### micro no laboratório...Mostrei isto para alunos meus
## e eles amaram.
### Bens substitutos
u<-function(x1,x2,a=2,b=3) { a*x1+b*x2
}
x1<-seq(0,10,by=1)
x2<-x1
z<-outer(x1,x2,u)
persp(x1, x2, z, theta = 30, phi = 30, expand = 0.5, col = "green")
contour(x1,x2,z)
image(x1,x2,z)
### Cobb-Douglas
u<-function(x1,x2,a=1/2,b=1/2) {
x1^a*x2^b
}
x1<-seq(0,10,by=1)
x2<-x1
z<-outer(x1,x2,u)
persp(x1, x2, z, theta = 60, phi = 30, expand = 0.5, col = 2)
contour(x1,x2,z)
image(x1,x2,z)
####
f <- function(x1,x2) {
x1*x2+5*(400-10*x1-4*x2)
}
### Derivadas
derivx <- expression( x1*x2+ 5*(400-10*x1-4*x2))
( D.x1 <- D(derivx, "x1") )
x2 <- 0:100
Dx1<-eval(D.x1)
derivy <- expression(x1*x2+ 5*(400-10*x1-4*x2))
( D.x2 <- D(derivx, "x2") )
x1 <- 0:100
Dx2<-eval(D.x2)
par(mfrow=c(2,2))
x1<-seq(0,100,by=1)
x2<-x1
z<-outer(x1,x2,f)
persp(x1, x2, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")
contour(x1,x2,z)
image(x1,x2,z)
plot(Dx2/Dx1,type="l",col=2)
