Public expenditure allocation, lobbying, and growth

I develop a two sector model of growth where the final good in each sector is produced using labor and a publicly provided private input (public input). The public input is funded by a proportional tax on the consumption of the two final goods. In the benchmark case, the government allocates the public input between the two sectors to maximize consumer welfare. I contrast the benchmark case to one where the public input allocation is determined via lobbying by firms in the two sectors. In this set up, I first show that allocation of the public input is determined by the relative lobbying power of the firms in the two sectors. Further, lobbying can generate the welfare maximizing allocation only under a very specific set of conditions and, if those set of conditions are not met, then an initial misallocation of the public input gets magnified over time.