The ‘John Mwanza’ formula – A comparative static analysis of tax revenue, compliance and evasion in Zambia

The private sector in Zambia and the government have for a long time been at loggerheads with regards to tax rates and revenue. Government wants more revenue which usually tends to support suggestions for increasing tax rates. This tendency can best be explained by the “Law of the instrument” a phrase from Abraham Maslow’s The Psychology of Science, published in 1966 which says “if all you have is a hammer, everything looks like a nail”. The private sector on the other hand have been searching and looking for ways to convince government to reduce tax rates and stimulate growth which will lead to higher revenue. The private sector has recently stressed the effects of tax evasion on tax revenue loss. This apparent catch 22 motivated a more critical look at the factors affecting tax revenue in Zambia.

In this paper Kampamba Shula a Zambian Mathematical Economist proposes how tax rate cuts can increase revenues by improving tax compliance whilst reducing tax evasion especially in a substantially informal economy like Zambia. In this paper, a theoretical model of tax evasion, inspired by Gary S Becker’s Crime and Punishment: An Economic approach, is briefly presented. A renewed mathematical approach called the “John Mwanza“ formula is introduced extending into comparative static analysis discussing tax evasion, compliance, complexity and even tax audit probability all in the vein of formulating a model that can at the margin gives us a clearer structure of the rather daunting task of increasing tax revenue whilst lowering tax rates.

  • Z=f(C) = rC

Where Z is tax revenue, r is the tax rate and C is Compliance.

  • Z=f(C, E) = r(C/E)

Where Z is tax revenue, r is the tax rate, C is Compliance, E is evasion.

  • Z=f(C, E, S) = r*p*S*(C/E) – A

Where Z is tax revenue, r is the tax rate, C is Compliance, p is probability of tax audit, E is evasion (or Tax avoidance), S is simplicity of the tax system and A is the cost of revenue collection to the authority.


John Mwanza Formula

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