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April 9th, 2018, 02:28 AM   #1
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Macro-economics

Hello

Can you help me please about the next question:

For a certain family, a private consumption curve/function that has a marginal tendency to consume is constant at any available income (the income after deduction because of debts, tax and more) level which equal to 0.75.
It is known that when the available income level is zero, the planned consumption of the family is positive and equal to 120.
Find the private consumption and available income of the family if in the current available income level, the average tendency to consume is equal to 0.81.

I'm trying to solve this exercise but I don't even know what is the current available income level or how to find it.

Thanks!

And of course if you didn't understand something, I will explain again.
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April 9th, 2018, 04:16 AM   #2
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I THINK that this is what you are looking for, but the question does not seem well enough worded for me to be at all sure.

$c(a) = \text { PLANNED consumption.}$

$a = \text { available income.}$

$x(a) = \text { average tendency (???) to consume.}$

$c'(a) = 0.75 \text { given } a \ge 0.$

$x(a) = \dfrac{c(a)}{a} \text { given } a > 0.$

The above is what I think the question means in math. If I am correct in what I think that problem is trying to say, the solution is mathematically simple.

$\displaystyle c'(a) = 0.75 \implies c(a) = \int 0.75\ da = 0.75a + K.$

$c(0) = 120 = 0.75(0) + K \implies K = 120 \implies c(a) = 0.75a + 120.$

$x(a) = 0.81 = \dfrac{0.75a + 120}{a} \implies 0.06a = 120 \implies$

$a = 2000 \implies c(a) = 0.75 * 2000 + 120 = 1620.$
Thanks from IlanSherer
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April 9th, 2018, 10:27 AM   #3
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Quote:
Originally Posted by JeffM1 View Post
I THINK that this is what you are looking for, but the question does not seem well enough worded for me to be at all sure.

$c(a) = \text { PLANNED consumption.}$

$a = \text { available income.}$

$x(a) = \text { average tendency (???) to consume.}$

$c'(a) = 0.75 \text { given } a \ge 0.$

$x(a) = \dfrac{c(a)}{a} \text { given } a > 0.$

The above is what I think the question means in math. If I am correct in what I think that problem is trying to say, the solution is mathematically simple.

$\displaystyle c'(a) = 0.75 \implies c(a) = \int 0.75\ da = 0.75a + K.$

$c(0) = 120 = 0.75(0) + K \implies K = 120 \implies c(a) = 0.75a + 120.$

$x(a) = 0.81 = \dfrac{0.75a + 120}{a} \implies 0.06a = 120 \implies$

$a = 2000 \implies c(a) = 0.75 * 2000 + 120 = 1620.$
I found it, the average tendency to consume - it's APC (Average propensity to consume).
And thanks for answering, I will read it later.
If there are another words which you didn't understand, just say and I will try to find a way to explain you
IlanSherer is offline  
April 10th, 2018, 03:47 AM   #4
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Quote:
Originally Posted by JeffM1 View Post
I THINK that this is what you are looking for, but the question does not seem well enough worded for me to be at all sure.

$c(a) = \text { PLANNED consumption.}$

$a = \text { available income.}$

$x(a) = \text { average tendency (???) to consume.}$

$c'(a) = 0.75 \text { given } a \ge 0.$

$x(a) = \dfrac{c(a)}{a} \text { given } a > 0.$

The above is what I think the question means in math. If I am correct in what I think that problem is trying to say, the solution is mathematically simple.

$\displaystyle c'(a) = 0.75 \implies c(a) = \int 0.75\ da = 0.75a + K.$

$c(0) = 120 = 0.75(0) + K \implies K = 120 \implies c(a) = 0.75a + 120.$

$x(a) = 0.81 = \dfrac{0.75a + 120}{a} \implies 0.06a = 120 \implies$

$a = 2000 \implies c(a) = 0.75 * 2000 + 120 = 1620.$
Yes, you understood the question correctly, thanks a lot!
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