The representative consumer has the following utility function: U(c, l) = ln c + ln l where c is the consumption good, and l is the leisure hours. She has h hours of time available which she can allocate between work and leisure. For each hour of work, she earns w units of consumption good. She also earns as dividend (profit) income which is measured in consumption goods. The government collects revenues using a consumption tax; in particular, the representative consumer pays t units of goods to the government for each unit of consumption good she buys. Note that there is no lump-sum tax. (a) Determine the consumer's budget constraint. (b) Solve for the c and l that maximize the utility of the consumer. (c) Suppose that the tax rate t increases. What is the impact of this increase in the tax rate, t, on the consumer's choice for c and l? What is the impact of this on the labour hours of the consumer?