We shall try to know here the effects of the tax on a constant cost competitive industry in the short run and in the long run.

**The Short-Run Effects of the Tax****:**

Let us suppose that the picture of a typical firm is given in part (a) of Fig. 12.3 and that of the industry is given in part (b) of the figure. In part (b), the demand curve for the good has been given to be DD. On the other hand, the supply curve of the industry before the imposition of the tax has been given to be SRS_{0} which is the horizontal summation of the SMC curves of the individual firms in the industry.

The number of such firms is, say, n_{0}. Initially, i.e., before the imposition of the tax, the demand-supply equilibrium price, p_{0}, of the good has been determined at the point of intersection F_{0} of the demand (DD) and supply (SRS_{0}) curves.

We have assumed that at p = p_{0}, the firm is in short-run and long-run equilibrium at the minimum point of its average cost curves (the long-run AC curve has not been shown), producing q = q_{0}. Therefore, at p = p_{0}, the industry output has been n_{0}qo at the point F_{0}.

To obtain the effects of a lump-sum tax, let us now suppose that the government imposes such a tax of a lump-sum amount of T (Rs) per period, on the good. The firm that produces the good will take it as an increase in its total fixed cost (TFC) per period, and as TFC increases by T, the firm’s total cost (TC) would also increase by T at each output.

The firm’s short-run average cost (SAC) also increases by T/q at any output q, and so its SAC curve will shift upwards from SAC_{0} to SAC_{t}.

The vertical gap between the SAC_{t} and SAC_{0} curves at any output q is equal to T/q, and, for obvious reasons, it falls as q increases. Since the imposition of the lump-sum tax keeps the firm’s total variable cost (TVC) function unaffected, it keeps the firm’s MC function also unaffected, i.e., the firm’s MC function would remain the same as it was before the imposition of the tax—it would remain the same SMC_{0}, and so, the SRS_{0} curve of the industry which is the horizontal summation of the SMC curves will also remain the same after the imposition of the tax, given the number of firms.

As we know, the SMC curve crosses the SAC function at the latter’s minimum point. Therefore, the SMC_{0} curve would cross the SAC_{0} and SAC, curves at their minimum points, E_{0} and E_{t}. Since the SMC curve at E_{0} is positively sloped, the point E_{t} would lie upward towards right of point E_{0}, i.e., the firm’s output q_{t} at E_{t}, would be larger than the output q_{0} at the point E_{0}.

ADVERTISEMENTS:

Since the SRS curve of the industry, viz., SRS_{0}, does not change its position as a result of the imposition of the tax, the price of the good would remain the same at p = p_{0}, and since the SMC curve of the firm would not change its position, the output of the firm, q_{0} would remain the same, and the number of firms remaining the same at n_{0}, the industry output would also remain unchanged at n_{0}q_{0}.

But now the SAC curve of the firm has shifted upwards from SAC_{0 }to SAC_{t}. Therefore, at the p = MC point E_{0 }(p_{0}, q_{0}), the firm would have p < SAC, i.e., the firm would earn economic losses in the short run as a result of the imposition of the lump-sum tax.

**The Long-Run Effects of the Tax****:**

In the long-run adjustment process, some of the firms would be leaving the industry to avoid economic losses. Therefore, the SRS curve of the industry being a horizontal summation now of a smaller number of SMC curves, would be shifting to the left of SRS_{0}.

The DD curve remaining in the same position, the price of the good now would be rising from p_{0}. The process would continue till the number of firms diminishes to, say, n_{1} (n_{1} < n_{0}), and the SRS curve shifts to the position of SRS_{t} that intersects the DD curve at F_{t} to give us p = p_{t} which is a price that puts the firm again in the normal profit-earning equilibrium, for, at p = p_{t}, and at the point E_{t}, the firm’s AR = MR curve touches the SAC_{t} curve and intersects the SMC curve.

ADVERTISEMENTS:

At p = p_{t}, the firm’s output would be q = q_{t} which would be larger than q_{0}, and the industry output (at the point F_{t}) would be n_{1}q_{1}, which is less than the initial level of n_{0}q_{0}. This is because the number of firms in the industry has decreased although the output of each firm has increased.

**We may summarise the short-run and long-run effects of the tax in the following table:**