Question

A) Suppose the Commissioner General (CG) of the Ghana Revenue Authority considers reforming the income tax schedule in line with the president’s election campaign promise. The government introduced a GHS4000 exemption per family member. The proposed tax schedule is presented in the following table
Income
Tax rate

First GH₵ 20,000 ..... tax at 10%

Next GH₵30,000.......tax at 25%

All taxable income above GH₵ 50,000..... tax at 40%

In the final stages of the policy design you have been hired to perform the following tasks and advice the CG accordingly.

i. Suppose the Adams Family has three members (Joses, the sole earner – and his two sons), and earns GHS54,000 per year. Calculate their marginal and average tax rates. How much will the family pay in taxes?

ii. The Asare Family has four members (Serena, the sole earner – and her three daughters), and earns GHS74,000 per year. Calculate their marginal and average tax rates. How much will the family pay in taxes?

iii. Suppose the new tax system considers levying taxes at the household level (i.e. the marginal tax rates apply to combined spousal income). Will Joses and Serena have any financial incentive to marry each other?

B) Now suppose a flat tax rate of 30% is considered under the proposed reform, keeping the GHS4,000 per family member exemption. Furthermore, suppose that all other families in Ghana are identical to either the Adams or Asare families, and in fact these two types of families exist in equal numbers (e.g. if there are 40 families in Ghana, 20 are identical to the Adams’).

i. Would this change in the tax system make the system more progressive, more regressive, or neither? Explain. Which family (or family type) will likely benefit from the new tax system - or are both types better off?
How has the incentive or disincentive for marriage changed from that in the previous system described in part A?

ii. Suppose you have been able to gather enough information from previous tax reforms and found that the elasticity of pre-tax income with respect to the marginal tax rate is -0.2.

iii. Why is it necessary to know the elasticity of pre-tax income with respect to the marginal tax rate to correctly identify the revenue costs or gains of this change in the tax system?
Assuming that the elasticity of -0.2 is a correct estimate, would revenues increase or decrease from the tax system in (A)?

Answer 1

The average tax rate is the total amount of tax divided by total income.

The marginal tax rate is the incremental tax paid on incremental income.

qA ]]

1. Taxable income for the Adams family (or families) is (54000 - 3*4000) = 42000. They fall in the second tax bracket i.e. tax at 25%. Total taxable amount = 10500 and so average tax rate is 10500/54000 = 19.4%. Marginal tax rate is 25% - for an additional unit of currency earned, 0.25 units goes tax.

2. Taxable income for the Asare family (or families) is (74000 - 4*4000) = 58000. They fall in the third tax bracket i.e. tax at 40%. Taxable amount = 40% of 58K = 23200 so average tax rate is 23200/74000 = 31.4%. Marginal tax rate is 40%.

3. If Joses and Serena married, the family's total taxable income would be 58000 + 42000 = 100000. The joint family would fall in the third tax bracket, so taxable amount would be 40000. Average tax rate would be { 40000/(74000 + 54000) } = 31.2%. Marginal tax rate is 40%.

Because Joses' family is now in a higher tax bracket, he loses more of his income to tax - he has a higher average tax rate - while any additional money he'd earn would also be taxed more (25% vs 40%). In this case he has no incentive to marry Serena.

Serena doesn't lose money by marrying Joses - her average and marginal tax rates are the same. She is indifferent between marrying and not marrying Joses.

Thus one person loses while the other gains nothing - there is no incentive to marry here.

qB ]]

A regressive tax is a tax imposed in such a manner that the tax rate decreases as the amount subject to taxation increases. The rate progresses from high to low, so that the average tax rate exceeds the marginal tax rate.

A progressive tax is a tax in which the tax rate increases as the taxable amount increases.A taxpayer's average tax rate is less than their marginal tax rate.

Taxable income for the Adams family (or families) is (54000 - 3*4000) = 42000.

Taxable income for the Asare family (or families) is (74000 - 4*4000) = 58000

i. Asare family's taxable income is greater than Adams', but both are taxed equally i.e. tax rate does not change with taxable amount. Thus the tax system is neither progressive nor regressive.

Adams' family's average tax rate is { (30% of 42000) / 54000} = 23.3%

Asare family's average tax rate is { (30% of 58000) / 74000 } = 23.5%

Clearly Adams' family loses more money to tax from this system - from 19.4% of total income to 23.3%.

Asare family pays substantially lesser tax under this system - from 31.4% to 23.5% which, given the higher taxable income base, amounts to a good sum.

If marriage happens the combined taxable income = 100,000 while combined income = 128000.

With taxable amount 30,000, average tax rate becomes = 23.4%

The incentive structure has changed insofar that there is no long a strong disincentive to marry. However, there is a slight disincentive to marry for Joses.

Biii) Taxes trigger a host of behavioral responses designed to minimize the burden on the individual. In the absence of externalities or other market failures, and putting aside income effects, all such responses are sources of inefficiency, whether they take the form of reduced labor supply, increased charitable contributions, increased expenditures for tax professionals, or a different form of business organization, and thus they add to the burden of taxes from society’s perspective.

Because in principle the elasticity of taxable income can capture all of these responses, it holds the promise of more accurately summarizing the marginal efficiency cost of taxation than a narrower measure of taxpayer response such as the labor supply elasticity.

-----

An elasticity of taxable income = - 0.2 implies for a 1% change in marginal tax rate, taxable income decreases by 0.2% i.e. the benefit outweights the cost. Thus revenues will increase under the proposed system.