It is widely recognized that the social security systems in many western democracies will face substantial shortfalls between anticipated revenues and promised benefits over the coming decades.
A: Various ideas have emerged on how we should prepare for this upcoming shortfall.
(a) In order to analyze the impact of different proposals, begin with a graph that has “consumption now” on the horizontal and “retirement consumption” on the vertical axes. For simplicity, suppose we can ignore periods between now and retirement. Consider a worker and his choice set over these two “goods”. This worker earns some current income I , and he is currently promised a retirement income R from the government. Illustrate how this establishes an “endowment point” in your graph. Then, assuming an interest rate r over the period between now and retirement, draw this worker’s choice set.
(b) Some have proposed that we need to cut expected retirement benefits for younger workers— i.e. we need to cut R to R′ < R. Illustrate the impact this has on our worker’s choice set.
(c) Others have argued that we should instead raise social security taxes — i.e. reduce I to I ′ < I — in order to prepare for the upcoming shortfall. Illustrate how this would impact our worker’s budget constraint.
(d) Assuming that r is not impacted differently by these two policies, could you argue that they are essentially the same policy?
(e) Yet others have argued that we should lower future retirement benefits R but at the same time subsidize private savings — i.e. increase r — through policies like expanding tax deferred savings accounts. Illustrate the impact of lowering R and raising r.
(f) Which of these policies is the only one that has a chance (though by no means a guarantee) of making some individuals better off?
B: Define I, R and r as above.
(a) Write down the mathematical description of the current inter temporal budget for our worker — in terms of I, R and r. Let c1 denote current consumption and let c2 denote retirement consumption.
(b) In your equation, show which parts correspond to the vertical intercept and slope in your graphs from part A.
(c) Relate your equation to the changes that you identified in the graph from each of the policies.