Consider a static labour supply model for an individual. Assume that the person works a positive number of hours. Assume that the utility function is of the following form: U=x^a(T-h)^(1-a) where x is consumption and h is hours of work. There is an income tax, 1>t>0, that is applied to all income. Assume that the only source of income is wage earnings.

1. Specify the utility maximization problem.

2. What is the Lagrange function and solve for the first order conditions.

3. Solve for the marginal rate of substitution between consumption and leisure.

4. Explain intuitively how an increase in the tax rate, t, is likely to affect hours of work. You may appeal to the answers from a) through c) and/or use a graph to support your answer.