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Need help with econ/maths introductory question!

Suppose an economy produces two goods X and Y under conditions of no joint production and constant returns to scale. Input requirements per unit of gross output are given by the following input-output table.

X. Y
X. 0.1. 0.2
Y. 0.7 0.4

Find the gross outputs when the required net outputs of X and Y are 30 and 10 respectively.

--> Supposed to be easy but I keep getting the wrong answer when I use simultaneous equations!
The answer is meant to be x=50 and y=75. Wld appreciate it if anyone could help!
Reply 1
bump
Reply 2
someone please helppp
Reply 3
I've not seen a problem like this. I had a quick go on the back of an envelope does the answer involve y = 1350?
Reply 4
Original post by TFP_SA
I've not seen a problem like this. I had a quick go on the back of an envelope does the answer involve y = 1350?

Thanks for your reply! I didn't come across that number, but I'm curious how you got there?
I tried simultaneous equations
x*=0.9x-0.7y
y*=0.6y-0.2x
then subbed in x=30 and y=10
and I got 37.5 and 625/9 :frown:
Reply 5
Original post by olivier_
Thanks for your reply! I didn't come across that number, but I'm curious how you got there?
I tried simultaneous equations
x*=0.9x-0.7y
y*=0.6y-0.2x
then subbed in x=30 and y=10
and I got 37.5 and 625/9 :frown:


My earlier answer was rubbish, I tried to do it in my head, more or less.

I think your simultaneous equations aren't quite right, you're suppose to read across the rows of the table rather than down the columns. So the right starting equations are:

A: 30 = x-0.1x-0.2y = 0.9x-0.2y
B: 10 = y - 0.7x - 0.4y = 0.6y-0.7x

then if you say multiply A by 3 you have:

C: 90 = 2.7x - 0.6y =>
D: 0.6y = 2.7x-90

then you use D to insert a new term for 0.6y into B, you get:

10 = 2.7x-90-0.7x;
100 = 2x
x = 50

etc.
Reply 6
Original post by TFP_SA
you're suppose to read across the rows of the table rather than down the columns

thank you so much, it's cleared my head now!

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