StudySpace: Economics in Development, 6th Edition

Worked Example: Tax Rates and Tax Revenues

Teenagers in Buibui fall in love with a cartoon about a superhero named Spidercomrade. As a result, Spidercomrade T-shirts become the country’s major import. These T-shirts are imported at $5 = Sh50 each (Sh stands for shillings).

The demand curve for T-shirts is curve DD in Figure 12–1. This curve is drawn so that the demand is highly price elastic. Initially the T-shirts are imported duty free, so the domestic price equals the world price, P0 = Sh50. At this price Q0= 1,000 T-shirts are bought (per day). The government then decides to levy an import duty of t = Sh20 per T-shirt. As a result, the domestic price jumps to P1= Sh70 = world price + tariff. Figure 12–1 shows that the quantity demanded consequently drops to Q1 = 364. The government collects tariff revenue equal to R1 = Sh7280 (=364 shirts ×Sh20 per shirt).

FIGURE 12-1

In an effort to collect even more revenue, the government doubles the tariff to t = Sh40. With the new tariff, the domestic price rises to P2 = Sh90. The demand curve shows that consumers will buy only Q2 = 171 at this price. So government revenue from the duty is R2 = Sh6840 (= 171 ×40). Officials at the tax department are chagrined to find that revenues dropped as a result of the higher duty.

They are even more chagrined to find that a new domestic industry soon sprouts in response to the high, duty-ridden price of imported T-shirts. Local entrepreneurs begin to import unfinished T-shirts at $10 each. (Since these are raw materials for domestic industry, no tariff is charged). Then they silk screen the Spidercomrade logo and sell their product for P3 = Sh80. In Figure 12–1, the curve Sd shows the domestic supply curve for T-shirts. You can see that domestic production becomes profitable only when the price of imported shirts rises above Sh70. Because of the domestic supply response to so-called accidental protection, imports of Spidercomrade T-shirts fall to zero. So does the revenue from import duties. The increased tax rates led to a precipitous drop in tax revenues.

(A subsequent effort to introduce a tariff on unfinished T-shirts failed in the face of intense opposition from the new domestic T-shirt industry.)

Had the tariff remained Sh20 per shirt, tax revenue would have grown over time as the demand curve shifted outward. With rising income and population, the tax base would grow and generate additional tax revenues. If the demand for Spidercomrade T-shirts—and later, Batcomrade T-shirts—is income elastic, then revenues will expand faster than GDP, and this will lead to a rising tax ratio. Together with prudent controls on the growth of public consumption expenditure, this income-elastic revenue source can facilitate public-sector investment and contribute to macroeconomic stability.

Exercises

1. This exercise gives you a turn to investigate the relationship between tax rates and tax revenues in Buibui, as discussed in the Worked Example.

a. (i) From among the avrious tariff rates shown in Table 12–1, government tariff revenues will be maximized when the tariff is t^* = Sh per T-shirt and the domestic price is P^* = Sh per T-shirt.

(ii) Briefly explaing why tax collections would decline if the tariff rate were increased beyond t^*.

b. Now let’s stop ignoring the domestic supply response.

(i) Look at the domestic supply curve Sd in Figure 12–1. What quantity of Spidercomrade T-shirts will be produced domestically when the tariff rate is t^* and the price is P^* (from part b above)?

Qs = T-shirts.

(ii) Given the quantity demanded and the quantity supplied domestically at price P^*, what quantity will be imported at this price?

Qm = T-shirts.

(iii) So what will be the actual amount of government tariff revenue when the tariff level is t^*?

Revenue = Sh .

(iv) Briefly explain why government revenues from a tariff of t^* fall so far short of the amount you calculated when completing Table 12–1.

(v) Taking into account the domestic supply response, the government would maximize revenues with a tariff rate of

t^* = Sh per T-shirt.

(Note: Limit your attention to those tariff rates shown in Table 12–1.)

c. Suppose that the government had adopted an excise tax on Spidercomrade T-shirts, instead of an import duty. The excise tax is levied on domestically produced units as well as imports.

(i) With the excise tax, what revenue would hte government collect with a tax of Sh25 per shirt?

Revenue = Sh .

(ii) What revenue would the government collect with a tax on Sh40 per shirt?

Revenue = Sh .

d. Now pull together some conclusions about tax policy.

(i) Comparing your calculations in parts c and d, which tax—the excise tax or the import duty—is more effective in raising revenue? Why?

(ii) Which tax is superior in terms of tax neutrality? Explain.

(iii) With the excise tax instead of the import duty, will a tax rate above Sh20 per shirt still induce domestic production in place of imports? Explain.

(iv) Which tax is superior in terms of resource allocation efficiency? Explain. (To answer this, you might find it useful to know that the production of logo T-shirts is a very low priority in the development plan for Buibui.)

(v) Which tax is likely to have lower tax administration costs? Explain.

2. This exercise examines some data facts relating to Wagner’s law of expanding state activity, and then explores the determinants of taxable capacity.

a. Table 12–1 in the textbook presents data on central government expenditures as a share of GNP for the four standard income groups (defined in terms of PPP $ for 1992). Combine those group averages with the following per capita income figures (which are simply midpoints for the four income ranges):

(i) Plot the four points for these income groups on Figure 12–2 and connect the points. Label this line G/Y.

FIGURE 12-2

(ii) Does the graph suggest that Wagner’s law (which was formulated a century ago) is a reasonable description of the relationship between the size of government and per capita income in 1992?

(iii) Refer again to textbook Table 12–1 to find group average data on housing, social security, and welfare expenditures as a share of GNP. Plot this information on Figure 12–2 and connect the points. Label this line WELFARE/Y.

(iv) What does the graph tell you about how spending on social services varies with per capita income, on average? What is the reason for the relationship you observe?

b. The relative size of government can also be measured in terms of the tax ratio, which is the ratio of tax revenues to GNP. Columns 1 and 2 in Table 12–2 provide data on per capita income and the tax ratio for twenty countries that are selected to span the full range of income from $1,000 to $15,000 in 1992 dollars (PPP).

Click here for Table 12-2

(i) In Figure 12–3 plot the tax-ratio data for these 20 countries as a function of per capita income. Draw an approximate best-fit line representing the average relationship between these two variables. Label the line TR for tax ratio.

FIGURE 12–3

(ii) Does the line TR provide support for Wagner’s Law? Explain.

c. The TR line is sometimes interpreted as a measure of taxable capacity because it shows how much revenue (as a share of GNP) can be expected, on average, for any given level of per capita income.

(i) The point corresponding to Zimbabwe is far above the TR line; therefore, the actual tax ratio is quite high relative to the average for Zimbabwe’s level of income. Identify this point on the graph and label it as ZIM.

(ii) What factors might explain Zimbabwe’s high tax ratio? (Hint: Refer to the data in Table 12–2 for ideas. Keep in mind that trade is easy to tax, especially trade in bulk raw materials.)

(iii) For which three countries do you find the data plot is farthest below line TR? Label each of these three points with the first three letters of the respective country’s name.

(iv) Can the low tax ratios for these countries be explained by the data in columns 3 and 4 of Table 12–2?

d. Taxable capacity usually is measured as a function of several variables, not just per capita income. In fact, all three elements examined above— per capita GNP, the ratio of exports to GDP, and the share of exports consisting of fuels and minerals—are commonly used as determinants of tax capacity. Suppose that the equation defining an index of tax capacity (TC) is

TC = 12.13 + 0.0014(GNP per capita) + 0.0817(X/GDP) + 0.12 * (FMM/X).

(i) Compute the index of tax capacity for Kenya using the data given in Table 12–2. (Note: The result will be in percentage units.)

(ii) Is Kenya’s actual tax ratio higher or lower than the index of taxable capacity? Should this be interpreted as a good thing? Explain.

e.

(i) Now compute the tax capacity index for Korea. Compare the result with the actual tax ratio.

(ii) In 1992 Korea’s central government ran a deficit of 1 percent of GNP. In view of your answer to question (i), could Korea have easily erased this deficit by raising taxes? Explain.

(iii) If Korea were to increase the actual tax ratio to the estimated tax level of its tax capacity, would gross domestic saving necessarily increase? Explain briefly.

3. The text notes that the value-added tax (VAT) has become very popular in developing countries over the past decade and has steadily replaced other forms of sales tax. This question explores the essential mechanics of a VAT; in the process the reasons for its popularity will become clearer.

To set up the problem, suppose that there are just four firms in an economy, as follows:

Firm 1. Cotton farmer, who sells $100 worth of cotton to Firm 2.

Firm 2. Textile factory, which buys the cotton from the farmer, spins and weaves it into cloth, and sells it for $300 to Firm 3.

Firm 3. Garment factory, which buys the cloth from the textile maker, and makes shirts which it sells for $700 to Firm 4. Firm 4. Retailer, who buys shirts from the garment factory and sells them to you and me for $1,500.

a.

(i) A traditional retail sales tax would just tax the final output. Suppose the tax is 10 percent. How much tax will be collected?

(ii) Retailers can be difficult to tax, especially when they are very small businesses, as in most developing countries. How much revenue would the sales tax yield if it were levied at the manufacturer level (meaning that firm 3’s sales constitute the tax base)?

b.

(i) Value added is the value of sales minus the value of physical inputs. Assume that the cotton farmer buys no inputs. Then,

Value added by firm 1 is .
Value added by firm 2 is .
Value added by firm 3 is .
Value added by firm 4 is   $800   .
Total value added is .

Note that total value added is the same as the value of final sales, so taxing value added should yield just as much as taxing the value of final sales.

(ii) Under the most common form of VAT, a firm pays tax on the value of its sales and then deducts a credit for the VAT paid on its inputs. For example, if the VAT rate is 10 percent, firm 3 has to pay VAT of 10 percent ×$700 = $70. But if the supplier charged VAT on the sale of the cloth (10 percent ×$300 = $30) and provides proper documentation to firm 3, then firm 3 gets a $30 credit to deduct from its tax obligation. Net, firm 3 only has to pay $40 in tax. Thus, with a 10 percent VAT,

Firm 1 has to pay in VAT (net).
Firm 2 has to pay in VAT (net).
Firm 3 has to pay   $40  in VAT (net).
Firm 4 has to pay in VAT (net).
Total VAT paid is , which is percent of the total value added as tabulated in part (i).

(Note: If firm 3 lacked documentation that firm 2 paid VAT on the cloth, firm 3 could not qualify for the credit. So firm 3 has an incentive to ensure that VAT paid on purchased inputs is duly recorded. This is the so-called self-enforcing feature of the VAT.)

c. Until recently the VAT in Indonesia exempted retailers. If the VAT here did the same, how much VAT would each firm pay and how much VAT would be collected overall?

d. Return to the case where retailers are included in the tax base. Some countries exempt farmers from paying VAT on their sales. In our example, how much VAT would be collected in toto if farmers were exempted from VAT? (Be careful. Firm 2 no longer will be paying just $20 in VAT. Do you see why?)

e. Most countries do not wish to penalize exports by taxing them. So they zero rate exports. This means that exporting firms do not have to pay VAT on goods that are exported, yet they still get full credit for VAT paid on inputs. Exporters even may qualify for a refund from the government. Suppose that half the output of shirts is exported by the garment maker, firm 3. Will firm 3 be liable to pay VAT or will it qualify for a refund? How much?

In summary, VAT is favored over other forms of sales tax for several reasons. It makes it easy to remove tax from exports. It can collect substantial revenue even if retailers, or small firms in general, are excluded. It has certain self-policing properties that leave a paper trail, which can be helpful when tax inspectors conduct audits.

4. In this exercise we analyze the incidence of excise taxes.

a. Figure 12–4 shows the supply and demand for turbans in Hatistan. Near to the equilibrium, demand is inelastic, whereas supply is quite elastic. The initial equilibrium market price is P0 = Rs10 (10 rupees). The equilibrium quantity is Q0. Now let the government impose an excise tax of Rs5 per turban.

(i) One way to analyze this is to shift the supply curve upward to reflect the tax. For example, output Q0 would now be supplied at a market price of Rs10 plus the tax, or Rs15. Each point on the supply curve similarly shifts upward by the amount of the tax. Carefully draw in the new market supply curve; label it S′S′.

FIGURE 12–4

(ii) The new equilibrium price in the turban market will be P1 = Rs (to the nearest integer).

(iii) Why does the equilibrium price rise by less than the amount of the tax?

b.

(i) At the new equilibrium price the turban sellers receive a net revenue of Rs per hat, after taking out the Rs5 that goes to the government.

(ii) Compared with the pretax market equilibrium, consumers now pay

Rs per hat more than before, while sellers receive (net)
Rs per hat less than before.

(Hint: These two answers sum to Rs5, the amount collected by the government on each hat.)

(iii) In this simple example, the incidence of the tax is

Consumers bear percent of the tax burden.
Sellers bear percent of the tax burden.

c. Figure 12–5 shows the supply and demand for mangoes in Hatistan. Note that the demand curve for mangoes has the same form as in Figure 12–4, but now supply is quite inelastic. The initial equilibrium market price is P0 = Rs10 (10 rupees) per bag. The equilibrium quantity is Q0. Now suppose that the government imposes an excise tax of Rs5 per bag of mangoes.

(i) Carefully draw in th new market supply curve; label it S′S′.

(ii) The new equilibrium price in the mango market will be P1 = Rs per bag.

(iii) At the new equilibrium price, the mango sellers receive a net revenue of Rs per bag, after taking out the Rs5 that goes to the government.

FIGURE 12-5

(ii) Compared with the pretax market equilibrium, consumers are now paying Rs per bag more than before, while sellers are receiving (net) Rs per bag less than before.

(iii) In this simple example, the incidence of the tax is Consumers bear percent of the tax burden.

Sellers bear percent of the tax burden.

d. Consider the longer-run effects on the mango market.

(i) Following imposition of the excise tax on mangoes, the profitability of growing mangoes has .

(ii) In the short run, producers will not chop down mango trees and put in banana trees. But in the long run, the tax-induced change in the profit rate will cause mango production capacity to .

(iii) In the mango market the long-run change in the stock of mango trees will cause the curve to shift to the .

(iv) Therefore, in the long run the equilibrium price of mangoes will be than P1.

(v) Therefore, in the long run consumers will bear a share of the tax burden than in the short run.

5. More difficult. The graphs from Exercise 4 are used again here to study the excess burden of the excise taxes on turbans and mangoes.

Suppose that, in Figure 12–4, turban production were to increase from Q2 to Q2 + 1. The extra unit of turban production is of benefit to society. Its value is measured by the height of the demand curve; at Q2 the marginal social benefit is Rs15. But resources are needed to produce the extra turban. The opportunity cost of these resources is measured by the height of the (pretax) supply curve, which is Rs9 at Q2. The net benefit to society of producing this extra turban is therefore Rs6. In general, the vertical gap between the two curves at any value of Q shows the gain in social welfare achieved from having the marginal unit of output produced. Hence, the area enclosed by the supply and demand curves above any interval on the horizontal axis gives the total welfare gain that accrues when the corresponding units output are produced—or the total welfare loss when these units of output are foregone.

a. In Figure 12–4 darkly shade the triangle corresponding to the welfare loss caused by the drop in turban production when the excise tax is imposed.

b. In Figure 12–5 darkly shade the triangle corresponding to the welfare loss caused by the (short-run) drop in mango production when the excise tax is imposed.

c. Review the textbook’s Figure 12–2 so you understand that the rectangle represents the amount of tax revenue collected by the government. The same idea may be applied to Figures 12–4 and 12–5, in which you have already marked two prices (from Exercise 4): the price paid by buyers and the price, net of tax, received by suppliers.

(i) Lightly shade the area between these two prices, starting at the vertical axis and extending out to the market equilibrium quantity (posttax). This shaded area is the total tax revenue.

(ii) The lightly shaded area represent a loss of welfare to consumers and producers. But it is not included in measuring the excess burden of the tax. As defined in text, the excess burden is given by the heavily shaded triangle alone. Why?

d. In Figures 12–4 and 12–5, equal tax rates are imposed on turbans and mangoes, but the market responses are different.

(i) Is the excess burden of the tax in the market for mangoes greater than, equal to, or less than the excess burden in the market for turbans? Prove it. (Hint: The proof uses the formula for the area of a triangle: ¹/2 base × height.)

(ii) The tax rates and the demand elasticities are the same in Figures 12–4 and 12–5, but the supply elasticities are different. Formulate a simple rule linking differences in the supply elasticity to the size of the excess burden from the tax.

 

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