Question

4. Investment banker chooses between leisure and consumption good. The price of consump tion good is p. She has super-ability to work for any amount of time between 0 and 24 hours per day. Her per hour wage is w if she works less than 8 hours, and she gets paid overtime salary w' for each hour she works after the 8th hour. Assume that 0<w< w' Also if her income is higher than M, then she has to pay a tax equal to fraction t of her income on each dollar earned on top of M (the income below M is not taxed). Assume that M> 8w. (a) Draw the budget set of the investment banker in leisure-consumption space. (b) Describe it analytically (using formulas).

Answer 1

M= 8w + k*w', where k is the overtime hours she puts in..

This income is used to choose between Leisure and Consumption good.

So, from 16 hours available, she may work k hours and spend 16-k on leisure.

For taxation, if she pays tM as tax, she would get to keep M(1-t) with herself. This will be used to buy consumption good, p
Amount of consumption good she can buy= M(1-t) / p.

Please see the attached image. Let me know if something is missing.

M = 8w + k^* w^', where k is the overtime hours she puts in This income is used to choose between Leisure and Consumption good. So, from 16 hours available, she may work k hours and spend 16 -k on leisure. For taxation, if she pays tM as tax, she would get to keep M(1 - t) with herself. This will be used to buy consumption good, p Amount of consumption good she can buy = M(1-t)/p. Please see the attached image. Let me know if something is missing.