Indivisible Goods and Relative Wealth Concerns: Gambling, Under-Participation, and Lotteries
45 Pages Posted: 15 Dec 2019 Last revised: 27 Nov 2023
Date Written: November 21, 2023
Abstract
We study an endowment economy with heterogeneous agents and two complementary consumption goods, one of which is indivisible. Although agents have standard log-CES preferences, the indivisibility gives rise to Friedman-Savage convexity in indirect utility. Agents care about relative, not just absolute, wealth, as well as rankings. While agents dislike small risks, they like large ones. Poorer agents exhibit a preference for lottery-like assets with negative expected returns and also invest a smaller share of wealth than richer agents in assets with positive expected returns. If the difference in wealth is large, poor agents play a lottery among themselves with a single winner. In consequence, richer agents have a higher expected return on wealth and inequality is expected to increase. While initial inequality affects investment choices, it has only a minor effect on ultimate inequality. Therefore, standard prescriptions for reducing inequality may have little effect.
Keywords: Indivisible goods, Friedman-Savage, lotteries, skewness, non-participation
JEL Classification: G12
Suggested Citation: Suggested Citation