Essay About Following Parameter Values And Marks

Macroeconomics
1. (30 marks) Consider the life-cycle model discussed in Lecture 3-5. Now suppose thatcapital depreciates after production, and the capital depreciate rate is 0 < δ < 1.1(a) (10 marks) Formulate the individuals’ utility maximisation problem and solve itto find the optimal consumption plan and saving of a generation t individual.(b) (5 marks) Formulate the firms’ profit maximisation problem, and write down theequations that characterise the solution.(c) (5 marks) Write down the market clearing condition for the labour and capitalmarkets.(d) (5 marks) Combine the equations obtained in (a)-(c) to find the transition equationthat describes how kt ≡KtNevolves over time.(e) (5 marks) Show that national saving equals national investment.2. (30 marks) Assume the following parameter values: N = 100, A = 10, K1 = 150,α = 0.7, β = 0.3, δ = 0.6.2(a) (15 marks) Write down the equations you will use to compute the transition pathsof kt, rt, wt, cyt, cot, Kt, Yt, Ct ≡ Ncyt + Ncot, St, It, yt ≡ Yt/N, and st ≡ St/Yt.Then calculate their values (in Excel or other software) for periods 1 through 10, and report kt, rt, wt, cyt, cot, Yt, Ct, It, yt, and stin a table.1In Lecture 3-5, we assumed capital does not depreciate, i.e., δ = 0, so that old individuals can get backthe full assets they invest in firms plus interests. However with capital depreciation, the assets they investin firms will lose some value after production. This is the only difference from the lectures.2These values are more realistic than those used in Lecture 5, especially when a period in our model refersto 30 years. In particular, a higher value of α reflects that individuals value present consumption more thanfuture consumption, and δ = 0.6 implies an annual depreciation rate of roughly 3 percent.1(b) (7 marks) Plot the time paths of kt, yt, rt, wt, cyt, cot, and st (put wt and rt onone figure, and cyt and cot on one figure).(c) (8 marks) Calculate the steady state values of kt, Yt, yt, wt, rt, cyt, cot, and st.Compare them to the steady state values in Table 5.1 of Lecture 5 and explainany differences and similarities.3. (25 marks) Suppose in period 1 the economy is in the steady state calculated in problem