Carlos2007
New member
- Joined
- Mar 27, 2018
- Messages
- 6
Dear professors,
I am working with a constrained optimization set up. I have read several books and pdfs online but I haven't found an answer to my problem. All this problem that I will describe now is hypothetical because what I want is to know how to solve the problem. Let's start. In economics, we have utility functions which depend on consumption. Let's consider C1 first period consumption and C2 second period consumption and an utility function U=ln(C1) + Bln(C2) where B is a constant. And the (budget) constraints equal to Y(I)= L(1+r) + C2 and L = I + C1 where Y is total income in the second period, L is a loan that the consumer request in the first period (and (s)he decides between investing and consume in the first period) and I represents the investment in the first period. Note that what the agent wants is to maximize utility and utility is derived just from consumption. However (and of course), in part the more you invest, the larger the second period income and therefore the larger could be the second period (and maybe the total) consumption.
All the examples and textbooks that I have seen they maximize a function lets say F(x,y), subject to g(x,y)=K where K is a constant and of course the optimization can be with inequality or g(x)=K and h(x,y)= M where M is another constant or other kind of constraints. What really matters here is that they maximize F(x,y) subject to constraints where just x and y are the only variables (subject to optimization).
However, in the case of the problem that I presented, we have just two variables in the function that I want to maximize (C1, C2) and three variables are involved in the constraints (C1, C2, and I).
How should be solved this kind of problem?
max U=ln(C1) + Bln(C2)
s.t: Y(I)= L(1+r) + C2
L = I + C1
Where should be obtained the optimal C1, C2 and I
For me the most important thing is you to provide the way of solution but also a book or paper where I can read about this
I am extremely grateful in advance
Thanks in advance
I am working with a constrained optimization set up. I have read several books and pdfs online but I haven't found an answer to my problem. All this problem that I will describe now is hypothetical because what I want is to know how to solve the problem. Let's start. In economics, we have utility functions which depend on consumption. Let's consider C1 first period consumption and C2 second period consumption and an utility function U=ln(C1) + Bln(C2) where B is a constant. And the (budget) constraints equal to Y(I)= L(1+r) + C2 and L = I + C1 where Y is total income in the second period, L is a loan that the consumer request in the first period (and (s)he decides between investing and consume in the first period) and I represents the investment in the first period. Note that what the agent wants is to maximize utility and utility is derived just from consumption. However (and of course), in part the more you invest, the larger the second period income and therefore the larger could be the second period (and maybe the total) consumption.
All the examples and textbooks that I have seen they maximize a function lets say F(x,y), subject to g(x,y)=K where K is a constant and of course the optimization can be with inequality or g(x)=K and h(x,y)= M where M is another constant or other kind of constraints. What really matters here is that they maximize F(x,y) subject to constraints where just x and y are the only variables (subject to optimization).
However, in the case of the problem that I presented, we have just two variables in the function that I want to maximize (C1, C2) and three variables are involved in the constraints (C1, C2, and I).
How should be solved this kind of problem?
max U=ln(C1) + Bln(C2)
s.t: Y(I)= L(1+r) + C2
L = I + C1
Where should be obtained the optimal C1, C2 and I
For me the most important thing is you to provide the way of solution but also a book or paper where I can read about this
I am extremely grateful in advance
Thanks in advance