Question

#4. (14 marks) Mark's preferences are given by U = 8F4 x M4 x1, where F is food, M is manufacturing good and 1 is leisure per week. His total time endowment (after sleep) is 90 hours per week. Prices of F and M are $5 and $1 respectively. His hourly wage is $10. He also receives a fixed benefit of $60 per week. (a) What is Mark's weekly equilibrium consumption of goods and leisure? (HINT: since there are three goods you only need to write and use any two tangency conditions.) (b) If the government taxes his employment income only at the rate of 20%, what are his equilibrium consumption quantities? What is the tax revenue collected from Mark? (c) If the government taxes not only his employment income but also his benefit at the rate of 20%, what are his equilibrium consumption quantities? What is the tax revenue collected from Mark here? (d) How can you explain the increase in the tax revenue collected from Mark from (b) to (c)? Provide two main reasons for this increase. Also what ad valorem tax on F and M would be an equivalent to the 20% income tax used in (c)?

Answer 1

The solution of this problem would be......

Given u . 8ftmyxl Pm a $ 1. wage a $10. (Total hours per week Fixed benefit additional lumpcomé income - independent of hours worked) = $60. Total income - y = 60+ 10 (4) where (L = 90-l. no of tours worked. I wage per hour tal expenditure - - PE F +Pm.Mtd 57 +Mitd. Weekly consumption of goods and leisure is given by the following condition : - total income of total expendi- (weekly) ture (weekly

80+ 101 2758 time) - - 51 tm t l L tot 10 (90-1) 3ft mtl + lol 2 60 + 900 5t tmtlle Labor Weekly budget- constraint So, consemption bundle is given by the following condition:- maximise Utility for:- U= 8F 34 m l ③ Subject to : Budget constraint given by SF + m +1 l = 960 6 for simplicity, consider equality (income = expenditure)

between and The point of tangency gives the level of consumption of food, manufactured good and ligure. (6) Tax colleclid is on em income. t. Tax collected a eled - 2017. of (101) = 20% of 10 (90-6) = 20 a Too x 900-10) = 2ox qop 160 - 2008 189 W T = 180-22 when tax is imposed disposable income of the person falls. This, Consumption of the goods reduce according to his utility Preferences, erences

RI c) Tax collected al 20% of 6o) & rof of (104) - 20 x 60 + 20% of 104] = 180-2L (from part b. caleulation) = 12 + 180-227 = 16800 - 2L. amount now collected increased by $12. Tz lax .. The consumption of the goods further falls, as now, disposable income in further reduced by $12.

d) the increase in tax revenue can. be explained due to the tax being imposed on the total income (cumpsоmeſt variable); rather than only on the variable income (as in part (67) An ad valorem lax equal to Z of 201 on food Yu of 20 4. on manufacture sy on manufacture would be equivalent to 20%, of income tax in the partic) as the consumption of food and manufactured good is done in those respective proportions According to marks