5. Now suppose that instead of a luxury good, the consumer can chose between a consumption good c, and hours of work w. Here P: = $1, or: = 55D. and the consumer gets paid $2 for every hour of work they \"consume."r Further, assume work takes time and they can only consume at most 24 hours of work. Graph the consumption set with work on the '1" axis. What is the price of work: p\d. If after the tax the consumer consumes 3 units of the luxury good, how will the tax on the luxury good affect government revenue? If after the subsidy the consumer consumes 5 units of the consumption good, how will the subsidy affect government revenue? e. As discussed above, after the tax and subsidy have been implemented our consumer is consuming 3 units of the luxury good and 5 units of the consumption good. Suppose the growing US economy increases the consumer's income by $25. Graph the new budget constraint and write down the new budget constraint formula. Label where the constraint hits the axes. Assume that after the growth of the economy our consumer now consumes 5 units of the luxury good and 6 units of the consumption good. How has the growth in the economy affected government revenue? f. How would the increased income from the growing economy discussed above compare to the change in the budget constraint from an ad valorem sales subsidy of 10%? 5. Go back to the original budget constraint with P. = $1, , = $10, and m = $50. Imagine that the luxury goods did not only require money but also requires time to consume. This would be the case for luxury goods such as ski vacations. a. First assume each unit of a luxury good took 6 hours of time and a consumer only has at most 24 hours of time to spend. Graph the consumption set and label the axes. Graph both the budget constraint and the time constraint and label the points where they hit the X and Y axes. Shade the set of available bundles the consumer has to choose from. b. What if the luxury good took only 1 hour to consume. How would the choice set change from above? If this was the case, what would be an easy simplifying assumption to apply to this model?4. Suppose that the senate is considering how to best raise revenue to fund government spending. a. First the senate is considering placing a $2 per unit tax on the luxury good. Show how it will change the budget constraint of the consumer by graphing the new budget line and writing out the new equation of the budget line. Label where the constraint hits the axes, and the slope of the budget line. b. Suppose that after implementing the tax the senate decides to subsidize the price of the consumption good of the hypothetical consumer. To do this they will implement a $0.50 subsidy on the price of the consumption good. Show the new budget constraint by graphing the new budget line and writing out the new equation of the budget line after both the tax and subsidy are applied. Label where the constraint hits the axes and the slope of the budget line. c. Suppose our hypothetical consumer is relatively rich and consumes a large amount of the luxury good. Are they better off after the changes from a. to b. above? What if they were relatively poor and only consumed the consumption good