Equilibrium Prices - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

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Math 205 A B Quiz 02 (remake) page 1 09/26/2012 Name_SV4gestek Seltion 1. Suppose an economy has just three sectors C, N, S. Suppose that C consumes 20% of its own output while the rest of C’s output is divided equally for consumption by sectors N and S. Suppose N consumes 70% of its own product, S consumes 20% of N’s output and the remainder of N’s output is used by C. Finally, of what is produced by S, 90% is taken by N and the rest is used by C (so S takes none of its own output). 1A: In the space below, give both the exchange table for this economy and the corresponding system of equations that you need to solve in determining the equilibrium prices Po, Py and Pg for this economy. C|N |S Ld fb} oc 4 {tal WN [u|etels 1B: Find the set of equilibrium prices Pe, Py and Ps, if given that Ps = 100 million dollars. Show any RREF’d matrices involved in your solution. the Comepondli =& fl 1° 1 o26|e P. =.6P, a 4H 2-1el 2° CNN [Ra hee. Now, guen Py = $1COM, we Afurn P.~ 460M ot p,= f38OM 1C: Find the set of equilibrium prices Po, Py and Ps, if given that the price N pays C for what N consumes of C’s output. is 80 million dollars. J wo. & t mnt 17 P « O . wine gui that N consumes ol gC £ op » i fe c Het, 1p = 48m, tha [R i =* aR (MVext Gince- Pb =.6F ) we learn 4 200m = 64 be f = 333.35M 7 Frally, Py= 3 8P, = 3.8% $333,8M =*1206,60M3 wo] fy> Tiececm Pork 41h +IR — (O~- 8h eRe yp +.2P +R 1 Oe Me 8h tA at [oe othte ollie Toy svee nw 4 5 13 u 10 -1 0| 3 4 8 44 12 {01 10] 1 2% Let A=! 4 _; _5 3] ands=| “5 J. Isa fact that RREF(Als)is] 9 9 9 1 |_9 1-2-3 1 -1 00 0 0] o 2A. Find in parametric vector form all solutions to Ax = s. from RREF (Al?) we Aol s xX 3.4; 3 X = Xe = l - X32 ! % *3 0 Xy “2 =e A 2B. Find a non-trivial solution x to Ax = 0 or explain why — none. ‘i v6 fr. ‘ > t < ao AA x, |7 wher £ Av =6, ALL He sohls ome gwen by V,°—, 8, M31 , 7 a Tole 3 =i [6 exomp’) he obbainr Phe vont Mak wh &= if o °