1. Consider the following q problem in continuous time: v[K. 0] = max(), Jet(AF[Ka] - h - x* )at dt subject to 9 = /t, Ko is given. Here r is the interest rate, and A> 0 is the total factor productivity. Note that in the problem just stated the capital stock cannot be adjusted instantaneously without incurring prohibitive adjust- ment costs. More precisely, if /, is the amount of capital invested (or dis-invested), then the total cost of investment is given by hat : , where X is a positive constant. (a) Does the model you have a stationary equilibrium? If your answer is affirmative, draw a phase diagram to explain the convergence to the stationary equilibrium. (b) Show that the value of the Hamiltonian - evaluated at each instant t along the optimal traject tory - gives the permanent level of utility, i.e., the permanent level of real income, of the representa- tive agent from instant ton until the end of time