Could you please provide the solution to parts g), h) and i) (bottom of image)?

Please draw graphs, diagrams, tables etc if needed to answer the question and show FULL working out when doing calculations.

3. Alice and Bob: payroll taxation and inequality [32%] We now assume that the wage paid by the employer is unchanged, but there is a payroll tax I: = 9 levied per hour of labour. This implies that while the employer pays w = 20, Alice and Bob only receive w t = 11 per hour. The tax revenue is used to fund a basic income (unconditional) transfer to both Alice and Bob, equal to Z = 422. We assume that the economy is composed of many Alice-clones and Bob-clones, in proportions 60% of Alice-clones and 40% of Bob-clones. Indifference curves and the new budget constraint are represented in Figure 3. Ignore points 29, and x3 for now. a. What is the slope of the budget constraint with payroll tax? b. Find Alice's optimal choice of free time, consumption, and hours worked. 0. Find Bob's optimal choice of free time, consumption, and hours worked. d. How much tax revenue does the government collect from each Alice-clone? e. How much tax revenue does the government collect from each Bob-clone? f. Check that the govemment's budget is balanced, i.e. the total tax revenue collected is just enough to nance the basic income transfer Z = 422. Figure 3 contains two points, 26,, and x3. Allocation x, where Alice-clones choose 26,, and Bob-clones choose x3, stands as an alternative to the equilibrium allocation with payroll taxation tax found in questions 3.b. and 3.0 (hereafter allocation 3). g. Show that allocation x is feasible, by showing that total consumPtion in allocation 2: is equal to total income. h. Prove that moving from allocation 3 to allocation x is a Pareto improvement. i. What can we conclude about the efciency of payroll taxation? Figure 3 - Alice and Bob's consumption-leisure tradeoff under payroll taxation - Indifference curves Alice - - Indifference curves Bob - - Budget constraint with payroll tax t=9 and basic income Z = 422 .... Budget constraint with w=20 wage rate 4000 3900 3800 3700 3600 3500 3388 IT..... 3200 3100 3000 . . . . . . 2900 2800 2700 2600 2500 2400 3280 +2100 -. . . . .... . . . . . ..es. .. . . . . .em. . . . . ..mr. ....w.. .. . . ...e.. . . ............ 2000 - - - - - - - - - + - - - - - 1900 61800 1700 -- -+-- 1600 1500 1490 XA 1337. 1200 1114. 1000 854.4 672.9 500 422. 300 200 100 88 93 60 98 105.1 118 136.7 145.2 158 168 18 28 38 48 58 68 78 128 Weekly free time (hours)