We will use the assumption of constant returns to scale to analyze all quantatites in per-worker terms. First, let's build up some intuition for the idea of constant returns to scale.

We consider that the economy has K=4K=4 units of capital and L=2L=2 units of labour. Hence output YY equals:

Y=F(4,2)=40.320.7=2.46Y = F(4, 2) = 4^{0.3} 2^{0.7} = 2.46

This economy is represented by point A on the graph. Constant returns to scale predicts that if we increase both KK and LL by some constant zz, we will also increase YY by that same constant:

2.46z=F(4z,2z)2.46 z = F(4 z, 2 z)

We can verify that this equality holds by varying zz:

zz

1.00
0123

We can see graphically that for the given zz, output equals 2.46, or 2.46z2.46 z. Hence we have shown that scaling the inputs by some constant zz has the effect of scaling YY by the same constant.

Geometrically, the economy moves along a straight line that goes through the origin as we scale it's inputs. This is equivalent to saying that the production function is homogenous of degree 1.


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