Suppose a representative consumer has preference over consumption (c) and leisure (1). His indif- ference curve is described by the following function: u(c, 1) = 3 In(c) + 2 ln(1). His endowment over time is given by h = 1. His wage rate is 2 in terms of consumption goods. Suppose he has 2 units of dividend income from firm and 1 unit of lump-sum tax from the govern- ment. (2) Compute this consumer's optimal choice over consumption, leisure and working time. (15 points) (3) Now suppose there is an increase in the lump sum tax. Diagram the effects on consumer's optimal consumption and labor supply. Explain your results. (15 points) Note: under the above utility function, MRSL.c