Implications: rapid population aging. 1-child policy means that cost of pensions, health care, and social services will thus rise.

• 1 in 6 now above 60
• 1 in 4 above 2030
• 1 in 3 by 2050

“get old before getting rich”

demography

1980-2010

• low dependency ratios
• high household savings rate
• large lavor supply
• “age of abundance”

decline

• rapidly aging population
• rapidly rising dependency ratios
• ageing population / rising health / retirement costs
• shrikning labor force, rising wages
• declining of deposits in bank system
• less capital

resulting dynamics

• labor force shrinking by 2 million workers per year
• manufacturing wages rising faster
• labor cost advantage almost gone

wages keep going up

You got the lights on in the afternoon

And the nights are drawn out long

And you’re kissin’ to cut through the gloom

With a cough drop coloured tongue

And you were sittin’ in the corner with the coats all piled high

And I thought you might be mine

In a small world, on an exceptionally rainy Tuesday night

In the right place and time

When the zeros line up on the 24 hour clock

Given a convex set, we want to find the “center” of this set.

• Chebyshev center; this is not unique
• center of the maximum volume inscribing ellispsoid—this is also affine invariant

Lowner-John Ellipsoid

minimum volume surrounding ellipsoid

Consider a set of ellipsoid \(C\). Minimum volume ellipsoid \(\epsilon\) with \(C \subset \epsilon\). We can parameterize \(\epsilon\) as \(\epsilon = \qty {v \mid \norm{Av + b}_{2} \leq 1}\); where we assume \(A \in \mathcal{S}_{++}^{n}\).

The volume is proportional to \(\text{det} A^{-1}\). Thus to find minimal-volume ellipsoid, solve:

\begin{align} \min_{A,b}\quad & \log \text{det} A^{-1} \\ \textrm{s.t.} \quad & \text{sup}_{v \in C} \norm{A v + b}_{2} \leq 1 \end{align}

In convex optimization, relax and round / polishing is a procedure by which you perform a local search after coming up with a relaxation, and round into the actual feasible set (such as integers).