Question

1.6.4 Question Help 503 Suppose an economy has four sectors: Mining, Lumber, Energy, and Transportation. Mining sells 10% of its output to Lumber, 70% to Energy, and retains the rest. Lumber sells 15% of its output to Mining, 40% to Energy, 20% to Transportation, and retains the rest. Energy sells 20% of its output to Mining, 10% to Lumber 30% to Transportation and retains the rest Transportation sells 10% of its output to Mining, 20% to Lumber, 40% to Energy, and retains the rest a. Construct the exchange table for this economy. b. Find a set of equilibrium prices for this economy a. Complete the exchange table below Distribution of Output from: Mining Lumber Energy Transportation Purchased by: Mining Lumber Energy Transportation (Type integers or decimals.)

Answer 1

drstribution of output from: Mentag Lumber Enesgy Trasepatation purchesed by O. 15 O.10 O.20 MPning O .10 O.20 Lumber O:4 O.40 O.40 Enesagy O:30 O.30 Transportation 0.2x, to.15, to:278g toilx4 = 2, 0.1x + 0.25 x_40.1x3 + Ou2Xq= Xz ○、4スto4x-tov4 Ttoi44=x, o x +0.2x,t0.3.xgt O.3 X4= X4 we Can tuag thes Roto a by martng all the Vasezables to the left stde . homageneoy system The result s -0.8x, + 0.15X3+Oi2 X%+ 0.1 X4= 0 O.1x,- 0.75x+0.12+0.r Xq=0 0.7x, +0.4x_-0.6x 3 + 0.4g=0 -0.7 Xq= the augumented matsix which can be row reduced to find Pauelebatum podces 98 O.15 O.2 -0.8 O.l -0.75 oi O.4 6.4 0-7 To.2 O-3 -0. 4 The row redu ced echelon form of the abore matrix 391 The cauelibriuug -242 1 prices cill be teken from they matrie, 391 -751 391