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Math Help - Consumption Function

  1. #1
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    Consumption Function

    I'm stumped on this qustion because I cant figure out a or the y intercept.
    Question is...If your marginal propensity to save is always 20% and your break-even point is $10,000 then with $12,500 of disposable income, your consumption would be?
    Using the consumption function formula I've got C= a + (.80)(12500). I'm stumped on how to determine a since his examples in class always gave us a. Appreciate any guidance!
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  2. #2
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    Re: Consumption Function

    Quote Originally Posted by bp802 View Post
    I'm stumped on this qustion because I cant figure out a or the y intercept.
    Question is...If your marginal propensity to save is always 20% and your break-even point is $10,000 then with $12,500 of disposable income, your consumption would be?
    Using the consumption function formula I've got C= a + (.80)(12500). I'm stumped on how to determine a since his examples in class always gave us a. Appreciate any guidance!
    Ok, so when x = 10,000, \ y=0

    So 0=a+.8*10,000
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  3. #3
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    Re: Consumption Function

    Great. Thanks so much that makes sense now. I'm getting the C=10,000

    C=-8000+22,500(.80)
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  4. #4
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    Re: Consumption Function

    I would interpret "break even at 10000" to mean that you spend all of your income at that point, ie C(10000)=10000

    a + 0.2 \cdot 10000 = 10000

    a = 8000

    (ie, positive, not negative).
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  5. #5
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    Re: Consumption Function

    Thank you both for your answers. Some people in my class got C = 12,500 and others got C= 10,000. Perhaps I should frame the question exactly as written.

    The actual question is if your MPS is always 20% and your break-even point is $10,000, then with $12,500 of disposable income, your consumption would be:

    a)$10,000
    b)$2,500
    c)$4500
    d)$12,000
    e)$12,500
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  6. #6
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    Re: Consumption Function

    oopsie, i got MPS and MPC the wrong way around. The MPC is 0.8 as per post #2 but i still think "break even" implies C(10000) = 10000, so:

    a + 0.8(10000) = 10000
    a=2000

    So C(12500) = 2000 + 0.8*12500 = 12000
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  7. #7
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    Re: Consumption Function

    I've never encountered "break even" in my economic studies, but my intuition is with SpringFan25. The first way presented just cannot work because the first term (i.e., "autonomous consumption") is assumed to always be positive. Therefore, a value of -8000 doesn't make sense. We can write the consumption function as

    C(Y^d) = c_0 + c_1 \times Y^d

    Where Y^d is disposable income (= income minus taxes and other transfers), c_0 is autonomous consumption (you always consume that much, equivalent to a fixed costs of a firm's production function) and c_1 is the marginal propensity to consume (MPC = 1 - MPS). Then, as SpringFan25 pointed out, with the break even condition, we have

    C(10,000) = 10,000 = c_0 + (0.8)(10,000) = c_0 + 8000 \Rightarrow c_0 = 2,000

    Thus, this consumer always consumes $2,000 regardless of income. It is their "fixed consumption" we have to account for at any income. Thus,

    C(12,500) = 2,000 + (0.8)(12,500) = 12,000

    Therefore, although the marginal propensity to consume leads the consumer to spend 80% of their disposable income, this is only in addition to their $2,000 fixed consumption ("autonomous consumption").
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