Consider a world economy consisting of N identical countries, each endowed with one unit of labor. Labor is immobile. The world economy also contains one unit of capital that is freely mobile across countries. All countries have identical production functions given by F(L; K) = L3/4K1/4, where L denotes labor and K denotes capital. The price of output is fixed at $1.
a. Suppose that none of the countries tax either capital or labor. Find the equilibrium interest rate and allocation of capital across countries. What is the total income received by capitalists (the owners of the fixed factor of production) and workers? Evaluate the interest rate and income levels for N = 2 and N = 20.
b. Consider the impact of a tax at rate τ on capital income in country 1 if other countries do not tax capital income. Assume that tax revenues are used to buy output at the fixed price of $1. What is now the after-tax return on capital invested in country 1? What is the equilibrium interest rate and allocation of capital across countries? Find the total income received by capitalists and workers and the tax revenues in country 1 as a function of N and τ.