I (and others, I think) have problems understanding what you're trying to do. I know efficiency wage models, but I still don't understand what you're after. As I wrote earlier, it would help if you would spell out clearly what you're looking for -- is it a real-valued function f(e), satisfying a certain profit-maximization problem? is it an effort function e(w)

Please define your notation:

e = amount of effort (as measured by the amount of sweat and stress produced by the worker, say)
L = amount of labor (as measured by the effective number of hours spent at work, whether sweating or whether chilling out)
f(e) = some unknown function
w = the wage rate (per hour spent at work irrespective of effort)
b = some parameter of something
lambda = some parameter of the same thing that b is a parameter of, whatever that is
etc.

Please define your problem:

select w or e or both to maximize f(e)-w*L subject to some constraint?

Please define your assumptions:

e = endogenous
w = exogenous/endogenous?
L = exogenous/endogenous?

Explain clearly when you're looking at a function or a constant. Is L is a known constant? A constant to be determined? a known function L(w)? a function L(w) to be determined? Same question for e(w) and f(e).

If you clarify the above, I may be able to help (though I can't promise of course).

Having said that, the elasticity condition you derive (known as the Solow condition, after Robert Solow, yes the same Solow who got a Nobel for his growth model) allows you to solve for e(w), a simple linear ode of the Euler type (the same Euler of the Euler equation of the calculus of variations, but the use of Euler here refers to another of his contributions):

> dsolve( w*diff(e(w), w) = e(w) );

                             e(w) = _C1 w

This is inconsistent with some other thing you write,

e := ((w-b)/b)^lambda:

Is the above an assumption, a result ? Are you merging two models?

diff( int( x^n, x), x);

                                (n + 1)
                               x
                               --------
                                  x

int( diff( x^n, x), x); 

                                   n
                                  x

It helps remember the implicit assumption that x must be different from zero

diff( int( x^n, x), x);

                                (n + 1)
                               x
                               --------
                                  x

int( diff( x^n, x), x); 

                                   n
                                  x

It helps remember the implicit assumption that x must be different from zero

That's a lot more information Alex. It looks usable. Unfortunately it's 2am in my country, so I must sign off, but I will check back tomorrow. Someone from some other part of the planet will probably have solved it by then!

Patrick.

That's a lot more information Alex. It looks usable. Unfortunately it's 2am in my country, so I must sign off, but I will check back tomorrow. Someone from some other part of the planet will probably have solved it by then!

Patrick.

Hi Amanda,

I'm glad you've managed to do your assignment. It's a good thing you did it by hand as you will not have Maple to help you during the exam. Maple is a great assistant, but you need to know what you are doing -- it rarely substitutes for a clear understanding of the issues: it does require your input. As you can see you will always find people to look at your Maple problems here, so you should definitely consider using Maple more often as an assistant.

And remember to work on your assignments ahead of time ;-)

Patrick.

Hi Amanda,

I'm glad you've managed to do your assignment. It's a good thing you did it by hand as you will not have Maple to help you during the exam. Maple is a great assistant, but you need to know what you are doing -- it rarely substitutes for a clear understanding of the issues: it does require your input. As you can see you will always find people to look at your Maple problems here, so you should definitely consider using Maple more often as an assistant.

And remember to work on your assignments ahead of time ;-)

Patrick.

I'm half-expecting someone to reply "why should it?"

I'm half-expecting someone to reply "why should it?"

maybe you want this (or something like it):

convert(1/factor(z^2*(z^2+9),complex),parfrac);

maybe you want this (or something like it):

convert(1/factor(z^2*(z^2+9),complex),parfrac);

Next time simply copy-paste the entire code into your worksheet, instead of re-typing one letter at a time.

Next time simply copy-paste the entire code into your worksheet, instead of re-typing one letter at a time.

Alex, can you give more information? I don't understand your assumptions (It looks like a labor economics problem, which is my area by the way).

Are you saying

f := e -> (e-a)^2;

for some constant a? or does f also depend on w?

What is L? a constant or a function?

Alex, can you give more information? I don't understand your assumptions (It looks like a labor economics problem, which is my area by the way).

Are you saying

f := e -> (e-a)^2;

for some constant a? or does f also depend on w?

What is L? a constant or a function?