This paper examines the relationship between price variability and trading volume in speculative markets, extending previous theories in two ways. First, it derives the joint probability distribution of price change and trading volume over any time interval within the trading day from economic theory. Second, it determines how this joint distribution changes as the number of traders in the market increases or decreases. The model's parameters are estimated using daily data from the 90-day T-bills futures market. The results show that the variance of the daily price change decreases as the trading volume increases, which is contrary to the findings of previous studies. The model explains this paradox by showing that the mean trading volume increases linearly with the number of traders, while the variance of the price change decreases due to the averaging effect of inter-trader differences. The model also predicts that the mean trading volume per trader is independent of the total number of traders, and that the average trading volume per trader may decline as the market expands. The paper concludes by discussing the implications of these findings and suggesting directions for further research.This paper examines the relationship between price variability and trading volume in speculative markets, extending previous theories in two ways. First, it derives the joint probability distribution of price change and trading volume over any time interval within the trading day from economic theory. Second, it determines how this joint distribution changes as the number of traders in the market increases or decreases. The model's parameters are estimated using daily data from the 90-day T-bills futures market. The results show that the variance of the daily price change decreases as the trading volume increases, which is contrary to the findings of previous studies. The model explains this paradox by showing that the mean trading volume increases linearly with the number of traders, while the variance of the price change decreases due to the averaging effect of inter-trader differences. The model also predicts that the mean trading volume per trader is independent of the total number of traders, and that the average trading volume per trader may decline as the market expands. The paper concludes by discussing the implications of these findings and suggesting directions for further research.