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reduce Poverty and Unemployment, in Nigeria as well as on the entire continent of Africa. These feats are accomplished at acceptable returns on investments to ...
G20 INVESTMENT ‘COMPACT WITH AFRICA’, THE EXPECTED RETURNS ON INVESTMENTS, AND THE POTENTION FOR UNEMPLOYMENT AND POVERTY ALLEVATION IN AFRICA Hans E. Alagoa Monarch Business School, Switzerland Abstract: The G20 Africa Partnership is a central project of Germany’s G20 presidency. Utilizing the Cobb-Douglas production functions for Africa’s largest economy, Nigeria, as well as that for the entire continent of Africa; and Labour Force, Population, Poverty Rate, and Unemployment Rate data for Nigeria and for the entire continent, from the World Bank; the investment from the G20 Africa Partnership, is shown to significantly reduce Poverty and Unemployment, in Nigeria as well as on the entire continent of Africa. These feats are accomplished at acceptable returns on investments to the G20 Africa Partnership investors.

Electronic copy available at: https://ssrn.com/abstract=3035430

1.0 INTRODUCTION The G20 acknowledges its special responsibility to join forces in tackling the challenges facing the poorest countries, especially in Africa. The Compact with Africa initiative aims to boost private investment and investment in infrastructure in Africa. Such investment is an essential precondition for strong, balanced and sustainable growth. The G20 Africa Partnership is a central project of Germany’s G20 presidency. Its aim is to improve conditions for sustainable private sector investment, investment in infrastructure, economic participation, and employment in African countries. A key pillar of the G20 Africa Partnership is the Compact with Africa, an initiative within the G20’s finance track, which is coordinated by the German Federal Ministry of Finance (Government of Germany, Federal Ministry of Finance, 2017). What returns on investments (ROI) can investors involved in the Compact with Africa initiative expect to get. In this essay the Production Function, a mathematical expression relating the amount of Output produced to quantities of Capital and Labour utilized, (Abel, Bernanke, & Croushore, 2008), is used to predict the Output expected for Capital invested. In addition the Labour required, will be used to determine the impact that the investment could have on the alleviation of Unemployment and Poverty on the African continent, and in its largest economy, Nigeria. The essay begins with the determination of such development indicators as, the Population, size of the Labour force, and levels of Unemployment and Poverty, for All of Africa, and for Africa’s largest economy, Nigeria. Next the Production Function of All of Africa, as well as that of Nigeria is determined. The potential return on investment from the Compact with

Electronic copy available at: https://ssrn.com/abstract=3035430

Africa initiative, as well as the potential impact of the investment on the alleviation of poverty and unemployment is then determined.

2.0 SOME PERTINENT DEVELOPMENT INDICATORS FOR AFRICA Table 2.1 below shows some pertinent development indicators for all of Africa, and for Nigeria. Table 2.1 in addition shows the aggregate indicators for Sub-Saharan Africa, and the indicators for each of the countries of North Africa. These were then used to develop the aggregate indicators for all of Africa. These development indicators, which are; • a Total Population of 1,224.4 million; • a Labour Force of 477.2 million; • a Poverty Rate of 57.2% of the Population or 700.7 million; and • an Unemployment Rate of 8.2% of the Labour Force or 39.0 million persons; will serve as benchmarks as the impact of the investments associated with the G20’s Compact with Africa initiative, on Unemployment and Poverty alleviation on the African continent, and in Africa’s largest economy, Nigeria is accessed.

Electronic copy available at: https://ssrn.com/abstract=3035430

3.0 THE PRODUCTION FUNCTION The production function Productivity, Output, and Employment is a mathematical expression relating the amount of output produced to quantities of capital and labor utilized (Abel, Bernanke, & Croushore, 2008). A convenient way to write the production function is Y = AF(K, N),

Eqn. 3.1

Where Y = Real output produced in a given period of time; A = Number measuring overall productivity; K = Capital stock, or quantity of capital used in the period; N = Number of workers employed in the period; F = a function relating output Y to capital K and labor N. Abel, Bernanke, & Croushore (2008) explain that the Production Function in Eqn (3.1) applies both to an economy as a whole (where Y, K, and N

refer to the economy's Output, Capital Stock, and Number of Workers, respectively) and to an individual firm, in which case Y, K, and N refer to the firm's output, capital, and number of workers, respectively. According to Eqn. (3.1), the amount of output Y that an economy (or firm) can produce during any period of time depends on the size of the capital stock K and the number of workers N. The symbol A in Eq. (3.1), which multiplies the function F(K, N), is a measure of the overall effectiveness with which capital and labor are used; and is referred to as Total Factor Productivity, or simply Productivity. A more specific Production Function that works well in macroeconomics, is the Cobb-Douglas Production Function, Eqn. 3.2, shown below (Abel, Bernanke, & Croushore, 2008) Y = AKαN(1-α)

Eqn. 3.2

In this essay the Production Function used is shown below: Y = AK0.3N0.7

Eqn. 3.3

Note: The parameter α (0.3) corresponds to the share of the income received by the Owners of Capital, and α-1 (0.7) corresponds to the share of the Income received by Labour.

4.0 THE MINIMUM ATTRACTIVE RATE OF RETURN (MARR) According to Park (2007), in business and engineering, the minimum acceptable rate of return, often abbreviated MARR, is the minimum rate of return on a project a manager, company, or investor, is willing to accept

before starting a project, given its risk and the opportunity cost of forgoing other projects. The MARR is often decomposed into the sum of the following component range of typical values shown (Lang, & Merino, 1993): Traditional inflation-free rate of interest for risk-free loans: 3 to 5% Use 4% Expected rate of inflation: 5% Use 5% The anticipated change in the rate of inflation, if any, over the life of the investment: Usually taken at 0% Use 0% The risk of defaulting on a loan: 0 to 5% Use 3% The risk profile of a particular venture: 0 to 5% and higher Use 5% An MARR of 4 + 5 + 0 +3 + 5 = 19% is used for the analyses in this essay.

5.0 THE PRODUCTION FUNCTION OF NIGERIA Table 5.1 shows the values of key factors of production, Capital and Labour, for Africa’s largest economy, Nigeria. Using equation (3.3), Table 5.1 shows how Output, Y, relates to the use of factors of production, Capital, K, and Labour, N, and to Productivity, A, in Africa’s largest economy, Nigeria; Table 5.1 presents data on these variables for Nigeria for 11 years beginning in 2005. Columns (1), (2), and (3) show Output (real GOP), Capital stock, and Labour for each year. Real GOP and the Capital stock are measured in billions of 2005 dollars, and Labour is measured in millions of employed

workers. Column (4) shows the economy of Nigeria’s Productivity for each year. Table 5.1

The Production Function of Nigeria, 2005 - 2015 Y e a r

(1) Real GDP, Y

(2) Capital Stock, K or Gross Capital Formation

(Billions of 2005 $)

(Billions of 2005 $)

(Millions of 2005 $)

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

180.5 191.4 203.7 216.5 231.5 249.7 261.9 273.1 287.8 306.0 314.1

14.7 27.6 33.1 32.8 44.3 52.4 48.2 49.9 53.8 60.7 60.9

43.3 44.4 45.7 47.0 48.3 49.7 51.2 52.6 54.2 55.8 57.5

(3) LABOUR, N

(4) PRODUCTIVITY, A = Y/(K0.3xN0.7)

5.8 5.0 4.9 5.1 4.9 4.9 5.2 5.3 5.3 5.3 5.4

SOURCE: UN National Accounts Statistics, World Bank, & Author's Calculations

5.1 The Production Function of Nigeria Relating Output and Capital Figure 5.2 below shows how much Output the Nigerian economy could produce for each level of Capital Stock, holding Nigerian Labour as follows; Employed Labour = Total Labour – Unemployed = 59.1–3.0 = 56.1 million 25% of Poverty alleviation due to employment = 0.25 x 83.8 = 21.0 million, 50% of Unemployment alleviation = 0.50 x 3.0 = 1.5 million, and Total Nigerian Labour = 56.1 + 21 + 1.5 = 78.6 million

Using Productivity at the most recently available value, that is 5.4. The production function (Eq. 3.3) becomes Y = AK0.3 N0.7 = (5.4)(K0.3)(78.60.7) Y = 114.6K0.3. This relationship is graphed in Fig. 5.2, with Capital stock K on the horizontal axis and Output Y on the vertical axis. Table 5.2 below shows the range of values of Investments K, where the ROI is greater than or equal to 19%. Table 5.2

The Production Function of Nigeria Relating Output and Capital, with Labour at 78.6 million and Productivity at 5.4 Investment, K (Billions of 2010 $)

Output, Y (Billions of 2010 $)

Return on Investment (ROI) Percent

13.09 23.81 39.68 61.05 87.21 116.28 145.35 171.00 190.00 200.00

247.9 296.6 345.7 393.4 437.9 477.3 510.4 535.9 553.1 561.7

5.3 8.0 11.5 15.5 19.9 24.4 28.5 31.9 34.4 35.6

SOURCE: World Bank & Author's Calculations

As Table 5.2 shows, for Investments, K, greater than or equal to $81.9billion, the Return on Investment (ROI) is greater than or equal to 19%; which is the MARR value estimated in section 4.0.

6.0 THE PRODUCTION FUNCTION OF THE AFRICAN CONTINENT Table 6.1 below shows the values of key factors of production, Capital and Labour, for all of Africa. Using equation (3.3), Table 6.1 shows how Output, Y, relates to the use of the aggregated factors of production, Capital, K, and Labour, N, and to Productivity, A, of all of Africa. Table 6.1 presents data on these variables for the African continent for 11 years beginning in 2005. Columns (1), (2), and (3) show Output (real GOP), Capital stock, and Labour for each year. Real GOP and the Capital stock are measured in billions of 2005 dollars, and Labour is measured in millions of employed

workers. Column (4) shows the Productivity of the economy of the entire continent of Africa for each year. Table 6.1

The Production Function of All of AFRICA, 2005 - 2015 (2) (4) Total Gross (3) PRODUCTIVITY, Capital Labour, N (Millions of 2010 $) A = Y/(K0.3xN0.7) Formation, K (Billions of 2010 $)

Y e a r

(1) Real GDP, Y (Billions of 2010 $)

2005

1,558.5

285.3

350.0

4.7

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

1,661.2 1,772.2 1,865.9 1,919.8 2,016.3 2,040.0 2,106.0 2,192.2 2,278.7 2,351.1

331.9 387.6 430.5 437.8 467.2 467.6 493.3 518.5 545.3 556.1

359.1 369.5 380.5 390.9 402.0 412.8 424.2 437.2 449.8 463.5

4.7 4.7 4.7 4.7 4.8 4.8 4.7 4.8 4.8 4.8

SOURCE: World Bank & Author's Calculations

6.1 The Production Function of Africa Relating Output and Capital Figure 6.2 on the next page shows how much Output the Nigerian economy can produce for each level of Capital Stock, holding Labour of Africa as follows; Employed Labour = Total Labour – Unemployed = 477.2–39.0 = 438.2M 25% of Poverty alleviation due to employment = 0.25 x 700.7 = 175.2M, 50% of Unemployment alleviation = 0.50 x 39.0 = 19.5M, and Total Labour of Africa = 438.2 + 175.2 + 19.5 = 632.9 million

Using Productivity at the most recently available value, that is 4.8. The production function (Eq. 3.3) becomes Y = AK0.3 N0.7 = (4.8)(K0.3)(632.90.7) Y = 438.71K0.3. This relationship is graphed in Fig. 6.1, with Capital stock K on the horizontal axis and Output Y on the vertical axis. Table 6.2 below shows the range of values of Investments K, where the ROI is greater than or equal to 19%. Table 6.2

The Production Function of the African Continent Relating Output and Capital, with Labour at 632.9million and Productivity at 4.8 Investment, K (Billions of 2010 $)

Output, Y (Billions of 2010 $)

Return on Investment (ROI) Percent

104.76 190.47 317.44 488.38 697.68 930.24 1,162.80 1,368.00 1,520.00 1,600.00

1,771.1 2,119.0 2,469.9 2,810.6 3,128.1 3,410.0 3,646.1 3,828.3 3,951.2 4,012.5

5.9 9.0 12.9 17.4 22.3 27.3 31.9 35.7 38.5 39.9

SOURCE: World Bank & Author's Calculations

As Table 6.2 shows, for Investments, K, greater than or equal to $556.7billion, the Return on Investment (ROI) is greater than or equal to 19%; which is the MARR value estimated in section 4.0.

7.0 CONCLUSION The G20 Africa Partnership is a central project of Germany’s G20 presidency. This essay has shown that the investments made under this Compact with Africa, can reduce Unemployment and Poverty on the continent of Africa as a whole, but do it at a reasonable profit to the investors, with a Minimum Attractive Interest Rate (MARR) of 19%. With a Total Population of 1,224.4 million, a Labour Force of 477.2 million; a Poverty Rate of 57.2% of the Population or 700.7million people; and an Unemployment Rate of 8.2% of the Labour Force or 39.0 million persons; the

continent of Africa non the less has an average annual Productivity of 4.85. With this level of Productivity, a Labour force of 632.9 million, which

comprises 438.2million currently employed people, 175.2million or 25% of the continents Poor, and 19.5million or 50% of the continents Unemployed, can produce Output, at MARR of 19%, with investments of $556.7 billion or more. Africa’s largest economy, Nigeria, has similarly impressive potential. With a Total Population of 182.2million, a Labour Force of 59.1million; a Poverty Rate of 46% of the Population or 83.8million people; and an Unemployment Rate of 5% of the Labour Force or 3.0million persons; Nigeria has an average annual Productivity of 5.2. With this level of Productivity, a

Labour force of 78.6million, which comprises 56.1million currently employed persons, 21.0million or 25% of the Poor of the country, and 1.5million or 50% of the country’s Unemployed, can produce Output, at MARR of 19%, with investments of $81.9billion or more. These analyses show that far from being a charity case, investments in Africa have the potential of producing very profitable dividends.

8.0 ABOUT THE AUTHOR At the writing of this essay, the author Hans E. Alagoa is a candidate for the Doctor of Applied Management degree from the Monarch School of Business, Switzerland. In his doctoral dissertation, ‘The Ideal Trade Relationship between a Developed Country and a Developing Country’, he shows the effects on the key development indicators of both countries, and on the Human Development Index of the developing country, of an ideal trading relationship.

9.0 APPENDICES 9.1 Table of Aggregate Production Data for Sub-Saharan Countries, 2005 - 2015 Table 9.1 Aggregate Production Data for Sub-Saharan Africa Countries, 2005 - 2015 Capital Stock, K or Gross Capital Formation

Y e a r

(Billions of 2010 $)

(Billions of 2010 $)

(Millions of 2010 $)

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

1,037.5 1,110.7 1,189.2 1,253.3 1,289.0 1,358.5 1,417.3 1,470.0 1,540.0 1,610.6 1,659.2

162.1 194.5 226.6 244.0 251.1 277.1 283.7 302.8 322.5 343.5 345.1

290.6 299.0 307.5 317.2 326.2 335.8 345.5 355.6 366.9 378.4 390.6

Real GDP, Y

LABOUR, N

SOURCE: Development Indicator's of the World Bank

9.2 Table of Production Data for each of the North African Countries, 2005 - 2015 Table 9.2a Factors of Production Data for Algeria, North Africa, 2005 - 2015

Y e a r

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Real GDP, Y

Capital Stock, K or Gross Capital Formation

LABOUR, N

(Billions of 2010 $)

(Billions of 2010 $)

(Millions of 2010 $)

142.3 144.6 149.5 153.1 155.6 161.2 165.9 171.5 176.2 182.9 189.8

50.9 50.0 55.6 59.2 64.9 66.8 61.6 70.4 77.7 85.1 92.5

10.0 10.2 10.4 10.6 10.8 11.1 11.3 11.5 12.0 12.2 12.4

SOURCE: Development Indicator's of the World Bank

Table 9.2b Factors of Production Data for Egypt, North Africa, 2005 - 2015

Y e a r 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Real GDP, Y

Capital Stock, K or Gross Capital Formation

LABOUR, N

(Billions of 2010 $)

(Billions of 2010 $)

(Millions of 2010 $)

162.2 173.3 185.6 198.9 208.2 218.9 222.9 227.8 232.6 237.7 247.7

26.7 30.4 37.4 43.3 39.6 42.7 42.0 44.0 40.3 41.0 44.5

24.0 24.0 25.2 25.9 26.7 27.4 27.8 28.4 29.1 29.6 30.2

SOURCE: Development Indicator's of the World Bank

Table 9.2c Factors of Production Data for Libya, North Africa, 2005 - 2015 Capital Stock, K or Gross Capital Formation

Y e a r

(Billions of 2010 $)

(Billions of 2010 $)

(Millions of 2010 $)

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

61.7 65.7 69.9 71.8 71.2 74.8 28.4 26.1 24.1 22.2 20.4

4.5 11.6 17.6 26.0 23.9 22.0 20.3 18.7 17.2 15.9 14.6

2.2 2.2 2.3 2.3 2.4 2.4 2.4 2.4 2.4 2.4 2.3

Real GDP, Y

LABOUR, N

XXX Estimates SOURCE: Development Indicator's of the World Bank

Table 9.2d Factors of Production Data for Morocco, North Africa, 2005 - 2015 Capital Stock, K or Gross Capital Formation

Y e a r

(Billions of 2010 $)

(Billions of 2010 $)

(Millions of 2010 $)

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

73.0 78.5 81.3 86.1 89.8 93.2 98.1 101.1 105.6 108.3 113.2

21.9 23.8 27.0 33.2 32.3 31.8 35.0 34.7 36.8 35.4 33.5

10.9 11.0 11.1 11.3 11.3 11.5 11.7 11.7 11.9 12.1 12.3

Real GDP, Y

LABOUR, N

SOURCE: Development Indicator's of the World Bank

Table 9.2e Factors of Production Data for Tunisia, North Africa, 2005 - 2015 Capital Stock, K or Gross Capital Formation

Y e a r

(Billions of 2010 $)

(Billions of 2010 $)

(Millions of 2010 $)

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

35.3 37.1 39.6 41.3 42.6 44.1 43.2 44.9 46.3 47.6 48.1

7.0 7.7 8.7 9.5 10.6 11.8 10.7 11.6 12.3 13.1 13.8

3.4 3.5 3.6 3.7 3.7 3.8 3.9 4.0 4.0 4.1 4.1

Real GDP, Y

LABOUR, N

XXX Estimates SOURCE: Development Indicator's of the World Bank

Table 9.2f Factors of Production Data for Sudan, North Africa, 2005 - 2015 Capital Stock, K or Gross Capital Formation

Y e a r

(Billions of 2010 $)

(Billions of 2010 $)

(Millions of 2010 $)

2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

46.4 51.1 57.0 61.4 63.4 65.6 64.3 64.7 67.5 69.3 72.7

12.2 13.8 14.7 15.3 15.2 15.1 14.3 11.1 11.6 11.4 12.1

8.9 9.1 9.3 9.5 9.7 10.0 10.3 10.6 10.9 11.2 11.5

Real GDP, Y

LABOUR, N

SOURCE: Development Indicator's of the World Bank

10.0 REFERENCES 1. Abel, Andrew B., Bernanke, Ben S., and Croushore, D. (2008). Macroeconomics (6th Eds.). Boston, MA: Pearson, Addison Wesley. 2. AfDB, IMF, and WBG (2017). G-20 Compact with Africa: A Joint AfDB, IMF, and WBG Report. Retrieved from https://www.bundesfinanzministerium.de/ Content/EN/Standardartikel/Topics/Featured/G20/2017-03-30-g20compact-with-africa-report.html 3. Lang, Hans J., and Merino, Donald N. (1993). The Selection Process for Capital Projects. New York: J. Wiley & Sons. 4. Park, Chan S. (2007). Contemporary Engineering Economics (4th Edition). Prentice Hall. p. 216.