Production function_2

     Real
interest
       rate

Production function_1

A_1 to A_2: Technological 
change causes the 
per-worker production 
fucntion to shift up.

A_0 to A_1: Increases in capital 
per worker lead to diminishing 
increases in output per hour 
worked. The per-worker
production function is NOT
changed.

Real GDP per
  hour worker,
                  Y/L

Capital per hour
        worked, K/L

Production function_1

Production function_2

$\frac{Y}{L}=(\frac{K}{L})^{\alpha}$

The per capita production function with constant 

returns to scale is defined as                        .

Effect of technological advancement on per worker production function

α = 0.61142208 (slider from 0.58729208 to 0.63, step 1.0E-5)
g(x) = x^(α)
f(x) = x^(0.5872920751)
A_1 = Point(f)
X_1: (x(A_1), 0)
a = Ray(X_1, A_1)
A_2 = Intersect(g, a, (53655.62812591504, 779.4552994904313))
Y_1: (0, y(A_1))
Y_2: (0, y(A_2))
b = Segment(Y_1, A_1)
c = Segment(Y_2, A_2)
A_0 = Point(f)
X_0: (x(A_0), 0)
Y_0: (0, y(A_0))
d = Segment(Y_0, A_0)
e = Segment(A_0, X_0)
u = Vector((0, 0), (0, 1200))
v = Vector((0, 0), (90000, 0))
h = Segment(X_1, A_2)
A = Point(g)
B = Point(f)