This paper studies the optimal ratio of government debt based on the
heterogeneous agents model. The optimal ratio is determined where the
marginal benefit is equal to the marginal cost. The benefit of increasing
government debt is the consumption smoothing through loosening the
borrowing constraints of households, but the cost is that government debt
crowds out private capital and raises the interest rate. This paper shows that
there is an hump-shaped relationship between the government debt ratio and
social welfare. It also finds that one percentage point increase in government
debt ratio induces interest rate to increase by 1.02 basis points, but the effect
is larger as the debt ratio increases.