Consider the unit-elastic RBC model discussed in section 15.5.1 of the text. Change the lifetime utility...

Transcribed Image Text:

Consider the unit-elastic RBC model discussed in section 15.5.1 of the text. Change the lifetime utility function (15.59) to: Et At Et T-t 1+0L EA = E (11) [ecin ( 1 LL (7)L) (1 Ec)LT], T=t _ YL 1+0L 4) (Q15.20) where G+ is government consumption and a is a constant parameter (0 a 1). The felicity function is linear in labour supply so we make use of the lottery model developed by Hansen. The household views G as an uncontrollable stochastic pro- cess that is not dependent on any endogenous variables. The stochastic process for G+ is given by: In Gt = G+PG ln G-1 +, 0 < PG < 1, (Q15.21) where & is the innovation term which is identically and independently distributed with mean zero and variance 2. Technology is deterministic. The rest of the model is unchanged. (a) Solve the household's optimization problem, using the Lagrangian method ex- plained in the text (see equations (15.62)-(15.65)). Consider the unit-elastic RBC model discussed in section 15.5.1 of the text. Change the lifetime utility function (15.59) to: Et At Et T-t 1+0L EA = E (11) [ecin ( 1 LL (7)L) (1 Ec)LT], T=t _ YL 1+0L 4) (Q15.20) where G+ is government consumption and a is a constant parameter (0 a 1). The felicity function is linear in labour supply so we make use of the lottery model developed by Hansen. The household views G as an uncontrollable stochastic pro- cess that is not dependent on any endogenous variables. The stochastic process for G+ is given by: In Gt = G+PG ln G-1 +, 0 < PG < 1, (Q15.21) where & is the innovation term which is identically and independently distributed with mean zero and variance 2. Technology is deterministic. The rest of the model is unchanged. (a) Solve the household's optimization problem, using the Lagrangian method ex- plained in the text (see equations (15.62)-(15.65)).