Analysing the welfare effects of policy interventions - the long-run effects of a specific tax

Much of the analysis in this book blends positive and normative analysis. To illustrate the basic approach, suppose that our market is initially in a long-run competitive equilibrium with a market price of P*, and with each (identical) firm producing q* units of the good. The equilibrium number of firms is denoted by n*. As discussed above, this price must equal marginal cost and average cost.

Now suppose that a specific tax of $t is imposed on production, and that this tax is paid by firms in the industry. Total costs for each firm are now C(q) + tq. This tax adds therefore an amount t to each firm's marginal costs and average costs. Marginal costs are now C'(q) +1 and

^ C(q) ,

average costs are +1.

q

In the short run, with the market price still at P*, each firm's marginal costs are equal to C'(q*) +1 > P*. Firms produce less, make a loss, and as a result some firms exit the industry. As firms exit the long-run supply curve shifts up, which pushes up the market price as well as the quantity supplied by each individual firm that remains in the industry. In the long run, each remaining firm continues to produce what it did originally, since the quantity that minimises the new average costs

The long-run effects of a specific tax

Figure 1.2.2 The long-run effects of a specific tax

C(q) +1 also minimises the old average costs ?Mt. The new long-run q q

equilibrium market price is:

This is simply the original price, plus the tax. In the long run, the economic incidence of the tax falls entirely on consumers, even though the legal incidence falls entirely on producers.

The initial and final long-run competitive equilibria are illustrated in Figure 1.2.2. The initial market quantity is Q* and the final quantity is Q' . The tax shifts the average and marginal cost curves up for each firm by the amount of the tax. Each firm continues to produce q* in the new long-run equilibrium. The new long-run supply curve is LRS1.

The welfare loss of the tax is shaded in the right-hand panel, and is the difference between the loss of consumer surplus and the revenue raised from the tax, which is t Q'.

 
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