2. Consider the infinite horizon optimal growth model learned in class. Assuming the log utility, the model consists of the following Euler equation and the capital evolution equation. CH1 :I'STI'FCKAKal {+1 C r' Km _Kr : AK? _Cr a. Plot a phase diagram on capital (IQ) and consumption (C, ). In the graph, indicate the steady state level of the two variables, including the saddle path. b. Assume the baseline economy initially lies at the steady state and stays there forever. Now consider the counterfactual economy, which has the same environment with the baseline one, except the initial level of capital stock is higher. Plot a phase diagram of this counterfactual economy and compare the graph with the one drawn in part a. You should include a point indicating the initial point of capital and consumption of the counterfactual economy in the graph (Note: The initial capital stock and consumption in the counterfactual economy are assumed to follow the infinite horizon budget constraint). Explain the dynamics of consumption and the capital stock in the counterfactual economy. c. Explain how the lifetime consumption (the summation of present value of consumption for every period) would differ between the baseline and the counterfactual economy. How about the lifetime income in both economies