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Universal basic income in a financial equilibrium

Kim Weston

TL;DR

The paper develops a continuous-time financial equilibrium model for universal basic income in which Nash-type labor responses and a uniform tax redistribution shape consumption, investment, and asset prices. It proves the existence of an equilibrium via a decoupled quadratic BSDE system, constructs prices for the stock and annuity, and derives optimal strategies for consumption, labor, and trading. The results show that labor participation and welfare respond monotonically to redistribution under certain conditions, while stock-market effects are nonmonotone and depend sensitively on the influence parameter governing perceived responses. This framework provides a rigorous link between UBI design and financial-market outcomes with implications for policy design and financial stability.

Abstract

Universal basic income (UBI) is a tax scheme that uniformly redistributes aggregate income amongst the entire population of an economy. We prove the existence of an equilibrium in a model that implements universal basic income. The economic agents choose the proportion of their time to work and earn wages that can be used towards consumption and investment in a financial market with a traded stock and annuity. A proportion of the earned wages is uniformly distributed amongst all agents, leading to interconnectedness of the agents' decision problems, which are already dependent on one another through the financial market. The decision problems are further entangled by Nash perceptions of labor; the agents respond to the labor choices of others and act upon their perceived income in their decision problems. The equilibrium is constructed and proven to exist using a backward stochastic differential equation (BSDE) approach for a BSDE system with a quadratic structure that decouples. We analyze the effects of a universal basic income policy on labor market participation, the stock market, and welfare. While universal basic income policies affect labor market participation and welfare monotonically, its effects on the stock market are nontrivial and nonmonotone.

Universal basic income in a financial equilibrium

TL;DR

The paper develops a continuous-time financial equilibrium model for universal basic income in which Nash-type labor responses and a uniform tax redistribution shape consumption, investment, and asset prices. It proves the existence of an equilibrium via a decoupled quadratic BSDE system, constructs prices for the stock and annuity, and derives optimal strategies for consumption, labor, and trading. The results show that labor participation and welfare respond monotonically to redistribution under certain conditions, while stock-market effects are nonmonotone and depend sensitively on the influence parameter governing perceived responses. This framework provides a rigorous link between UBI design and financial-market outcomes with implications for policy design and financial stability.

Abstract

Universal basic income (UBI) is a tax scheme that uniformly redistributes aggregate income amongst the entire population of an economy. We prove the existence of an equilibrium in a model that implements universal basic income. The economic agents choose the proportion of their time to work and earn wages that can be used towards consumption and investment in a financial market with a traded stock and annuity. A proportion of the earned wages is uniformly distributed amongst all agents, leading to interconnectedness of the agents' decision problems, which are already dependent on one another through the financial market. The decision problems are further entangled by Nash perceptions of labor; the agents respond to the labor choices of others and act upon their perceived income in their decision problems. The equilibrium is constructed and proven to exist using a backward stochastic differential equation (BSDE) approach for a BSDE system with a quadratic structure that decouples. We analyze the effects of a universal basic income policy on labor market participation, the stock market, and welfare. While universal basic income policies affect labor market participation and welfare monotonically, its effects on the stock market are nontrivial and nonmonotone.
Paper Structure (9 sections, 5 theorems, 62 equations, 1 figure)

This paper contains 9 sections, 5 theorems, 62 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Model setting
  3. Equilibrium construction
  4. Universal Basic Income Effects
  5. Labor Market Participation
  6. Stock Market Effects
  7. Welfare
  8. Socialism versus Communism
  9. Proofs

Key Result

Theorem 2.3

Assume that the wage rates are nonzero for all $t\in[0,T]$, $\mathbb P$-a.s., and that for the dividend and wage rate dynamics coefficients, we have $\mu_D, \sigma_D, \mu_{w_i}, \sigma_{w_i} \in{\mathcal{S}}^\infty$ for $i=1,\ldots, I$. For any $\lambda_{keep}\in[0,1]$ and $\lambda_{ubi}\in[0,1-\lam

Figures (1)

  • Figure 1: Graphs of the market price of risk and interest rate as a function of the wage rate $w$ for varying $\delta$. The common set of parameters are $\lambda_{keep}=0.7$, $\lambda_{ubi}=0.2$, $I=2$, $\alpha_1=\alpha_2 = 0.2$, $\rho_1=\rho_2=1$, $\beta_1=-0.2$, $\beta_2=-0.4$, $\mu_{w_1} = 0.1$, $\mu_{w_2}=0.2$, $\sigma_{w_1} = 0.1$, $\sigma_{w_2}=-0.05$, $\mu_D = 01$, and $\sigma_D = 0.5$.

Theorems & Definitions (13)

  • Definition 2.1
  • Definition 2.2
  • Theorem 2.3
  • Definition 3.1
  • Definition 3.2
  • Proposition 3.3
  • Proposition 3.4
  • Theorem 3.5
  • proof : Proof of Proposition \ref{['prop:Li']}
  • proof : Proof of Proposition \ref{['prop:bsde']}
  • ...and 3 more