This problem is similar to Problem 3 in Section 1.6 of your book. Work accurate

Question

This problem is similar to Problem 3 in Section 1.6 of your book. Work accurate to two decimal places. Consider an economy with three sectors: Chemicals, Fuels, and Machinery. The following exchange table illustrates how goods move through the economy: Output from Purchased by Chemicals FuelsMachinery Chemicals 0.18 .35 0.47 0.4 0.45 0.15 0.75 Fuels 0.15 Machinery (a) Let pc PF, and pM denote equilibrium prices for chemicals, fuels, and machinery respectively. Write a system of equations in matrix form to find the equilibrium prices (b) If the equilibrium price for Machinery is 100 what are the other equilibrium prices?

Explanation / Answer

a)
pc =x, pf = y ,pm = z
.18 x + .75 y + .4 z = x
.35 x + .15 y + .45 z = y
.47x +.1y + .15z = z

y = 0.751292 x

z = 0.641328 x

b) z = 100

hence

x = 100/ 0.641328 = 155.926452611

y = 155.926452611 * 0.751292 = 117.146296435

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