The debt trap: A two-compartment train wreck… and how to avoid it

Abstract

We explore sustainable paths out of a debt trap with a highly stylized two-sector differential equations model for the stocks of money in Government and Society. The model fits the data for the U.S. between 1981 and 2012 with a coefficient of correlation of 0.996. The solutions provide detailed "escape conditions" from the debt trap. A primary surplus is required. Then a government can escape its debt trap either through sustained annual monetary outflows from society to the government (taxation) but with a low initial growth rate, or through annual monetary inflows into both sectors (stimulus) with higher initial growth rate. We illustrate the use of our model with simulations which show how five indebted countries can escape their debt trap in 30 (or 70) years.

A mathematical model for the customer dynamics based on marketing policy

“…We have the following result that shows that the total population in system (1) converges to the ratio γ/ε, independently of the nonnegative initial conditions considered.…”

“…One of the first natural issues to address when studying a compartmental model is the existence and stability of equilibrium solutions. We obtain several results on the existence and stability of equilibrium solutions in of model (1) in this section.…”

“…Thus we conjecture that condition (5) can be weakened. Adding the four equations in (1) and letting N (t) = C(t) + R(t) + P C (t) + P R (t), we get the differential equation…”

“…We believe that this type of model can be fruitfully explored in this context. This believe is based on the fact that compartmental models have proved to be an important tool not only in the natural sciences, particularly in mathematical epidemiology [3] and in population biology [15,17], but also, with increasing notoriety in recent years, in the context of economy and other social sciences [11,14,16,1].…”

Dysfunctional Markets: A Spray of Prey Perspective

“…The government wants to minimize the -bathtub‖ (-aggregate‖ or -population‖) of toxic products, including predatory mortgages, by pulling the plug, that is, by accelerating the rate of obsolescence. It therefore enacts tougher regulations to drain the market of toxic products and tricky, risk-hiding financial instruments (Artzrouni & Tramontana, 2014). A deceitful, toxic instrument is one with -terms and conditions that ultimately harm borrowers,‖ as stated by the U.S. Government Accountability Office 12 .…”