Consider Solow growth model $Y=F(K,AL)$ where $A$ measures knowledge progress, $K$ is capital and $L$ is label. I have suppressed temporal dependence. I am going to assume $L$, $A$ grow exponentially at rate $g,n$ respectively. Assume $\frac{d}{dt}K=sY-\delta K$ where $\delta$ is decay rate of capital and $s$ is saving rate. Assume saving is instantaneously used for capital purchasing as investment.

Let $k^\star$ be the current equilibrium. Leveling up consumption indicates $(1-s)Y$ increases which indicates saving rate should drop. However, dropping saving rate should drop overall $\frac{Y}{AL}$ effective production per capita. Thus overall $Y$ drops below previous equilibrium growth path. If I set $a_K$ as elasticity of product to capital, then elasticity of $Y$ to saving should be $\frac{a_K}{1-a_K}$. In general most countries are with $a_K=\frac{1}{3}$. In particular elasticity of $Y$ to saving is positive. In particular, $Y$ should grows and decays as saving grows or decays. Thus decreasing saving should decrease long term growth of $Y$.

Originally, I thought $Y$ should measure GDP which should have a component measuring consumption. If consumption increases, I should expect temporal increment of GDP or increment of GDP over long term.(That should be the reason why one wants to increase consumption during recession.) Or is that statement is a statement for out of equilibrium statement? Am I wrong on that part or wrong with understanding of Solow model?

Reference. Romer, Macroeconomics Chapter 1. Sec 4.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.