8. (15 pts in total) Suppose the consumer's preference over consumption and leisure is given by U (CI) = In C + 0.8 Inl. He/She has 16 disposable hours, earns a wage rate of $50 per hour, has dividend income of $360 and is subject to a proportional labor income tax t = 20%. (a) (5 pts) If the consumer can choose his/her hours freely, what is his/her optimal consumption and leisure? (b) (5 pts) Suppose now the tax rate is increased to 40%, what is his/her optimal consumption and leisure? Compare with part (a) and explain in terms of substitution and income effect. (c) (5 pts) Suppose now the consumer can only choose between working full-time (8 hours) and not working at all. Repeat part (a) & (b)