Question

Consider the one period model with endogenous labor supply we studied in class, where workers (consumers) are born with one unit of labor effort and no physical endowments. The total population of consumers is one. Furthermore, assume that workers have the following lifetime utility function: U(c, l) = ln c + ln l Production takes place by a representative firm that has access to a production technology of the Cobb-Douglas form: Y = AK α L 1−α and as usual profits are rebated back to consumers and P = 1. Unlike the model discussed in class, the firm pays (w + τ ) for every unit of labor time used, τ > 0 is a unit tax imposed by the government (or some type of regulation). In this manner, the firm pays τL to the government and wL to workers. Finally, the government does no collect taxes from workers but only from employers as mentioned above. Government revenue is used to finance spending, G where G does not directly affect the economy. The government’s budget constraint is such that: τL = G

A. Write down the individual’s problem of utility maximization. Be sure to derive the budget constraint for the problem. Provide economic interpretation for this model.