{60 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 n 3:: 0 denote dividends from rms. There is no lumpsum tax, but the consumer faces a proportional tax t on all income. (a) [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 satised by the optimal bundle. (b) [10} Using a new diagram {similar to the one in {a)], show how the consumer's optimal bundle changes if w increases. {c} (15} Suppose preferences for the consumer are described by the following utility function: U{C,') = (1 nr}log{C) + olog{}, o: E (0,1) Characterize the consumer's optimal bundle (C, E, and NS} as functions of pa rameters and variables the consumer takes as given. (d) [10} Continue with the environment in (c). Explain what happens to the con sumer's optimal bundle if the real wage decreases In a diagram, illustrate the consumer's labor supply curve. {e} (15} Continue with the environment in (c). Explain what happens to the con sumer's optimal bundle if the tax rate t decreases. In a diagram, show what happens to the labor supply curve of the consumer