The amount effect and marginal value

The amount effect of delay discounting (by which the value of larger reward amounts is discounted by delay at a lower rate than that of smaller amounts) strictly implies that value functions (value as a function of amount) are steeper at greater delays than they are at lesser delays. That is, the amount effect and the difference in value functions at different delays are actually a single empirical finding. Amount effects of delay discounting are typically found with choice experiments. Value functions for immediate rewards have been empirically obtained by direct judgment. (Value functions for delayed rewards have not been previously obtained.) The present experiment obtained value functions for both immediate and delayed rewards by direct judgment and found them to be steeper when the rewards were delayed--hence, finding an amount effect with delay discounting.