need help with calculus

[kaia_p]

Hello, apologies in advance my probably stupid question but I am stuck with one calculus. Below is the calculus given in the textbook and I fail to understand how come to Y = 12 292.7 - 73.2r. Would appreciate if anyone could simplify the last steps of the calculation

Many thanks in advance

Starting with the basic GDP identity Y = C + I + G + (X – M) and substituting for each expenditure component using the equations above gives

Y = 2,000 + 0.7(Y – T) + 400 + 0.2Y – 30r + 1,500 + 1,000 – 0.1Y Substituting in the tax equation and solving for Y, we get

Y = 2,000 + 0.7(Y + 200 − 0.3Y) + 400 + 0.2Y − 30r + 1,500 + 1,000 − 0.1Y

= 5,040 + 0.59Y − 30r

Y = 12,292.7 − 73.2r

[S2000magician]

@kaia\_p

Hello, apologies in advance my probably stupid question but I am stuck with one calculus. Below is the calculus given in the textbook and I fail to understand how come to Y = 12 292.7 - 73.2r. Would appreciate if anyone could simplify the last steps of the calculation

Many thanks in advance

Starting with the basic GDP identity Y = C + I + G + (X – M) and substituting for each expenditure component using the equations above gives

Y = 2,000 + 0.7(Y – T) + 400 + 0.2Y – 30r + 1,500 + 1,000 – 0.1Y Substituting in the tax equation and solving for Y, we get

Y = 2,000 + 0.7(Y + 200 − 0.3Y) + 400 + 0.2Y − 30r + 1,500 + 1,000 − 0.1Y

= 5,040 + 0.59Y − 30r

Y = 12,292.7 − 73.2r

This isn’t calculus; it’s algebra.

Look at the last equation:

Y = 5,040 + 0.59Y − 30r

0.41Y = 5,040 – 30r

Y = (5,040 – 30r) / 0.41 = 12,292.7 – 73.2r

[kaia_p]

So addition to math my English sucks as well Many thanks and much appreciated!

[S2000magician]

My pleasure.