Cobb Douglas and elasticities

CFA Level II Economics
#1

Is it just me or is it counterintuitive that the elasticity of output with respect to capital is also the % of income attributable to capital? This is in response to a Schweser mock q which stated, correctly, that a country with a higher % of income attributable to capital benefits MORE from capital deepening. I would think a country that already generates a lot of its income from capital probably has a lot of capital already, so the incremental investment in capital would have a lesser effect (all else equal). I know this isn’t the case bc the same number (% of income to capital) represents output elasticity with respect to capital.

Would love anyone who can give a logical explanation. Thank you!

#2

There is a difference between having a high level of Capital per capita (K/L), and having a big share of your potential GDP coming from capital (alpha, i.e. capital cost over total factor cost).

A high alpha (like in developping countries) suggest you will benefit more (since your economy is capital intensive) from capital deepening than a country with a low alpha. However, no matter the country, since capital has diminishing returns (assuming neoclassical theory), if you are very close to the steady growth rate, the marginal increment to the rate of growth due to capital deepening is very small.