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Math Help - Graphically depict the budget constraints for four different business plans

  1. #1
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    Graphically depict the budget constraints for four different business plans

    Here because I'm taking an economics class, have read the 2 chapters of the book we are supposed to have read and am confused.

    If someone wants to post the answer that's fine (as long as you're willing to explain it), but what I'm really looking for is the way that I need to approach this problem so that I can understand it and graph it in excel.

    Questions I have:

    1. How am I supposed to be arriving at these budget constraints and portraying them on a graph? i.e: This plan would give a grant of $10,000 to each high school in the state that the school could spend as it wished. Am I assuming it uses this money on computers? Other stuff? And this: This plan would give a $10,000 grant to any high school, so long as the school spent at least $10,000 more than it currently spends on computers. Any high school can choose not to participate, in which case it does not receive the grant, but it doesn't have to increase its expenditure on computers. Am I presuming that this grant is 10,000 dollars on top of the 20,000 already slotted for computers? How do I graph this? Is it 30,000 horizontally? Vertically?

    Thanks in advance.

    3. Moon high school has $60,000 to spend on computers and other stuff, so its budget equation is C + X = 60,000, where C is expenditure on computers and X is expenditures on other things. C.H.S. currently plans to spend $20,000 on computers. The State Education Commission wants to encourage "computer literacy" in the high schools under its jurisdiction. The following plans have been proposed.
    Plan A: This plan would give a grant of $10,000 to each high school in the state that the school could spend as it wished.
    Plan B: This plan would give a $10,000 grant to any high school, so long as the school spent at least $10,000 more than it currently spends on computers. Any high school can choose not to participate, in which case it does not receive the grant, but it doesn't have to increase its expenditure on computers.
    Plan C: Plan C is a "matching grant." For every dollar's worth of computers that a high school orders, the state will give the school 50 cents.
    Plan D: This plan is like plan C, except that the maximum amount of matching funds that any high school could get from the state would be limited to $10,000.
    a) Graphically depict the budget constraints for each of the four plans. You should use the following axes: the horizontal axis will be expenditures on computers, (C), while the vertical axis will be X, the expenditure on “other stuff.
    b) While you do not know the shape of the indifference curves between C and X, speculate on which plan the school is most likely to desire.
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  2. #2
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    C.H.S. currently plans to spend $20,000 on computers.
    Is CHS the same as Moon high school? I have assumed it is, so moon has a budget of 60k, and is planning on spending 20k on computers.

    A budget constraint represents the trade off between expenditure on computers (C) and all other goods (X). So if they dont spend anything on C, they will spend $60000 on X, and if they only consume C, they wont spend anything on X. So the budget constraint is the linear line between these two maximum expenditures.

    (a)
    Under Plan (a) They receive a lumpsum grant in which they can spend how they wish on the 2 goods. So it will shift the budget constraing (BC) out by $10,000.
    Plan (b) [Edit: Im not exactly 100% sure with part (b)] they receive the $10000 payment, however they must increase their expenditure on computers by $10000 first. I am assuming that once they have increased their expenditure, they are then free to use the grant money how they want. This causes the budget constraint to 'jump up' at their current level of expenditure on computers.
    Under plan (c) they will recieve 50c for each dollar spent on computers. So if they spend all 60k on computers, they will receive a 30000 grant, however if they spend $60000 on X they wont receive any grant at all. At $20,000 the grant would be $10000.
    Plan (d) is similiar to (c) only they cap the grant at $10000 instead of letting it be unlimited.

    Just drawing up some graphs in MS paint now to help explain what I mean
    Last edited by Robb; September 9th 2009 at 06:56 PM.
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  3. #3
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    Not the best pictures, but it gives you an idea.

    Part (b)
    Their choice on which plan they would prefer will come down to their indifference curves/prefernces for computers or all other goods (so whether they are normal goods or not etcd). From the graphs, we can see that the school will prefer plan (a) over plan (b), as plan (a) allows for greater flexibility in how the grant will be spent. And plan (c) to plan (d) as it allows for far greater benefits if they choose to spend more on computers as they keep getting 50c grant per dollar spent.
    So the choice is between plan (a) and plan (b). The school will prefer plan (a) if they would prefer to spend more on X then C once they have received the grant (its been a few years since i did micro, but refer to income / substition effects), but plan (c) if they would spend even more on computers. If you think of overlaying the graphs of part (a) and part (c) this will be clear from where the budget constraints will lie. For any expenditure on computers under 20k, the BC from (a) will lie above (c), and any expenditure over 20k the BC from (c) will lie above (a).

    Note that the indifference curves there are just for representation, they could look completely different.
    Attached Thumbnails Attached Thumbnails Graphically depict the budget constraints for four different business plans-part-.jpg   Graphically depict the budget constraints for four different business plans-part-b.jpg   Graphically depict the budget constraints for four different business plans-part-c.jpg   Graphically depict the budget constraints for four different business plans-part-d.jpg  
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