Some economists and observers are worried that certain developed countries have entered a period where increased total stocks of capital generate greater total income to capital, allowing capital holders to purchase more capital. Their fear is that this will induce a cycle whereby capital owners will use their greater income to purchase more capital, thus increasing their income even further, so that the proportion of total income accruing to capital will increase over time unabated.

We will think about this issue.

We will find it simpler to work with a production function of one variable, the capital per labor ratio (kK/L). Define the production function in terms of the capital-labor ratio as

f(k) =L1F(K,L) =F(K/L,1) =F(k,1).

1. Derive this function for the Cobb-Douglas production function with constant returns to scale.