Pensions and the sustainability of the welfare state

Explain how the Mexican pay-as-you-go pension system works: who pays today's pensions, and who will pay yours? How does it differ from a fully funded individual pension plan?

Define the dependency ratio (the ratio between elderly people and the working-age population) and explain what happens to the pension system when the population ages.

The figure shows the population pyramid of an imaginary highly aged country, with the population of each age group (in millions of inhabitants), males on the left and females on the right.

1. a) Describe the shape of the pyramid: what do its narrow base and wide top indicate?
2. b) Explain what problem this structure poses for pensions in twenty years' time.

In a country, there are two contributors for every pensioner, and the average pension is $\$24\,000$ per month.

1. a) Calculate how much each contributor should pay per month solely for pensions (excluding healthcare and other expenses).
2. b) What happens to that amount if the ratio drops to $1.5$ contributors per pensioner? Recalculate and comment.

Analyse the effect of immigration on the sustainability of pensions: average age of arrivals, contributions they make, and why many economists consider it part of the demographic solution.

Present three options to ensure future pensions (raising the retirement age, increasing contributions, encouraging complementary private pension plans) and analyse one social advantage and one disadvantage of each.

A televised debate concludes with the following statement: "The pay-as-you-go public pension system is a Ponzi scheme doomed to bankruptcy; the fairest and safest approach is for each worker to save in their own private fully funded pension plan in financial markets."

1. a) Imagine that the economy enters a ten-year cycle of high inflation ($6.5\ \%$ annually) and stock market crashes due to international financial crises. Compare and predict how this economic situation would affect a retiree under individual funding versus one under a public pay-as-you-go system. Justify what risks each system bears in the face of inflation and market fluctuations.
2. b) Analyze distributive equity: what lack of protection would workers with persistently precarious wages or with career interruptions due to unpaid family care face in a purely fully funded system? Justify why the pay-as-you-go system mitigates these individual risks.
3. c) Design a mixed proposal (multi-pillar system) that combines pay-as-you-go and funding, justifying what weight you would give to each pillar to balance intergenerational solidarity and financial returns.

A valley is losing its young people: $300$ residents remain with an average age of $58$ years, the local medical surgery reduces its opening hours, and the shop barely survives.

1. a) Analyse the valley's demographic and economic spiral: what feeds it and what sequential effects it triggers.
2. b) Propose two measures to reverse it and assess their realistic feasibility.

Design a "generational pact" for pensions.

1. a) Combine at least three measures (demographic, labor, fiscal, savings) and explain what each generation gives up and gains.
2. b) Which indicators would you monitor to determine if the pact is working in ten years' time?