• Consider the representative consumer's problem as follows.The representative consumer maximizes utility by choosing the amount of consumption good Cand the amount of leisure l. The consumer has h units of time available for leisure l and for working Ns, that is, h = l+Ns. Government imposes a proportional tax on the consumer's wage income.The consumer's after-tax wage income is then (1 t)w(h l), where 0 < t < 1 is the tax rate and wis real wage rate. The consumer takes w as given. In addition, the consumer earns profits fromowning the representative firm. There is no lump-sum tax, thus, T = 0.
• (1) write down the equation for the budget constraintfacing the representative consumer
• (2) Suppose that the marginal rate of substitution of leisure for consumption, MRSl,C ,is given by MRSl,C =C/al where a > 0 is also given. Solve for the consumer's optimal choices ofconsumption C and l.
• (3) Using the above results, obtain the labor supply function of the consumer.