Lucas economy with constant consumption prices & Matlab (Total: 10 Points) This problem should be solved with Matlab. Consider the 2-period Lucas endowment economy with constant consumption price (Topic 1, slides 25-31) and a representative agent equipped with power utility of consumption (U(c) = c ^1 /1 )).

(a) Download the total consumption consumption data from the course folder (file name RealExpUSA). Compute c and c. (2 Points)

(b) Assume that consumption growth and returns are are log-normally distributed and derive the real risk-free rate and the equity premium . Plot the real rate and the equity premium (assume rc = 0.0004) as a function of risk aversion. Find the level of risk aversion such that the risk free rate equals 1%. Find the level of risk aversion such that the premium equals 7%. (4 Points)

(c) Set = 3. Simulate the risk-free rate using the parameters above and for N = 10, 100, 1000, 10000 simulations. Compute absolute value of the difference between the simulated and the true risk-free rate as a function of N. (4 Points)