Macroeconomic Observations on Paying for and Funding Universal Basic Income

Malcolm Sawyer

doi:10.1515/bis-2023-0032

Article

Macroeconomic Observations on Paying for and Funding Universal Basic Income

Malcolm Sawyer

Published/Copyright: September 2, 2024

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From the journal Basic Income Studies Volume 19 Issue 2

Abstract

The paper undertakes macroeconomic analysis of Universal Basic Income (UBI). It focuses on issues of paying for and the funding of universal basic income. A number of proposals are examined and the limitations of borrowing and money creation for the funding of UBI are indicated. It is generally argued that funding of UBI should be examined in terms of funding through taxation. The effects of UBI on employment and national output and the macroeconomic limits on the scale on UBI in terms of work force participation and tax rates are investigated.

Keywords: universal basic income; budget deficits; money; full employment

Corresponding author: Malcolm Sawyer, Economics Division, University of Leeds, Leeds, West Yorkshire, UK, E-mail: m.c.sawyer@lubs.leeds.ac.uk

Acknowledgments

I thank two anonymous reviewers and Reinhard Huss for helpful comments on the first draft of this paper. I would like this or similar included.

Appendix

This sets out the equations which lie behind the simulations reported in the text.

The adult population (that is those who can legally undertake paid work) is labelled P, and the labour force L is e.P where e is the labour force participation rate. The labour force and paid employment are measured in terms of person hours (on say an annual basis).

The level of UBI for the adult population is labelled α and to allow for possible effects of UBI on labour force participation e = e(α) with the partial derivative of e being negative (or zero).

Employment is labelled N and output is directly related with employment Y = βN; the employment rate is r = N/e.P. UBI for children (child benefits) is related to adult rate as λ. α.

The ratio of children to adults is labelled μ, and the total UBI for children is then λ. α. μ. P.

The pre-tax income of a person in paid employment is y _i = α + w _i + π _i where w _i is the wage of the ith paid employee and π _i the profits received, and disposable income is α + (1 − t _w)w _i + (1 − t _π) π _i where t _w, t _π are tax rates on wages and profits respectively. Consumer expenditure for an individual is a linear function of disposable income, c ₀ + c ₁.yd. It is here assumed that all child benefits are spent. Aggregating over all individuals, consumer expenditure in total is given by:

(1) C = N c 0 + c 1 ( N α + ( 1 − t w ) ∑ w i + ( 1 − t π ) ∑ π i ) + ( P − N ) c 0 + c 1 ( ( P − N ) α + ( 1 − t π ) ∑ π j ) + α . λ . μ . P

Writing ∑w _i = w.N where w is average wage, ∑π _i + ∑π _j as π (total profits), and treating the distribution of income between wages and profits as π = mY, W = (1 − m).Y leads to

(2) C = P ( c 0 + c 1 α + α . λ . μ . ) + c 1 ( 1 − t w ) ( 1 − m ) . Y + c 1 ( 1 − t π ) m . Y

Aggregate demand sets the level of output, which leads to employment as follows:

(3) P ( c 0 + c 1 α + α . λ . μ . ) + c 1 ( 1 − t w ) ( 1 − m ) . Y + c 1 ( 1 − t π ) m . Y + G + I = Y = β N

where G is government expenditure on goods and services and to be treated as one of the policy variables, and I is investment treated as exogenous.

UBI Scaled on Level of National Income per Person Employed

The level of the UBI α is scaled against the level of national income per person employed = ϒ.β. Government expenditure on goods and services on a per capita basis is labelled g, hence government expenditure in total is g.β.P. Investment is treated as proportional to level of income I = iY.

(4) P ( c 0 + c 1 β γ + β γ . λ . μ . ) + c 1 ( 1 − t w ) ( 1 − m ) . β N + c 1 ( 1 − t π ) m . β N + g β P + i β N = β N

Dividing through by P and β yields:

(5) ( c 0 β + c 1 γ + γ . λ . μ ) + c 1 ( 1 − t w ) . ( 1 − m ) . r . e + c 1 ( 1 − t π ) . m . r . e + g + i . r . e = r . e

The budget deficit is t:

(6) b d = g + γ ( 1 + λ . μ ) − ( t w ) . ( 1 − m ) . r . e − t π . m . r . e

Simplify with tax rates on wages and profits the same:

(7) ( c 0 ′ + c 1 γ + γ . λ . μ ) + c 1 ( 1 − t ) . r . e + g + i . r . e = r . e

where c ₀′ = c ₀/β

(8) b d = g + γ ( 1 + λ . μ ) − t . e . r

At full employment (that is r = 1) and indicating dependence of participation rare e on UBI level:

(9) ( c 0 ′ + c 1 γ + γ . λ . μ ) + c 1 ( 1 − t ) . e ( γ ) + g + i . e ( γ ) = e ( γ )

This gives the relationship between tax rate and UBI rate:

(10) ( c 0 ′ + c 1 γ + γ . λ . μ ) + c 1 . e ( γ ) + g + i . e ( γ ) = t . c 1 e ( γ )

The budget deficit at full employment is:

(11) b d * = g + γ ( 1 + λ . μ ) − t . e ( γ )

(12) b d * = g + γ ( 1 + λ . μ ) − [ ( c 0 ′ + c 1 γ + γ . λ . μ ) + c 1 . e ( γ ) + g + i . e ( γ ) ] / c 1

The derivative of bd with respect to γ is negative in the range of values of the parameters which is considered.

UBI Scaled on Income per Adult

The level of UBI is treated as related with the per capita GDP (instead of with output per employed person). Equation (3) is replaced by:

(13) P ( c 0 + c 1 β . ( N P ) γ + β . γ . λ . μ ) + c 1 ( 1 − t w ) ( 1 − m ) . β N + c 1 ( 1 − t π ) m . β N + g β P + i β N = β N

Dividing through by P and β

(14) ( c 0 β + c 1 e . r . γ + γ . λ . μ ) + c 1 ( 1 − t w ) ( 1 − m ) . e . r + c 1 ( 1 − t π ) m . e . r + g + i e . r = e . r

Moving to uniform tax rate on wages and profits:

(15) ( c 0 ′ + c 1 e . r . γ + γ . λ . μ ) + c 1 ( 1 − t ) . e . r + g + i . e . r = e . r

where c ₀′ = c ₀/β

Putting r = 1 in this equation would provide equation relating to full employment:

(16) ( c 0 ′ + c 1 e . γ + γ . λ . μ ) + c 1 . e + g + i . e − e = c 1 . t . e

(17) b d * = g + γ . e ( γ ) ( 1 + λ . μ ) − [ ( c 0 ′ + c 1 γ . e ( γ ) + γ . λ . μ ) + c 1 . e ( γ ) + g + i . e ( γ ) ] / c 1

The derivative of the budget deficit with respect to ubi is negative.

Balanced Budget

The analysis is now conducted for a balanced budget. The level of UBI is treated as related with the per capita GDP, and eqn. (14) is the relevant one.

The budget deficit is given by βγ.N + β.γ.λ.μ.N + gβP − tβN so that a balanced budget would correspond to:

(18) γ . N + γ . λ . μ . N + g P = t N

Divide through by P to give

(19) γ . e . r + γ . λ . μ . e . r + g = t . e . r

Combining eqns. (17) and (19) gives:

(20) c 0 ′ + g t − γ ( c 1 γ + c 1 ( 1 − t ) + i − 1 + γ . λ . μ ) + g = 0

This equation is solved for the tax rate t for a specified level of UBI and government expenditure on goods and services g. From this the employment rate e can be calculated, and from equation above for e.r, r can be calculated.

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Received: 2023-08-21

Accepted: 2024-08-13

Published Online: 2024-09-02

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Articles in the same Issue

https://doi.org/10.1515/bis-2023-0032

Keywords for this article

universal basic income; budget deficits; money; full employment