Why are we using exp(.) as the functional form in the household maximization problem inside the RCK model?
Currently I'm studying the RCK model at my Advanced Macroeconomics I classes.
A question arose almost immediately when I saw the utility function of a household in this model.
The question is: why are we using exp(-ρt) inside this integral? I mean: why this functional form in particular? I love mastering every single aspect of every model I study, that's why I'm asking so.
Thank you really much in advance for your kind responses.
macroeconomics economic-growth balanced-growth
asked Dec 2 '18 at 17:46
Andrey E. Vedishchev
1185
add a comment |
Currently I'm studying the RCK model at my Advanced Macroeconomics I classes.
A question arose almost immediately when I saw the utility function of a household in this model.
The question is: why are we using exp(-ρt) inside this integral? I mean: why this functional form in particular? I love mastering every single aspect of every model I study, that's why I'm asking so.
Thank you really much in advance for your kind responses.
macroeconomics economic-growth balanced-growth
asked Dec 2 '18 at 17:46
Andrey E. Vedishchev
1185
1
It's just there for bringing future utility to present value in continuous time. $rho$ is the discount factor.
– Pedro Cavalcante Oliveira
Dec 2 '18 at 22:47
add a comment |
Currently I'm studying the RCK model at my Advanced Macroeconomics I classes.
A question arose almost immediately when I saw the utility function of a household in this model.
The question is: why are we using exp(-ρt) inside this integral? I mean: why this functional form in particular? I love mastering every single aspect of every model I study, that's why I'm asking so.
Thank you really much in advance for your kind responses.
macroeconomics economic-growth balanced-growth
asked Dec 2 '18 at 17:46
Andrey E. Vedishchev
1185
Currently I'm studying the RCK model at my Advanced Macroeconomics I classes.
A question arose almost immediately when I saw the utility function of a household in this model.
The question is: why are we using exp(-ρt) inside this integral? I mean: why this functional form in particular? I love mastering every single aspect of every model I study, that's why I'm asking so.
Thank you really much in advance for your kind responses.
macroeconomics economic-growth balanced-growth
macroeconomics economic-growth balanced-growth
asked Dec 2 '18 at 17:46
Andrey E. Vedishchev
1185
asked Dec 2 '18 at 17:46
Andrey E. Vedishchev
1185
edited Dec 2 '18 at 18:15
asked Dec 2 '18 at 17:46
Andrey E. Vedishchev
1185
asked Dec 2 '18 at 17:46
Andrey E. Vedishchev
1185
asked Dec 2 '18 at 17:46
Andrey E. Vedishchev
1185
1185
1
It's just there for bringing future utility to present value in continuous time. $rho$ is the discount factor.
– Pedro Cavalcante Oliveira
Dec 2 '18 at 22:47
add a comment |
1
It's just there for bringing future utility to present value in continuous time. $rho$ is the discount factor.
– Pedro Cavalcante Oliveira
Dec 2 '18 at 22:47
1
1
It's just there for bringing future utility to present value in continuous time. $rho$ is the discount factor.
– Pedro Cavalcante Oliveira
Dec 2 '18 at 22:47
It's just there for bringing future utility to present value in continuous time. $rho$ is the discount factor.
– Pedro Cavalcante Oliveira
Dec 2 '18 at 22:47
add a comment |
1 Answer
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I guess you already know that $exp(-rho t)$ is the the discount factor. In particular, it is obtained by continuously compounding the discount factor
$$exp(-rho t)=lim_{m to infty} left(1+ frac{rho}{m}right)^{mt}$$
answered Dec 2 '18 at 19:10
Patricio
1862
add a comment |
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I guess you already know that $exp(-rho t)$ is the the discount factor. In particular, it is obtained by continuously compounding the discount factor
$$exp(-rho t)=lim_{m to infty} left(1+ frac{rho}{m}right)^{mt}$$
answered Dec 2 '18 at 19:10
Patricio
1862
add a comment |
I guess you already know that $exp(-rho t)$ is the the discount factor. In particular, it is obtained by continuously compounding the discount factor
$$exp(-rho t)=lim_{m to infty} left(1+ frac{rho}{m}right)^{mt}$$
answered Dec 2 '18 at 19:10
Patricio
1862
add a comment |
I guess you already know that $exp(-rho t)$ is the the discount factor. In particular, it is obtained by continuously compounding the discount factor
$$exp(-rho t)=lim_{m to infty} left(1+ frac{rho}{m}right)^{mt}$$
answered Dec 2 '18 at 19:10
Patricio
1862
I guess you already know that $exp(-rho t)$ is the the discount factor. In particular, it is obtained by continuously compounding the discount factor
$$exp(-rho t)=lim_{m to infty} left(1+ frac{rho}{m}right)^{mt}$$
answered Dec 2 '18 at 19:10
Patricio
1862
answered Dec 2 '18 at 19:10
Patricio
1862
answered Dec 2 '18 at 19:10
Patricio
1862
answered Dec 2 '18 at 19:10
Patricio
1862
1862
add a comment |
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It's just there for bringing future utility to present value in continuous time. $rho$ is the discount factor.
– Pedro Cavalcante Oliveira
Dec 2 '18 at 22:47