Some Notes on O-ring
Halvor Mehlum 2008
This note is not self-contained. It suplements Halvor’s lecture on Jan 16.
First: In Kremer’s paper, in the expression below eq (7) there should be k
∗
Second: On the growth in y as q increases not R
∗ y = k
α q n nB r = αy/k w = (1 − α ) y/n the capital gets the marginal product r while the n workers share what’s left (( y − rk ) = (1 − α ) y ) .
It follows that capital income and wage income are fixed shares of production. The wage share is (1 − α ). It follows then that the wage increase in proportion to y .
dw w
= dy y
The elasticities of capital and quality is α and n dy y
= α dk k
+ n dq q
(1)
As long as k is fixed dw w
= dy y
= n dq q
If k varies optimally so that r = αy/k = r
∗ vary in proportion to y
αy k = r ∗
(where r
∗
⇒ dk k
= is the world market interest rate) dy y k will
(2)
By combining (1) and (2) we get dy y n
=
1 − α dq q
Hence, as long as k varies optimally dw w
= dy y n
=
1 − α dq q
This is a kind of multiplier effect. Note that the same holds in any production function of the sort y = k
α l
β
Then dy y
= α dk k
+ β dl l
As long as k varies optimally (satisfying r = αy/k = r ∗ ) d ( wl )
=
( wl ) dy
= y
β
1 − α dl l
Note that when there is constant returns to scale β = (1 − α )
1