PDE Department of Economics, Trinity X + X C File | C:/Users/Mrinalsareen/Pictures/Camera%20Roll/Department%20of%20Economics,%20Trinity%20College,%20Dublin[2832].pdf 8 of 9 Q K7 The last equations is the law of motion for productivity, EA,t are shocks to productivity at time r and PA represents the persistence of the shocks. The shocks are normally distributed random variables with mean zero and standard deviation o A. Solving the model with o B'me where it = 1 - 1/0 where o, y and B are positive constants. The budget constraint is C + Ki+ + Ti = Wilt + (1 + Re - 8) Ki where o is the depreciation rates and Te is the lump sum tax rate. The optimal choices of consumption and hours worked are given by 13.C a X W 9 IN ENG 1:03 Raining now KO 21-10-2022 2 INPDE Department of Economics, Trinity X + X C File | C:/Users/Mrinalsareen/Pictures/Camera%20Roll/Department%20of%20Economics,%20Trinity%20College,%20Dublin[2832].pdf 4 of 9 Q K7 There is an infinitely lived representative household that chooses consumption, savings and hours worked to maximise C1-1/8 1+4 t = 0 U => But where uht = 1-1/0 9 1+ + where o, 4 and B are positive constants. The budget constraint is Ct + Kuti + Te = Wilt + (1 + Pu - 8) Ke where o is the depreciation rate and It is the lump sum tax rate. The optimal choices of consumption and hours worked are given by Cut1 = BOP (1 + RH+1 - 8) OLi = Wt Simulating the RBC model The model has nine variables (output, private consumption, investment, capital, labour, produc- This implies that the rate of return on capital purchased at time t is 1 + Re41 - 5. This is because one unit of capital in period t has a value in period t+1 of 1 + Re+1 - 6. This is composed of a rental income in period t+1 of Re+1 plus the value of the remaining 1 - 6 units of capital. Therefore Ret1 - 6 is the rate of interest in this model. 13.C a W Raining now O X 9 N ENG 01:04 KO IN 21-10-2022 2PDE Department of Economics, Trinity X + X C File | C:/Users/Mrinalsareen/Pictures/Camera%20Roll/Department%20of%20Economics,%20Trinity%20College,%20Dublin[2832].pdf 5 of 9 Q K7 The optimal choices of consumption and hours worked are given by CanI = BCE (1 + Re+1 - 8) Wt Simulating the RBC model The model has nine variables (output, private consumption, investment, capital, labour, produc- "This implies that the rate. of return on capital purchased at time.t is 1 + Re+1 - 6. This is because one unit of capital in period t has a value in period t+1 of 1 + Rt+1 - 6. This is composed of a rental income in period t+1 of Rt+1 plus the value of the remaining 1 - 6 units of capital. Therefore Rt+1 - o is the rate of interest in this model. 22 13.C Raining now a X W 9 IN ENG 01:04 KO IN 21-10-2022 2PDE Department of Economics, Trinity X + X C File | C:/Users/Mrinalsareen/Pictures/Camera%20Roll/Department%20of%20Economics,%20Trinity%20College,%20Dublin[2832].pdf 6 of 9 Q K7 tivity, wages & the interest rate) and nine equations:4 Y = AKOL-a Ktti = 1+(1-p) Ke Put = QA, Ka-1LI-a Wt = (1 -Q) AK, L, a = BE 1 + Rt+1 - 6 OLY = log At+1 = PA log At + E At+1 The last equations is the law of motion for productivity, EAt are shocks to productivity at time t and PA represents the persistence of the shocks. The shocks are normally distributed random variables with mean zero and standard deviation q A. Solving the model with 6