thus the vari- able costs in both cases [Eqs. (7.7b) and (7.9)] are exactly the same. Only the fixed costs are different. Consequently the short-run marginal costs of production will be identical in the two cases and the firm will produce exactly the same amount of pollution and the good. In fact, the marginal costs from Eq. (7.9) are MC(y) = MVC(y) + as (7.10) which is exactly the same as Eq. (7.8) except we have an s here instead of a t. Consequently, our first result is that in the case of identical firms in the short run, ' Pigovian fees and subsidies yield exactly the same outcome. We should note that this re— i sult applies even if there is a more complex relationship between output and emissions than the fixed ratio assumed here. Showing that is more cumbersome mathematically so we omit it here. We now turn to an industry with heterogeneous firms. This may be because of dif- ferent technologies used by different firms due, for instance, to their different ages. This 126 PIGOVIAN FEES case is best understood graphically. Suppose we have an industry composed of two classes of firms, old firms and new firms. Newer firms may have higher fixed costs but lower variable costs. We are concerned with industry behavior in the short run under Pigovian fees and subsidies. Since this is the short run, no new firms may enter. Any firm may, however, choose to produce nothing, shutting down. If a firm produces nothing, the sub- sidy disappears. In other words, we only pay firms to produce less pollution. We do not continue to pay firms if they decide to go out of business. Figure 7.5 shows the marginal cost curves and average variable costs for these two types of firms. Since this is a short—run analysis, we are not concerned with total costs. The issue is whether prices cover average variable costs and, if they do, production will be at marginal cost equals price. As we saw above, the effect of a tax on marginal cost is identical to the effect of a subsidy on marginal cost—both raise marginal costs relative to the unregulated case. The U subscripts in the figure correspond to average variable cost (AVC) and marginal cost (MC) in the unregulated, pretax, or presubsidy case. The T and S subscripts refer to the case of a Pigovian tax or subsidy, respectively. Note in Figure 7.5 that although the tax and the subsidy raise the marginal costs by Goods output Goods output (a) (b) Figure 7.5 Variable costs for heterogeneous industry, short run. (a) Old firms; (b) newer firms. MCU, Marginal cost unregulated case; MCs, marginal cost, with emission control subsidy; MOT, marginal cost, with emission fee; AVCU, average variable cost, unregulated case; AVCs, average variable cost, with emission control subsidy; AVCT, average variable cost, with emission fee; pU, goods price, unregulated case; p3, goods price, with emission control subsidy; pr, goods price, with emission fee. FEES VERSUS SUBSIDIES 127 the same amount, the subsidy lowers average variable cost whereas the tax raises aver- age variable cost. The reason is that we have assumed the subsidy applies only if the firm is operating. The lump sum s é in Eq. (7.9) goes away if the firm shuts down. Thus it ’, counts as a variable cost. Fixed costs (F C) are incurred whether or not the firm shuts down (in the short run). Now we turn to determining what the market price of the good might be under these three regimes. Figure 7.6 traces out the short-run supply functions for this industry for the three cases, unregulated, Pigovian taxes, and subsidies. Also shown is a typical de- mand function for the good. Recall that firms will operate on the portion of their mar- ginal cost curve that lies above the average variable cost. We can see that with both the unregulated and subsidy cases, both types of firms are operating, yielding product prices of pu and ps, respectively. In the case of the Pigovian tax, only the newer firms operate, yielding product price pT. These prices are shown on Figure 7.5. Note that all prices are above average variable costs for the newer firms, which is why they operate in all three cases. However, for the old firms, pT is below AVCT, the average variable cost for the Pigovian tax case. This is why the old firms shut down in this case. Our conclusions are that taxes and subsidies have different effects in the short run. '1 A subsidy may allow firms to continue operating that would not continue in the case of ; a tax. Which is efficient? The subsidy requires a lump-sum transfer, which has to be ob- 1 tained from somewhere. Even more important, the subsidy involves the operation of firms 1 that are really losing money (negative profits). This is not efficient. B. The Long Run We now turn to the case of the long-run effects of Pigovian taxes and subsidies. We saw in Eq. (7.7)—(7.10) that the effect of a tax or subsidy was to raise marginal costs, but that a subsidy lowered average costs while a tax raised average costs. This applies in the short run as well as in the long run. If we assume a constant-cost industry, all firms will oper- 5 ate at the bottom of their average total cost curve, in long—run equilibrium. Thus the sup- 3 ply schedules for the industry will be horizontal and as shown in Figure 7.7b. The result Figure 7.6 Short—run supply and demand, heterogeneous indus- try, with and without taxes and subsidies. Supplyu, Goods sup- ply, unregulated case; Supplys, goods supply, with emission control subsidy; SuppIyT, goods supply, with emission fee; De- mand, goods demand; pU, goods price, unregulated case; p5, goods price, with emission con- trol subsidy; pT, goods price, with emission fee. Goods output 128 PIGOVIAN FEES qT ch, as Goods output Goods output (a) (b) Figure 7.7 Long-run supply and demand, constant cost industry, with and without taxes and subsi- dies. MCU, Marginal cost, unregulated case; MCTS, marginal cost, with emission control subsidy or emission fee; ATCU, average total cost, unregulated case; ATCS, average total cost, with emission control subsidy; ATC-r, average total cost. with emisison fee; D, goods demand; 8U, long-run sup- ply of good, unregulated case; 83, long-run supply of goods, with emission control subsidy; ST, long-run supply of goods, with emission fee; qu, equilibrium goods output, unregulated case; qs, equilibrium goods output, with emission control subsidy; qr, equilibrium goods output, with emis- sion fee. ‘ of this is that goods prices will be higher with a Pigovian tax than with a subsidy. Fur— thermore, there will be more firms in the industry with a subsidy than with a Pigovian tax. Other than the fact that a subsidy has to come from somewhere, a subsidy is unde- sirable because it does not allow the market to communicate the true costs of the prod- uct being consumed to the consumer. To be quite concrete, suppose we are dealing with ‘ paper mills producing paper from trees and polluting rivers at the same time (virgin mills). Other mills produce paper from recycled products and we will assume they are pollution free (which is not actually the case). A pollution subsidy to clean up the virgin mills will make virgin paper more attractive (compared to recycled paper) than if the virgin paper manufacturer had to pay a pollution tax. The result is that a subsidy results in the overuse i} of trees and underuse of recycled paper, compared to the case of a Pigovian tax. If a prod- ‘ uct generates pollution, we want consumers to see the full costs associated with produc- ing that product when the consumers decide what to buy and how much to buy. ...
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Subsidies_vs_taxes_Notes - Ill. FEES VERSUS SUBSIDIES The...

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