1. (50 points) Consider the simple model of consumer choice developed in class. The consumer is endowed with h. units of time which can be allocated to work and leisure. Let a > 0 denote dividends from firms. There is no lump-sum tax, but the consumer faces a proportional tax if on all income. (a) (b) (10) Under our standard assumptions about preferences, show in a diagram the optimal bundle for the consumer. Label carefully, and indicate the consumer's optimal C, E, and NS. State two conditions that must be satisfied by the optimal bundle. (10) Using a new diagram (similar to the one in (a)), show how the consumer's optimal bundle changes if 7? increases. (15) Suppose preferences for the consumer are described by the following utility function: U(C, f) = (1 o5)log(C) + (rlogf), a: E (U, 1) Characterize the consumer's optimal bundle (C, E, and NS) as functions of pa- rameters and variables the consumer takes as given. (10) Continue with the environment in (c). Explain what happens to the c011- sumer's optimal bundle if the real wage decreases. In a diagram, illustrate the consumer's labor supply curve. (15) Continue with the environment in (c). Explain what happens to the c011- sumer's optimal bundle if the tax rate if decreases. In a diagram, show what happens to the labor supply curve of the consumer