Consider the representative agent model, where the lifetime utility

Problem 2. Consider the representative agent model, where the lifetime utility max 1=0 is maximized subject to the budget constraint kil = (1 - T) [f(k ) - c]+ (1-6)k; Ki >O ko > 0 given where C = per capita consumption K = per capita capital stock T = tax on investment and the production function f(k,) and the utility function u(c, ) satisfy the standard neoclassical assumptions. (a) Write down the first order conditions and the transversality condition for this problem. (b) Derive the Euler equation assuming u(c) = C-e - 1 1-0 and f ( k. ) = kx (c) Does capital tax reduce per capita income? Show and explain