Question

Julia spends 60 hours a week on sleeping. The remaining 108 hours is shared between working and leisure. Julia's single employment opportunity is to wash the dishes at a restaurant, which earns her an hourly wage of 3000.

Draw the budget line such that you put the number of hours of leisure per week on the horizontal (x) axis, and the consumption per week on the vertical (y) axis.

Provide the following pieces of information.

The slope of Julia's budget line.

The budget line intersects the horizontal axis at (x,y) = (  , 0).

The budget line intersects the vertical axis at (x,y) = (0,  ).

If Julia decides to work 40 hours a week, she can spend a week on consumption.

If Julia wants to consume 150000 a week, she can afford hours of leisure a week.

Now assume that the government introduces a 20% income tax on the first 20 working hours in a week.

In this case, if Poor Tony decides to work 40 hours a week, he can spend  HUF a week on consumption.

If Poor Tony wants to consume 150000 HUF a week, now he can afford  hours of leisure a week.

Answer 1

Apart from sleep, the maximum available hours = 108.

If Julia does not work at all and uses 108 hours as leisure, she will have zero labor income and hence, the horizontal intercept will be 108, i.e., the budget line intersects the horizontal line at (x.y) = (108,0). On the other hand, if Julia chooses to use entire 108 hours to work (i.e., zero leisure), the maximum she can earn is 3000 * 108 = 324000, which becomes the vertical intercept. In other words, the budget line intersects the vertical axis at (x.y) = (0, 324000).

Hence, the slope if the budget line = -w = -3000. This can be verified by the fact that slope = -(vertical intercept / horizontal intercept) = -324000/108 = -3000

If Julia decides to work 40 hours, she can earn 3000 * 40 = 120000, which she can spend for consumption.

If Julia wants to consume 150000 a week, she needs to work 150000/3000 = 50 hours. Hence, she can choose leisure = 108 - 50 = 58 hours a week.

Now govt imposes a tax of 25% on first 20 working hours, i.e., for first 20 hours, the wage becomes 3000 * 0.8 = 2400.

If Poor Tony works for 40 hours, he can earn a wage of 2400 for first 20 hours and then a wage of 3000 for the rest 20 hours. Hence, his labor income would be 2400 * 20 + 3000 * 20 = 108000. Hence, he can spend 108000 a week on consumption.

On the other hand, if Poor Tony wants to spend 150000 a week on consumption. By working first 20 hours he can earn 48000. Rest amount 150000 - 48000 = 102000 can be earned at a wage rate of 3000 an hour. Hence, he needs to work for 102000/3000 = 34 more hours in addition to initial 20 hours. Hence, he needs to work for 20 + 34 = 54 hours which will enable him to spend 150000 a week on consumption.