Consider an economy with the following per capita production function: ???? = ???? ???? ; where ???? is the per capita capital owned by the representative consumer, and ???? is the per capita public infrastructure which is an accumulable input like physical capital. The government imposes a tax rate of ???? on income and spends the tax revenue on financing investment in public infrastructure. The representative consumer has an instantaneous utility function of the type ???? = . Suppose the government wants to maximize the consumer’s welfare here, taking into account the externality of the public infrastructure in the production function. a. Can you set up the government’s maximization problem and give the FONCs? b. Is there a steady-state equilibrium, defined as ????= ????= ????= ???? ?0?