-ax A small island economy produces mainly fish F. This final good is produced from two intermediate goods, boats X1 and fishing rods X2, as follows: F = X(X)- where a (0,1). Boats and rods are produced as follows: X; = EL; Vi 1,2 where L is labor and E is efficiency of production. There are I people living on the island and all of them are happy to supply their labor at any wage. (a) Show that aggregate TFP in the economy can be written as a combination of the efficiency of production and a geometric average of the allocation of the labor across the two intermediate good sectors: A = E[s"(1 $)l-a] where s is the share of labor allocated to boat production. (b) Derive s*, the share of labor allocated to boat production that maximizes aggregate TFP -ax A small island economy produces mainly fish F. This final good is produced from two intermediate goods, boats X1 and fishing rods X2, as follows: F = X(X)- where a (0,1). Boats and rods are produced as follows: X; = EL; Vi 1,2 where L is labor and E is efficiency of production. There are I people living on the island and all of them are happy to supply their labor at any wage. (a) Show that aggregate TFP in the economy can be written as a combination of the efficiency of production and a geometric average of the allocation of the labor across the two intermediate good sectors: A = E[s"(1 $)l-a] where s is the share of labor allocated to boat production. (b) Derive s*, the share of labor allocated to boat production that maximizes aggregate TFP