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1. Consider the representative consumer's problem as follows. The representative consumer maximizes utility by choosing the amount of consumption good and the amount of leisure l. The consumer has h units of time available for leisure I and for work- ing Ns, that is, h=1+N$. Government imposes a proportional tax on the consumer's wage income. The consumer's after-tax wage income is then (1 t)w(h, 1), where 00 is also given. Solve for the consumer's optimal choices of Page 4 of 5 consumption C and I. (C) (2 points) Using the above results, obtain the labor supply function of the consumer. 2. (2 points) The representative firm maximizes profits by choosing the optimal labor input nd, its production function displays constant returns to scale. Suppose that the marginal product of labor is given by MPN = az(Ndja-1, in which 00 is also given. Solve for the consumer's optimal choices of Page 4 of 5 consumption C and I. (C) (2 points) Using the above results, obtain the labor supply function of the consumer. 2. (2 points) The representative firm maximizes profits by choosing the optimal labor input nd, its production function displays constant returns to scale. Suppose that the marginal product of labor is given by MPN = az(Ndja-1, in which 0