Inclusive growth is measured using the concept of the social opportunity function which is an offshoot of the utilitarian social welfare function. Within this framework inclusive growth is achieved when the social opportunity function is maximized. This depends on increasing the average opportunities available to the population and the equitable distribution of the available opportunities among the population. Greater weights are associated with the opportunities enjoyed by the poor. Such weighting ensures that the opportunities created for the poor are greater than those for the non-poor. Emphasis is that the extra opportunities are created for the poor without making the non-poor worse-off.
Following Ali and Son (2007), supposing there are persons in the population having incomes x1,x2,x3,... ... ..., xn where the poorest individual in the population is x1 and the wealthiest xn. The social welfare function W which is an increasing function of income x is specified as;
Similarly, the social opportunity function O is expressed as an increasing function of income x. The Social opportunity function is denoted as
Where y1 denotes the opportunity enjoyed by the ith person having income x1.
Opportunity is expressed in the form of access to health, education or employment. y1 can take the form of a binary value of 0 and 100, when the ith person has access to a specified opportunity, it takes a value of 100, that is, having access to employment and 0 if there is lack of access. The percentage of the population, QN that has access to a given opportunity is denoted by the opportunity curve as;
Where; the cumulative percentage of the population is denoted by Given, that is a binary number which assumes the value o or 1, the average opportunity Y*(Q) is analogous to the percentage of the population having access to a particular opportunity. Maximizing Y*(Q) is a necessary but not sufficient condition in determining if inclusive growth has been achieved. To perform of a comprehensive assessment of inclusive growth, considering the distribution of opportunities across different income groups in the population is essential. Including distribution concerns requires that the opportunity function satisfy the transfer principle. The transfer principles connote that the transfer of opportunity form a non-poor individual to one who is poor will enhance the social opportunity function. This is captured by the opportunity curve. The opportunity curve also referred to as the partial approach to measuring inclusive growth is useful for determining the growth pattern in terms of access and equity of opportunity. However, it does not quantify the exact amount of change that has occurred in opportunities overtime.
To capture the magnitude of changes in opportunities overtime, the social opportunity function is utilized and an index from the area under the opportunity curve which is analogous to the concentration curve is estimated. The opportunity index is obtained as twice the area under the generalized concentration curve. This is denoted as;
Where; EIO = 1 - C is the equity index of opportunity and C the concentration index of opportunity. If EIO is greater (less) than 1 then opportunity is equitable (inequitable). The equation shows that the opportunity index is a product of the average opportunity and the equity index of opportunity (Son, 2011).
To ensure inclusive growth OI must increase, this can be achieved by increasing the average opportunities Y*(Q) or increasing the equity index of opportunity EIO, or increasing both the average opportunities and the equity index of opportunities. Differentiating both sides of equation 4.4
Where dOI quantifies the changes in magnitude of growth inclusiveness. Growth inclusiveness is increased if dOI is > 0. The first term on the right side of equation 4.5 is the contribution to growth inclusiveness as a result of a change in the distribution of opportunities when the average opportunity remains constant. The second term show the contribution of changes in the average opportunity to the inclusiveness of growth when the distribution of opportunity remains unchanged. The policy implication of the above formulation is that if there are improvements in the average opportunities accessible to the population and if these opportunities are distributed equitably then growth inclusiveness can be achieved.
The data utilized in this study to determine access and equity of opportunity was the General Household survey (GHS) which contains micro level information about the household. The GHS was conducted by the Nigerian National Bureau of Statistics in collaboration with the Federal Ministry of Agriculture and Rural development and The World Bank Living Standards Measurement Study (LSMS) team as part of the Integrated Surveys on Agriculture (ISA) program. It is a nationally representative survey of 5,000 households which are also representative of the six geopolitical zone in Nigeria which are grouped into urban and rural areas. The GHS offers information on demographics; education; healthcare utilization, labour, food and non-food expenditure. Specifically, two sets of the General household survey (GHS) of the National Bureau of statistics in Nigeria, 2012-2013 and 2015-2016 were utilized in the analysis. For 2012-13 we utilized 4,755 households in the study, while 2015-16 3,442 households were utilized.
 For more information on the application of opportunity curve in the measurement of inclusive growth see Ali and Son (2007), Adedeji, Du and Opoku-Afari (2013).