Question

b) Given reduced-form equations of a goods market (IS curve) and a money market (LM), respectively, as follows: Fl(Y“, i*; Co, M ) = Y* - Co-C(Y*, i*) = 0; F (Y', i; Ca, Mg) = L(Y', ) - M = 0; 0 < Cy <1, C; <0 Ly > 0, L < 0, where L(Y, i) is the demand for money, M, is the supply of money, Co is an autonomous consumption. i) Take the total differentials of both reduced-from equations above. (4 marks) ii) Rewrite your findings in i) into a matrix of form Jx=b. (3 marks) iii) Measure the effect on the equilibrium levels of Y* and i* of a change in Co. (6 marks) iv) Comment of your findings in iii) above. (3 marks)

Answer 1

i Is and LM equation is given by dd2 0224 y*_co-e (y + i) =0 oLeylt, eit LLY*, ix) - Mo = 0 lun Ly Li. Now taking total differentiation of both the equation we get: - O H. dyt-dco - 2 dyt ac de*=0+. => dy* -deo - cy dyt – ei di* = 6 -> (1-ey) dyt - Cê di* = doo --i ) and at dy* + 2L dit * 4 al di* dmo =0 ti Li di* = 0 I mo= constant] = Ly dy in Now rewritting equation (i) and (ii) in matrix form we get I cley) Will dyrl Ideol Lyk Li I din t o - TX = b T = 1 (1-cy) och Where Idcol ton b= I dy* f T and di* I Scanned with

in do dyshon so fug will Now effect on y due to a change Co is given by dytetan dco by crammens rule we get . I deo - al N2o1 l 0214 O gos oro deal 1-ey) in cil on (1-ey) Lit Lyci -li Lioel op ww ad fimis = dy*r (1-ey) Li thyce 7 = do Li 2'w 02200 АГАЛ 3 2 1 0 0 2007 0 0 L'ins22314 credit cu cel fare? LCD al coll sienos er [l-ey), La + Lyci] Now, yli Loto ey 22, or (ly-1) Lour song or (1-2y) > 0 meso, Li (1-ex) 20 Pode and Ly yo a Lo, so, Ly ci lo So denominator and numerator is negative This negative Sign Cancals out and a dragosteo so Ncwal aliw dyt

of change Also in effect on co will be it as a result de* dan po mo en convocacov) - DV deo olil oxid rule w rule we get by cramer's bikestad Il-ey deo Det of LY 0 son notarpis o= ono to ang gaano to - deoLy 1-ex) Litary show né il buo (i) Notarp prilly 100% 1 Now de deody dcosy ci it lily) di * Crey is Ly - deo run my CroE (1-cy) Liteily] d Now Ly>O and = Ly Lo ex 21 = (1-ey) >0 LiLo - Li (1-ey) 20 Ci Lo, Lyyo => Ci Ly 2o.

So, numerator and denominator box negative sign so negative sign car and di* be conces positive dco so, dino minator both have Sign Cancels out dco o (1) Now From (ili) we can say that due to a change in co both y* and i increases. So Co has an expansionary effect on both y* and it CamScanner