Maximize

[EC1000]

Max x1, x2 of U(x1) + Beta U(x2) subject to x1+x2=I

1)determine first order conditions
2)show second order conditions for a max must hold
3)suppose u(x) = In(x), Beta =3/4, and I = 14
4) calculate x1* and x2* and verify U" (x)<0

 

[HallsofIvy]

I really don't understand what you are saying. What kind of objects are x1 and x2? Are they numbers or matrices? What is I?

I assume that U is some function of x. You say later "u(x)= In(x)". I guess that you mean U(x) but what is "In"? Do you mean ln(x), the natural logarithm function?

 

[HallsofIvy]

I really don't understand what you are saying. What kind of objects are x1 and x2? Are they numbers or matrices? What is I?

I assume that U is some function of x. You say later "u(x)= In(x)". I guess that you mean U(x) but what is "In"? Do you mean ln(x), the natural logarithm function? And what are x1* and x2*? Are they the values of x1 and x2 at which U has a maximum?

 

[EC1000]

I really don't understand what you are saying. What kind of objects are x1 and x2? Are they numbers or matrices? What is I?

I assume that U is some function of x. You say later "u(x)= In(x)". I guess that you mean U(x) but what is "In"? Do you mean ln(x), the natural logarithm function?

x1 and x2 are variable that sum to I. beta is a discount factor. yes natural log of x. I is total income. so the question is maximize x1 and x2 for the problem of U(x1) + BU(x2) subject to I = x1+x2.