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 IlanSherer April 9th, 2018 02:28 AM

Macro-economics

Hello :)

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.

 JeffM1 April 9th, 2018 04:16 AM

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.

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

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

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

$a = 2000 \implies c(a) = 0.75 * 2000 + 120 = 1620.$

 IlanSherer April 9th, 2018 10:27 AM

Quote:
 Originally Posted by JeffM1 (Post 591731) 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).
 Originally Posted by JeffM1 (Post 591731) 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. $\displaystyle c'(a) = 0.75 \implies c(a) = \int 0.75\ da = 0.75a + K.$ $c(0) = 120 = 0.75(0) + K \implies K = 120 \implies c(a) = 0.75a + 120.$ $x(a) = 0.81 = \dfrac{0.75a + 120}{a} \implies 0.06a = 120 \implies$ $a = 2000 \implies c(a) = 0.75 * 2000 + 120 = 1620.$