R optimization and curve()?

u <- function(x) {
? ? x1 <- x[1]
? ? x2 <- x[2]
?(x1^alpha)*(x2^(1-alpha))
}
utility <- function(x) x[1]^(alpha)*x[2]^(1-alpha)
p <- c(2,1)
i <- -100
alpha <- .3
umax <- function(p,i,u) {
res <- constrOptim(c(.5,.5), u, grad=NULL, ui=-p, ci=i, mu = 1e-04,
control=list(fnscale=-1))
return(res)
}
curve(umax, c(c(2,1),c(2,1)), c(10,100))

I don't see any question here.

However you must RTFM.

1) The returned value of umax() is a list.  How do you expect curve() to plot a list?

2) curve() requires that the function umax() must be vectorisable wrt its first parameter, 
i.e. you pass it a numeric vector and it returns a numeric vector of the same length.

3) you have to realise that curve() will only graph a 1-dimensional function

HTH,
Ray