The Effect of Consumption Commitments and the Liquidity Constraint on Labor Supply

In this article I present a comparative dynamic analysis of the effect of consumption commitments and the liquidity constraint on workers' labor supply response to a parametric change in the real wage. I define a consumption commitment as any decision by a worker to consume and pay for a good over some future period of time which, once the decision is made, involves significant transaction costs to change. Examples of consumption commitments include lease or mortgage housing commitments and purchasing durable goods such as a car on installment credit. The liquidity constraint has been offered by James Tobin and others as a realistic alternative to the wealth constraint, for use in the individual's utility maximization problem. They hypothesize that, due to capital market imperfections, workers may be unable to obtain credit on illiquid assets, or may obtain such credit only at a penalty rate of interest. Thus, workers are constrained to at all times maintain non-negative liquid assets - or, in other words, are "liquidity constrained.”I demonstrate that workers who have consumption commitments or who are bound by the liquidity constraint will have a smaller elasticity of labor supply than similarly situated workers who are not so constrained. In the short run, consumption commitments prevent a worker from adjusting a portion of his or her current consumption bundle in order to accommodate a change in the real wage. As a result, a worker with consumption commitments can engage in less intratemporal substitution of leisure for other goods and will experience a greater income effect among the remaining variable consumption goods, including leisure. The effect of consumption commitments on labor supply is a short-run effect since in the long run a worker may vary his or her consumption commitments. Similarly, the liquidity constraint prevents a worker who wishes to borrow against future earnings from adjusting his or her future consumption bundle to accommodate a real wage change. This prevents intertemporal substitution of leisure for other goods and increases the income effect among the current consumption goods, including leisure. The effect of the liquidity constraint on labor supply will be asymmetric since the liquidity constraint prevents borrowing, but not saving. Workers who both have substantial consumption commitments and are bound by the liquidity constraint have the least flexibility in their current and future consumption bundle to respond to a real wage change. As a result these workers have a smaller elasticity of labor supply than similarly situated workers who suffer from neither or only one of these restrictions.This analysis has important implications for labor economics and public policy. First, my finding that consumption commitments increase the worker's short­ run income effect with respect to leisure tends to undermine the traditional assumption that income effects are small (see e.g. MaCurdy, 1981), at least with respect to workers with substantial consumption commitments. Second, my conclusions that consumption commitments and the liquidity constraint lessen a worker's elasticity of labor supply undermine the application of the intertemporal substitution hypothesis to such workers as an explanation of unemployment (Lucas and Rapping, 1969). Although wealthy workers with relatively low consumption commitments and high liquid assets may be able to substitute leisure for labor when wages are temporarily low and take "voluntary" unemployment, such an alternative would not be attractive for less wealthy workers with relatively high consumption commitments and no liquid assets.4 Finally, my analysis suggests that different groups of workers will have different elasticities of labor supply and thus respond differently to various public policies of taxes or wage subsidies.