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Math Help - [SOLVED] Labor Supply Practice Problem

  1. #1
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    [SOLVED] Labor Supply Practice Problem

    I've tried drawing the budget constraints for part a, but I just can't get them right. Any tips?

    A program provides cash assistance of $600 when the head of the household works at least 120 hours a month and when their monthly income (income from working) doesn't exceed a set limit.

    Consider a single parent family. Previously, monthly earnings for a single parent family had to be less than $1,500 to receive benefits from the program. Monthly limits on earnings were expanded to $2,500 for a single parent family.

    a. Assume that the parent in a single parent family could earn $10 an hour. Plot the individual's monthly leisure income budget constraint if the limit of earnings is $1,500 and plot the individual's monthly leisure income budget constraint if the limit of earnings is $2,500.
    Last edited by tathata; May 23rd 2010 at 06:03 PM. Reason: erased part b, not necessary
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  2. #2
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    Notation first:
    point: a dot on your graph indicating that this combination of leisure/income is on the constraint
    hollow point: a little circle on your graph indicating that all points up this this one are on the budget constraint, but the point itself is not (your professor may use a different notation for this)



    The way i think about these is to start with 100% of leisure, then think about what happens if you spend some more time working. Keep repeating this until you have 100% labour.


    Ill assume there are 30 days in the month, so the maximum leisure is 30*24=720. This corresponds to an income of 0.

    point
    leisure: 720
    income: 0

    for the first 120 hours, any additional work will credit him with $10 an hour. So you have another point at:
    hollow point
    leisure: 720 - 120 =600
    income: 10*120=$1200

    This is a hollow point because if you get there you will immediately be given the $600 allowance.


    Draw a stright line between them (because income/leisure are swapped at constant rate of $10 per hour)


    Now, at this point, he becomes eligible for the $600 grant; so we have a discontinuity. Draw another point:
    point
    leisure: 600
    income $1200 + 600=$1800

    Dont make the mistake of drawing a vertical line between the 2 points you just drew, this is not correct (presumably, you must take either the entire grant or none of it, so the points in between are not achievable).


    Now. assume the upper limit on earnings is $2500 (as in the quesion). i assume this means $2500 labour income, not $2500 total income (which would include the grant).

    To get the $2500 labour income, you'd have to work 250 hours, which is an additional 130 hours). So, up to that point our parent is just swapping leisure for income at the rate of $10/hour again:

    hollow point:
    leisure: 600-130 = 470
    income: 2500+600=3100

    Draw a line connecting the previous two points, because every space in between is acheivable.


    But, he is no longer eligible for the grant, so his income drops by 600:

    point:
    leisure: 470
    income: 2500



    Finally, there is no more assistance available after this, so the final point you must draw is 100% labour.


    point:
    leisure: 0
    income: 2500 + 470*10 =7200




    Ill see if i can draw it and attach in another reply.
    Last edited by SpringFan25; May 23rd 2010 at 01:38 PM.
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  3. #3
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    here is the graph (click thumbnail to see larger version)



    I haven't looked at part b as you said you were stuck on part a. Let me know if you need a bit more info on part b.
    Attached Thumbnails Attached Thumbnails [SOLVED] Labor Supply Practice Problem-income_leisure.jpg  
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  4. #4
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    Thank you so, so much! I've been having trouble with these types of graphs, so this is a big help.
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