This paper extends the Barro (1990) growth model with one aggregate government spending and one flat income tax to include federal and local public consumption, federal and local public capital formation, federal and local taxes, and federal transfers to locality. It derives the rate of endogenous growth and examines how the growth rate and welfare respond to changes in federal taxes, local taxes, and federal transfers.
Bis(imino) end-functionalized oligo(m-phenylene ethynylene)s were equilibrated in a closed system under conditions that promote reversible imine metathesis. The metathesis reaction joins two oligomers and produces a small molecule byproduct. In polar solvents, equilibration gave high molecular weight polymers while equilibration in chloroform produced only low molecular weight oligomers. This polymerization is hypothesized to be driven by the free energy gained from the folding of the long polymer chains directed by the noncovalent, intramolecular aromatic stacking and solvophobic interactions. This polymerization was also conducted in a series of solvents in which m-phenylene ethynylene oligomers have previously shown varied, intermediate folding stabilities. These experiments revealed a good correlation of the product molecular weight with the stability of the m-phenylene ethynylene helix. The equilibrium state of the metathesis reaction was also demonstrated to depend on the chain length of the starter sequences. With a pair of trimeric precursors, macrocyclization instead of polymerization takes place. Consistent with the notion that the polymerization is a consequence of the intramolecular solvophobic chain association, higher degrees of polymerization followed from enhanced solvophobicity of the m-phenylene ethynylene backbone, achieved by appending a methyl substituent to half of the repeat units. The considerably longer equilibration time required by these more stabilized sequences suggests that the elongation process may involve unfolding or partial unfolding of the chain; alternatively, intermolecular association may be responsible for the slow chain growth.