Effects of Ad Valorem Taxes (With Diagram)

In this article we will discuss about the effects of ad valorem taxes in a competitive industry.

An ad valorem tax is a value-based tax. It is imposed as a fixed percentage of the price of a commodity. It is sometimes called a sales tax. We shall assume here that the tax is collected from the buyers rather than from the sellers. For, this will make our task of explaining the effects of the tax easier.

 

Let us suppose that the demand curve for a good is DD in Fig. 12.2 and the supply curve before the imposition of the tax is SRS₀. Therefore, the market equilibrium occurs at the point E₀. At this point the price has been determined to be p₀ and the quantity bought and sold in the industry has been obtained to be n₀q₀ where n₀ is the number of firms in the industry and q₀ is the output of each firm.

It is assumed that the firms and the industry are in long-run and short-run equilibrium initially, i.e., at p = p₀, the typical firm is in equilibrium at the minimum point of its short-run and long-run average cost curves. The firm’s picture is not shown in Fig. 12.2.

Now, if an ad valorem tax is imposed on the good and the buyers are to pay the tax, then the price that the buyers would pay, would include the tax and the sellers will receive the price net of tax. The demand curve DD shows the price that the buyers would pay at each quantity purchased, and the curve D_tD_t shows the price net of tax that the sellers would receive at each quantity sold (or supplied).

The vertical gap between DD and D_tD_t curves gives us the absolute amount of the tax at any particular q. Let us suppose that the ad valorem tax has been imposed at the rate of fraction s (0 < s < 1), of the price (the buyers pay) of the good.

As the quantity bought and sold increases and the price decreases, the absolute amount of the tax also decreases. That is why, in Fig. 12.2, the vertical gap between the DD and D_tD_t curves diminishes as the quantity increases.

The pre-tax or the initial equilibrium point is the point E₀ and the price-output combination at that point has been (p₀, q₀) for the firm and (p₀, n₀q₀) for the industry. Let us now suppose that an ad valorem tax at the rate of fraction s (0 < s < 1), is imposed on the good.

After the imposition of the tax, the point E₀ would no longer be the demand-supply equilibrium point. For, at this point, to supply the quantity of n₀q₀, the sellers want a price of p₀, but they are getting the price net of tax which is equal to P’₀ < p₀.

In the post- tax situation the market would be in equilibrium at the point of intersection E’_t between the D_tD_t and SRS₀ curves, for, here, at q = n₀q_t, the buyers are willing to pay the price p_t, and the sellers are getting the price net of tax which is p,’ and which they are actually demanding.

Therefore, the post-tax price-quantity combination would be (p_t, n₀qt) at the point E_t, p_t > p₀ and n₀q_t < n₀q₀, i.e., in the post-tax situation, price would be higher and the output of the industry smaller. Since the number of firms remains unchanged at n₀ and the industry output decreases from n₀q₀ to n₀q_t, the output of each firm, q_t, is now smaller than q₀.

Therefore, in the short run, the effects of imposition of an ad valorem tax will be: the price will increase, the firm’s output and industry output will decrease, the firms would earn economic losses and the number of firms would remain unchanged.

At p = p₀, the firm earns only the normal profit, p₀ being equal to the minimum average cost. Therefore, at the net-of-tax price which is equal to p’_t <p₀, the firms are not able to earn even the normal profit, i.e., they are having losses. So, in the long-run adjustment process, some of the firms would be leaving the industry.

Since the SRS curve of the industry is a horizontal summation of the SMC curves of the firms, this curve will now be shifting to the left from its present position of SRS₀.

This process would continue, i.e., the number of firms would be decreasing and the SRS curve of the industry would be shifting to the left and the price would be rising till the price (including the tax) rises to pi in the long run, and the net-of-tax price rises to p₀ so that the firms that are still remaining in the industry, will be able to earn normal profit again.

This post-tax long-run equilibrium will be obtained when the SRS curve takes the position of SRS₁ and cuts the D_tD_t curve at the point E₁.

Also, at E₁, the industry output is n₁q₀ where n₁ is the number of firms still remaining in the industry (n₁ < n₀) and q₀ is the output of each firm. It may be noted here that in a constant cost competitive industry, the position of the cost curves would not be affected by the long-run adjustment process.

That is why, at p = p₀, the firm’s output would remain the same at q = q₀, and, as we have assumed, at this price the firms would earn only normal profit and the firms and the industry will be in long-run equilibrium.

Therefore, the long-run effects of imposition of an ad valorem tax on a constant cost competitive industry would be: price would increase, firm’s output would remain unchanged, number of firms would fall, the industry output would fall, and the firms would earn normal profit.

We have summarised the effects of an ad valorem tax in the following table.