Some Notes on O-ring Halvor Mehlum 2008

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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

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