Consider the expanding input variety model of Section 13.1.
(a) Suppose that a benevolent government has access only to research subsidies, which can be financed by lump-sum taxes. Can these subsidies be chosen to ensure that the equilibrium growth rate is the same as the Pareto optimal growth rate? Can they be used to replicate the Pareto optimal equilibrium path? Would it be desirable for the government to use subsidies to achieve the Pareto optimal growth rate (from the viewpoint of maximizing social welfare at time t = 0)?
(b) Suppose that the government now has access only to subsidies to machines, which can again be financed by lump-sum taxes. Can these be chosen to induce the Pareto optimal growth rate? Can they be used to replicate the Pareto optimal equilibrium path?
(c) Will the combination of subsidies to machines and subsidies to research be better than either of these two policies by themselves?