# (p.xv) List of Figures

# (p.xv) List of Figures

3.3 Endogenous fluctuations: example of a stable equilibrium. 64

4.2 Function Ψ(

*Z*): Psychological transformation of calendar time and relative desired balances. 754.3 Function Ψ(

*Z*), for α =*b*= 1, relative desired balances/psychological transformation of calendar time. 775.2 Stable equilibrium with pseudo-periodic convergence. 104

5.4 Echo bubble. 110

6.1 Interdependence of the HRL formulation of the demand for money and of the fundamental equation of monetary dynamics. 116

6.2 Japan 1955–2006, joint test of the HRL formulation and the FEMD. 124

6.3 Japan 1955–2006, joint test of the HRL formulation and the FEMD. 124

(p.xvi) 7.1 Zimbabwe: asymptotic convergence of the perceived rate of inflation toward the instantaneous rate of inflation. 135

7.2 Zimbabwe: perceived rate of inflation and distribution of forecasting errors. 139

7.3 S&P 500 daily returns: distribution of forecasting errors. 141

7.4 Brazil: perceived rates of inflation and money depreciation. 147

7.5 Rate of memory decay, perceived growth rate (dynamic equilibrium rate) and elasticity as functions of

*z*. 1497.6 Time needed to converge toward the average annualized rate. 149

7.7 Two artificial time series differing only by their volatility. 150

7.8 Sensitivity of the perceived rate of growth to the volatility of inputs. 150

8.1 US AAA corporate bond yields and the HRL formulation. 160

9.3 Margin debt and perceived equity returns: a nonlinear relationship. 190

9.4 Bank debits in New York City and the present value of past equity returns. 191

9.5 Margin debt and the present value of equity returns. 192

10.3 Cardinal utility functions defined up to a linear transformation and local linearity. 208

10.4 Distribution parameters of a constant-gain, variable-probability prospect. 214

10.5 Distribution parameters of a constant-loss, variable-probability prospect. 215

(p.xvii) 10.6 Comparison of the moments of two risky prospects. 218

10.7 Representation of observed cardinal utility on a lin-log graph. 227

10.8 Empirical invariant cardinal utility: rescaled observations. 228

10.9 Allais’s invariant cardinal utility function for gains. 230

11.1 United States: corporate bonds yields ratio and the perceived risk of loss on equities. 246

11.2 S&P 500: implied volatility, estimate based on the S&P 500 perceived upside and downside volatilities. 247

11.3 Cumulative drawdowns on the Tokyo Stock Exchange Price Index (TOPIX) and the perceived risk of loss in the Japanese equity market. 248

11.4 Perceived return and risk of loss in the Japanese bubble. 249

11.5 Perceived risk of loss on US equities, Cowles commission stock index chained with S&P 500 after 1928. 249

11.6 S&P 500: cyclically adjusted PE and perceived risk of loss. 250

11.7 S&P 500: cumulative drawdowns and perceived risk of loss. 251

E.5 Marginal utility. 338 (p.xviii)