Simple growth model including debt

Here's a simple growth model which includes debt.

Suppose the consumers in an economy borrow a net amount D to finance spending. The output in the economy is assumed to rise to meet the increased demand for goods. Thus, output is Y+D, where it would be Y without debt. The increase is thus a factor of 1 + d, where d=D/Y.

The increase may generated by increased capacity usage, if the labour and capital markets are not flexible, or by increased factor accumulation if they are. In the former case, with a growth model of output (Y) = factor productivity (A) * factor terms (F) , the output would change to A*(1+d)*F. In the latter case, the output would be A*F as before. Economies are partially flexible in reality, so the model is Y = A*(1+d)^a*F, where a is a constant.

Taking logs and differencing,

growth in output = a*growth in (1+d) + growth in F

The model allows for debt-funded booms and sharp downturns when the credit has to be repaid. Assuming a personal debt limit of say 200 percent of earnings on average, ten percent interest rates, and debt able to increase by twenty percent per year, then starting from no debt, an economy can expand through debt for a maximum of ten years before the repayments would inevitably lead to a slowdown.

The adjustments in capital and labour would not be instantaneous, so the debt funded growth and contractions would be subject to delay rather than being instantaneous as here, and capacity may not be available in an inflexible economy, so inflation would result rather than expansion. For all of its limitations, the model is not bad for empirical estimations.