Question

subject to the budget constraints: at = (n - n)at + Wt - Ct - it he = u - (6 + n)hi (a) Briefy interpret this decision problem, including the parameters O and p. (b) Use the optimal control theory to find the first-order conditions for an interior solution. (c) Derive from the first-order conditions the Keynes-Ramsey rule and a no- arbitrage equation showing a relationship between w = w/h and r. (d) Assume now, for simplicity, that the aggregate production function is Cobb-Douglas: Y = AK"(hL)1-a Determine the real rate of interest in equilibrium at time t. (e) The no-arbitrage equation, which is needed for an interior solution to the household's decision problem) requires a specific value of K = H to obtain. Determine this value and explain what happens to begin with if the historically given K/H ratio in the economy differs from it; and explain what happens in the long run.\f