4. Foster-Greer-Thorbecke poverty measure Consider two cases under the Foster-Greer-Thorbecke (FGT) measure: . PP= 1CNN|1 - 1(xx z> where x= 0 pp=1ENN|1 - 1(xxS z)|where x= 1 Now, suppose an economy - with Nindividuals each indexed by itwith income xx- contains one individual with income xx= 2 and another with income xx = zz 1. Assume zz 3. Using the Dalton principle of transfers (e.g. make a transfer of 2 from xxto x , show whether each of these poverty measures above satisfies weak equity preference. 5. Multidimensional Poverty Index In 2010, the Multidimensional Poverty Index (MPI) was developed as a new poverty measure. Answer the following questions, with the help of background documentation to the MPI found here: http://hdr.undp.org/en/2020-MPI. a) Name and describe at least three key differences between the MPI and conventional poverty measures e.g. the headcount ratio. (b) In the MPI, each individual inis assigned a deprivation score s = 2,;=,cedd, which sums binary indicators do of jjdeprivations (jj= 1,..., 10) that the individual experiences, and where each deprivation is given a pre-assigned weight ce An individual is deemed "poor" when s > 1/3; in turn, the multidimensional headcount ratio for a country is defined as HA - ZINnn X 1(ss > 1/3) ENNnn Using these notations, write down a statistical expression for the intensity of poverty A, and for the MPI. (c) In the MPI, all individuals are assigned the same deprivation score within the household. What might be the consequence(s) for measurement? (d) There is no doubt that MPI help us quantify dimensions of deprivations beyond income. However, like other composite indices, it is not immune to problems. Name and describe a list of problems that you believe are relevant to the MPI