Can growth-enhanced monetary policy improve welfare when people seek social status?

Abstract

This paper examines the growth and welfare effects from an increase in the rate of money supply in an Ak type growth model with a relative wealth-enhanced social status motive, production externalities, and liquidity constraints. When only consumption is constrained by liquidity, fast money supply can hasten output growth unless seigniorage revenue is wasted and production externalities do not exist. We find that even though money growth normally promotes economic growth, it does not improve welfare when capital stock is over-accumulated. In general, an optimal monetary policy minimizes seigniorage. Our results also conclude that the optimal monetary policy rarely follows the Friedman rule.

Appendix A: Find the economic growth rate and nominal interest rate (R) when \(\mu ^*=0\) in the case that \(\alpha <1\) and \(\theta =0\)

In the case that $\alpha <1$ and $\theta =0$, the steady-state economic growth rate equals:

$$\begin{aligned} \hat{\phi }=\alpha A-\rho +\beta {\upsilon }^{\prime }(1)\frac{\hat{x}}{1+\hat{z}}=A-(1+\mu )\hat{z}=\mu -\frac{\hat{x}}{\hat{z}}+(1+\alpha A). \end{aligned}$$

(36)

When $\mu ^*=0$, (36) becomes:

$$\begin{aligned} \hat{\phi }^0=\alpha A-\rho +\beta {\upsilon }^{\prime }(1)\frac{\hat{x}^0}{1+\hat{z}^0}=A-\hat{z}^0=1+\alpha A-\frac{\hat{x}^0}{\hat{z}^0}, \end{aligned}$$

(37)

where $\hat{\phi }^0$, $\hat{x}^0$, and $\hat{z}^0$ respectively denote the steady-state $\phi$, $x$, and $z$ under a zero rate of money growth, $\mu ^*=0$.

From Eq. (37), we have:

$$\begin{aligned} (\hat{z}^0)^2+\left[ {1-\frac{\rho }{1+\beta {\upsilon }^{\prime }(1)}-(1-\alpha )A} \right] \hat{z}^0-\frac{(1-\alpha )A+\rho }{1+\beta {\upsilon }^{\prime }(1)}=0. \end{aligned}$$

(38)

By the mean value theorem, it is easy to prove that the positive root of Eq. (38) follows the relationship: $\frac{\rho }{1+\beta {\upsilon }^{\prime }(1)}<\frac{\rho +(1-\alpha )A}{1+\beta {\upsilon }^{\prime }(1)}<\hat{z}^0<\frac{\rho }{1+\beta {\upsilon }^{\prime }(1)}+(1-\alpha )A$. Because $\hat{\phi }^0=A-\hat{z}^0$, the inequality, $A-\frac{\rho }{1+\beta {\upsilon }^{\prime }(1)}>\hat{\phi }^0>\alpha A-\frac{\rho }{1+\beta {\upsilon }^{\prime }(1)}$, thus holds. The nominal rate of interest, $R^*=\alpha A+(\mu ^*-\hat{\phi }^0)=\hat{z}^0-(1-\alpha )A,$ follows to satisfy the inequality of $\frac{\rho }{1+\beta {\upsilon }^{\prime }(1)}>R^*>\frac{\rho }{1+\beta {\upsilon }^{\prime }(1)}-(1-\alpha )A$.