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Math Help - Interpret its economic meaning?

  1. #1
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    Interpret its economic meaning?

    For the money market line:

    C1 = PV(1+r) - (1+r)C0

    has the slope -(1+r). Interpret its economic meaning.



    Any help would be appreciated.

    Anybody got any ideas?
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  2. #2
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    Re: Interpret its economic meaning?

    Quote Originally Posted by Joker37 View Post
    For the money market line:

    C1 = PV(1+r) - (1+r)C0

    has the slope -(1+r). Interpret its economic meaning.



    Any help would be appreciated.

    Anybody got any ideas?
    My first idea is that it would be extremely helpful if you deigned to share with us the meaning of your variables.

    In some applications it is traditional for r to stand for risk-free rate of return, but r may stand for anything.

    Are P and V distinct variables or are they supposed to represent the present value of some unspecified variable?

    The MEANING of an equation depends on the meaning of its constituent variables, and you have not provided those. It sounds harsh, but you are expecting us to be mind readers. Please help us so that we can help you.
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  3. #3
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    Re: Interpret its economic meaning?

    Consider an individual confronted by the net cash flows C_0_ in period-0 and C_1_ in period-1. Assume the individual can borrow and lend at the same constant interest rate r. She may borrow at most \frac{C_1_}{(1+r)} in period-0 and increase current consumption to C_0_ + \frac{C_1_}{(1+r)}. (6)
    In period-1, the loan must be repaid with accrued interest. The amount is:
    \frac{C_1_}{1+r}(1+r) = C_1_, (7)

    which is exactly the amount available to her in period-1. Consumption in period-1 is zero.

    The present value (PV) of this consumption mimx is given by:

    PV = C_0_ + \frac{C_1_}{1 + r} (8)

    where PV is the maximum the individual can consume in period-0.

    Next, (8) is rewritten as:

    C_1_ = PV(1+r)-(1+r)C_0_

    which is a ________________________ that indicates for a given PV (of consumption) the set of possible consumption bundles ( C_0_, C_1_).

    By borrowing and __________________ at r, the consumer can move the _____________________ as she wishes, adjusting the consumption bundle without changing the ______, hence the name the money-market line.

    Above is what is written on my notes.

    I believe the above relates to the question I already orignally posted.

    Anyway, any help would be much appreciated!
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  4. #4
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    Re: Interpret its economic meaning?

    Quote Originally Posted by Joker37 View Post
    Consider an individual confronted by the net cash flows C_0_ in period-0 and C_1_ in period-1. Assume the individual can borrow and lend at the same constant interest rate r. She may borrow at most \frac{C_1_}{(1+r)} in period-0 and increase current consumption to C_0_ + \frac{C_1_}{(1+r)}. (6)
    In period-1, the loan must be repaid with accrued interest. The amount is:
    \frac{C_1_}{1+r}(1+r) = C_1_, (7)

    which is exactly the amount available to her in period-1. Consumption in period-1 is zero.

    The present value (PV) of this consumption mimx is given by:

    PV = C_0_ + \frac{C_1_}{1 + r} (8)

    where PV is the maximum the individual can consume in period-0.

    Next, (8) is rewritten as:

    C_1_ = PV(1+r)-(1+r)C_0_

    which is a ________________________ that indicates for a given PV (of consumption) the set of possible consumption bundles ( C_0_, C_1_).

    By borrowing and __________________ at r, the consumer can move the _____________________ as she wishes, adjusting the consumption bundle without changing the ______, hence the name the money-market line.

    Above is what is written on my notes.

    I believe the above relates to the question I already orignally posted.

    Anyway, any help would be much appreciated!
    $\text{Let r = rate of interest available.}$

    $\text{Let c}_i \text{ = cash flow for period i, where }i \in \{0,1\}.$

    $\text{Let p = present value of cash flows } = c_0 + \dfrac{c_1}{1 + r}.$

    $\text{Let f = future value of cash flows } = c_0(1 + r) + c_1.$

    All of this was presumably in your lecture. (Note that I HATE the economists' bad habit of assigning a compound of letters to one variable, which ends up looking like a product.)

    Now we need another pair of variables, namely

    $\text{Let s}_i\text{ = spending for period i, where }i \in \{0,1\}.$

    I strongly recommend always noting the meaning of your variables in writing. It takes one load off your memory and is a great help in communicating with others.

    Now consider a Cartesian plane where the horizontal axis is s1 and the vertical axis is s0.

    The line between $(0,\ p)\ and\ (f,\ 0)$ delineates the maximum amount of spending that can be done across the two periods.

    Do you see that?

    Now if we imagine a family of utility curves (with each curve of higher utility further from the origin) and make the standard assumptions about convexity, the curve of maximum ACHIEVABLE utility will be tangent to the line between $(0,\ p)\ and\ (f,\ 0).$

    I have never heard this line called the money market line before; it delineates the feasible region for the individual. However, if you sum the points of tangency for all individuals, it provides the net supply curve for money at a single interest rate.

    EDIT: Trying to decipher notes from a lecture that I did not hear is a dangerous effort. Furthermore, I last took a course in the economics of financial markets in 1970 so my recollection is perhaps hazy. Please do not hesitate to seek clarification. Maybe I have misconstrued what your professor was communicating.
    Last edited by JeffM; August 11th 2014 at 02:29 PM.
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  5. #5
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    Re: Interpret its economic meaning?

    By the way the slope of the line running from (0, p) to (f, 0) is

    $\dfrac{p - 0}{0 - f} = -\ \dfrac{p}{f}.$

    $But\ p = c_0 + \dfrac{c_1}{1 + r} \implies p(1 + r) = c_0(1 + r) + c_1 = f.$

    $p(1 + r) = f \implies -\ \dfrac{p}{f} = -\ \dfrac{p}{p(1 + r)} = -\ \dfrac{1}{1 + r}.$

    All this means is that the way your professor labeled the horizontal and vertical axes was reversed from my way.
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  6. #6
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    Re: Interpret its economic meaning?

    In the answers is says:
    A unit increase in current consumption C_0_ requires a -(1 + r) decrease in future consumption C_1_. This can be thought of as the repayment -C_0_ plus the interest paid -rC_0_.
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  7. #7
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    Re: Interpret its economic meaning?

    Quote Originally Posted by Joker37 View Post
    In the answers is says:
    A unit increase in current consumption C_0_ requires a -(1 + r) decrease in future consumption C_1_. This can be thought of as the repayment -C_0_ plus the interest paid -rC_0_.
    OK That makes sense, provided that the consumer is maximizing consumption subject to a budget constraint. I point out, however, that not all consumers do maximize consumption.
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