Suppose, as in the federal income tax code for the united states, that the representative consumer faces a wage income tax with a standard deduction. that is, the representative consumer pays no tax on wage income for the first x units of real wage income, and then pays a proportional tax t on each unit of real wage income greater than x. therefore, the consumer’s budget constraint is given by c = w(h - l) + pi if w(h - l) > x, or c = (1 - t)w(h - l) + tx + pi if w(h - l) > x. now, suppose that the government reduces the tax deduction x. using diagrams, determine the effects of this tax change on the consumer, and explain your results in terms of income and substitution effects. make sure that you consider two cases. in the first case, the consumer does not pay any tax before x is reduced, and in the second case, the consumer pays a positive tax before x is reduced.

John and daphne are saving for their daughter ellen's college education. ellen just turned 10 at (t = 0), and she will be entering college 8 years from now (at t = 8). college tuition and expenses at state u. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. ellen should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own. tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11).so far, john and daphne have accumulated $15,000 in their college savings account (at t = 0). their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. they expect their investment account to earn 9%. how large must the annual payments at t = 5, 6, and 7 be to cover ellen's anticipated college costs? a. $1,965.21b. $2,068.64c. $2,177.51d. $2,292.12e. $2,412.76