Consider a single parent household in a developing country consisting of a mother and her son. The mother plans to stop working at some time in the future and will extract some of the son's income to live on when she stops working. The child's future income depends on acquiring schooling (human capital) and the mother chooses to provide education to her son because she cares about the utility his future income will bring her in the future. Her utility function can be written as U(Y,S) = m logY - h(S) with m>0, and where Y is the son's future income and h(S) represents the costs of schooling. The son's income is well represented by the following log-linear form: logY = + S, where S is the years of schooling, Y is his income and and are parameters. Assume the marginal cost of schooling, dh(S)/dS, is given by h'(S) = + S, where (gamma) and (phi) are positive parameters.

a.Interpret the h'(S) function.

b. What is the interpretation of and how does it affect the optimal amount of schooling provision to the child?

Now assume the mother attaches an intrinsic value to more education for the child amounting to (delta) per year of schooling.

c. State the new utility function of the parent and the optimal amount of education provided for the child. Is this greater or smaller than the answer in part (b)? Explain your answer.

d. It is generally claimed that the output of schooling, measured by test scores of pupils, is a positive function of school resources, therefore providing more resources for schools, for example textbooks, raises the test results of pupils. What is the evidence presented in Banerjee and Duflo, Poor Economics, regarding distribution of more textbooks in schools in Western Kenya?