Consider an economy with the general Cobb-Douglas production rnction: Yt = AKtaLtl_a. Answer the following questions assuming that labour grows at the rate it = 0 and adopting the assumptions made in lecture. The equation describing capital dynamics is: Kc+1 = Kc + It th where d is a constant parameter. a) Obtain the steady state levels of the capital stock (K), output (1'), capital per worker 0:), output per worker (y), consumption per worker (C/L), total savings (S), private investment (1), real wages (w) and real interest rates (r). Make sure to show all your work. b) Assuming that s = 0.4, d = 0.1, a = 0.2, E = l and fl = I, calculate the steady state values of the variables in (a). Now, assume the policy-maker successfully implemented policies that resulted in the increase of the total factor productivity level to 2 (i.e., I = 2), ceteris paribus. c) Using the help of the Solow-Swan diagram developed in lectures and tutorials, explain the effect of this policy on the standard of living of the economy. Make sure to include: i) The economic explanation of why the economy experienced a change in the steady state level of capital per worker; ii) A diagram illustrating what happened to the relevant curves. iii) Another diagram illustrating the dynamics of the stock of capital in the economy (before, at and after the technological shock). iv) What must have happened to the growth rate of output per worker in the transition between the initial equilibrium and the nal one? e) Is the current savings rate (s = 0.4) the golden rule of savings? Hint: you don't need to calculate the actual golden rule, just to show that the current one is not the golden rule