Question 3
A common way to measure human capital per worker is to suppose it is a function of schooling, namely h(s) = e” where s is years of schooling and q is a parameter. Let the income of a person with human capital h be W h.
a) Suppose Aisha is a representative worker in the economy and has completed s years of schooling, which means that she can earn We” in any given year forever (she is in-finitely lived).
Find an expression for her present discounted lifetime income V(s) if the economy’s interest rate is r > 0, V(s) = We” + 1±„We” + (1÷,.)2 We” +
b) Next, suppose that today, Aisha can decide to go to school for an additional year. During this year she cannot earn any income.
In addition, she needs to pay an upfront tuition fee that is proportional to her yearly income, iWe”.
From the next year onward she then earns an income Weg(‘±’) forever. Compute her present discounted lifetime in-come, V(s + 1).
c) Find the value of q such that Aisha is indifferent between going or not going to school for an extra year. Provide an intuition for your finding.
3Ftemember that geometric series are such that if 0 E (0,1), then EZ,, = 1+6 + =
d) In developed economies, the estimated return to an extra year of schooling is esti-mated to be roughly q = 0.068. The average interest rate is on the order of r = 0.04.
What value of ry is consistent with these numbers? Moreover, given that Aisha is a rep-resentative worker, we can think of her income to be representative of the economy. In the UK, it amounts to roughly GBP 27,000. What, then, is the implied tuition fee in GBP?
e) Caselli (2005) uses the following function to estimate human capital across countries as a function of thee average years of schooling of their workers, h = e0(‘) where /0.134 x s if 8 4 0(s) = 0.134 x 4 + 0.101 x (s — 4) if4<s<8 0.134 x 4 + 0.101 X 4 + 0.068 X (s — 8) if 8 < s. What does this piece-wise linear function capture?