Question

3. Suppose you have 24 hours to allocate between leisure and working at $10 an hour. One day the government simultaneously institutes a new program consisting of two policies: a 50% income tax and a plan whereby everybody in the country receives a gift from the government of $60 a day. (a) Draw the two budget lines (you may draw a total of three budget lines since the program contains two separate parts.) (b) Suppose that the government chose the level of $60-per-day for the gift because it precisely exhausts the revenue they generate from the income tax, Explain why this means that the average taxpayer must be paying exactly $60 per day in tax. (Consider three groups of people on the diagram - those who pay more tax than the $60 received, those who pay less, and those who pay exactly $60). (c) Assume that you are the average taxpayer. Indicate your new optimum along with the necessary indifference curve. (NOTE that the tangency occurs on the budget line WITH THE NEW PROGRAM!) (d) From this, can you infer your optimum on the original budget line (one without the program)?? Indicate this original optimum. Are you working harder or more hardly working (i.e. 'less hard', if you're confused!) than before the program went into effect? Are you happier or less happy? Show graphically. (e) With all this in mind, comment on such programs in an educated and non-judgmental manner

Answer 1

60---I- 0. 0 o 12-y 12 ... 12.4 12 24 Initial budget: r= 10824 - b) = Budget with program: r= 5(24-2) + 60 Both cwere intersect at L=12 the working howe for average tax payer. 1. b) To pay $60 in tax a person need to work: 60 = 12 hours. In is howes his income is 12x10 = 120 After 50% ta the tax payable is 0.5x120 = $60. Let there are three people who work less than 12 houres; W = 12-x , more than 12 hours W = 12 + x , and exactly 12 nowes. Govt. tax revenue from three perople is:

TR = 5(12 + x) + 5x12 + 5 (12-x) - 5 [12*x + 12 + 12-2] Then average tax from each person in (c) Then average tax payer pays $60 tax. The average tax payer works for 12 howes then takes leisme n = 24-12 = 12 hours Total income : Y = 5(24-12)+60 = 120 The optimal along new budget line CDB is point E. (d) The usual shape of the indifference curve denotes that the marginal rate of substi tution for leisure to income is higher. That is, the consumer prefere more incom to leisure. Then the original equilibrium was at the left of E. This is depicted by F as tangency between AB and nitial indifference curve no. From the graph at f the consumer took less than a howes of leisure. As income falls the consumer shifted to higher all and a lower IC.

This implies the worker works less hard and less happly than before. (e) from the effect of this program on the average consumer is practically nothing ambiguous. Those who worked more than 12 howes are made worse off and those who worked less than 12 hours are made better off. The average welfare effect is decided by the 'weigtage of for the two type of people. issons wire less rows $12 -22; mests?