2. [60 points] Consider a Ramsey growth model with the following CRRA utility function u(c)=1c11 and the Cobb-Douglas production function Y(t)=BK(t)L(t)1, where B>0 is a constant. Assume n>0. (a) Write down the complete growth model. That is, (i) define and solve the household's problem using the Hamiltonian and derive the Euler equation, (ii) derive the firm's problem, (iii) formally define an equilibrium in this economy and state the two differential equations in the variables (c,k). Provide a brief intuition of these steps. (b) Consider the case of an increase in productivity. That is, do the following comparative dynamics exercise: B>B. For that, first draw the phase diagram for the baseline case, and suppose that k is equal to k for this case. Then draw the modified phase diagram, indicating what has changed with the higher value of B. Draw the modified time paths of k and c, indicating how they compare with the baseline time paths. What is the intuition? 2. [60 points] Consider a Ramsey growth model with the following CRRA utility function u(c)=1c11 and the Cobb-Douglas production function Y(t)=BK(t)L(t)1, where B>0 is a constant. Assume n>0. (a) Write down the complete growth model. That is, (i) define and solve the household's problem using the Hamiltonian and derive the Euler equation, (ii) derive the firm's problem, (iii) formally define an equilibrium in this economy and state the two differential equations in the variables (c,k). Provide a brief intuition of these steps. (b) Consider the case of an increase in productivity. That is, do the following comparative dynamics exercise: B>B. For that, first draw the phase diagram for the baseline case, and suppose that k is equal to k for this case. Then draw the modified phase diagram, indicating what has changed with the higher value of B. Draw the modified time paths of k and c, indicating how they compare with the baseline time paths. What is the intuition