Question

1. State Kaldor’s stylized facts (4 of them). Derive their implications for the share of national income paid to the owners of capital, the capital income share. Assume firms combine capital and

labor to produce output according to Y = K α N 1−α where α is the elasticity of output to capital, i.e. the percentage change in output for a given percentage change in capital. What type of data would be informative of the value this elasticity? Explain your answer and any assumptions you may need to reach your conclusion.

Answer 1

Stylized facts is education significantly raises lifetime income Another stylized fact in economics is: "In advanced economies, real GDP growth fluctuates in a recurrent but irregular fashion".

However, scrutiny to detail will often produce counterexamples. In the case given above, holding a PhD may lower lifetime income, because of the years of lost earnings it implies and because many PhD holders enter academia  instead of higher-paid fields. Nonetheless, broadly speaking, people with more education tend to earn more, so the above example is true in the sense of a stylized fact.

With the CES case and an elasticity substitution
less than one, we require that all tasks are automated. If only a fraction of the tasks
are automated, then the scarce factor (labor) will dominate, and growth rates do not explode. We show in this section that with Cobb-Douglas production, a Type II singularity can occur as long as a sufficient fraction of the tasks are automated. In this sense,the singularity might not even require full automation.Suppose the production function for goods is

Yt = Aσ t Kαt L 1−α (a constant pop-ulation simplifies the analysis, but exogenous population growth would not change things).The capital accumulation equation and the idea production function are then specified as.

In this setup, the endogenous growth case corresponds to γ = 1. Not surprisingly, then,
the singularity case occurs if γ > 1. Importantly, notice that this can occur with both α
and β less than one that is when tasks are not fully automated. For example, in the case
in which α = β = φ = 1/2, then γ = 2 · σ, so explosive growth and a singularity will
occur if σ > 1/2. We show that γ > 1 delivers a Type II singularity in the remainder of
this section. The argument builds on the argument given in the previous subsection.

With γ > 1, the growth rate grows at least as fast as At raised to a positive power. But even if it grew just this fast we would have a singularity, by the same arguments given before. The case with gKt > gAt can be handled in the same way, using K’s instead of A’s. QED.