The Social Marginal Valuation of Income: Australian Estimates from Government Behaviour*

Alternative public policies frequently incorporate distributional goals. The elasticity of the social marginal valuation of income, ε, can help to derive welfare weights for different individuals in different income groups. Estimates are presented of the elasticity of the social marginal valuation of income implied by the Australian personal income tax, in the period 1968–69 to 1975–76. Both equal absolute (EAS) and equal proportional sacrifice (EPS) models are used to infer the elasticity values. Using taxable income as a proxy for income, the consistent value of ε under EAS was found to range from 2.07 to 2.57; the EPS range was 1.76 to 2.40. A number of considerations suggested a best-guess magnitude of about 2.2. Caution is urged in the interpretation and use of these results.     

The Pricing of Options on Assets with Stochastic Volatilities

One option-pricing problem that has hitherto been unsolved is the pricing of a European call on an asset that has a stochastic volatility. This paper examines this problem. The option price is determined in series form for the case in which the stochastic volatility is independent of the stock price. Numerical solutions are also produced for the case in which the volatility is correlated with the stock price. It is found that the Black-Scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity.