The paper incorporates into a standard two-period-lived overlapping generations model with Cobb-Douglas utility and Cobb-Douglas production technology a government that levies a tax on consumption and households that have an opportunity to choose the fertility rate. The government spends all the tax revenue to finance
the policy aiming to increase the national birth rate. Each young household faces a binary choice between 'high fertility' and 'low fertility', depending on the level of the government’s expenditure on that policy. The government’s policy together with the fertility choice by the households can give rise to strong nonlinearity
in the transition equation of the economy. Numerical simulations show that the economic system exhibits endogenous cyclical or chaotic fluctuations in fertility for a large set of values of consumption tax rates. It is also numerically shown that some (inappropriate) choice of the tax rate by the government can cause persistent intergenerational inequality.