for question B in this question , using equation 4.7 which is Y=C+I+G , isnt it Y= (3600-2000r+0.1Y )+(1200-4000r)+1200 ?

why is the soltion wriiten as Y=(3600-2000r+0.1Y)-(1200-4000r)-1200 ?

in

Numerical problem y (not in textbook) An economy has full-employment output of 6000. Government purchases, G, are 1200. Desired consumption and desired investment are given by: Ca = 3600 - 2000r + 0.10Y |d = 1200 - 4000r where Y is output and r is the real interest rate. a. Find an equation relating desired national saving, So, to rand Y. We know S= Y - Co - G. Substituting in the above equations, we get: Sd = Y - (3600 - 2000r + 0.1Y) - 1200 = - 4800 + 2000r+ 0.9Y This equation relates So to the real interest rate (r) and output (Y). b. Using both versions of the goods market equilibrium condition, Eq's. (4.7) and (4.8), find the real interest rate that clears the goods market. Assume that output equals full-employment output. Using Eq. (4.7) Y = Cd+ /d + G Y = (3600 - 2000r + 0.1Y) - (1200 - 4000r) - 1200 Y = 6000 - 6000r + 0.1Y So, 0.9Y = 6000 - 6000r At full employment, Y = 6000. Substituting this into the above, we get 0.9 x 6000 = 6000 - 6000r Finally, solving for r, we get r = 0.10 (or 10%)