2. [Economics] This problem is similar to Problem 3 in Section 1.6 of Consider a

Question

2. [Economics] This problem is similar to Problem 3 in Section 1.6 of Consider an economy with three sectors: Chemicals, Fuels, and Machinery. The following exchange table illustrates how goods move through your book. Work accu the economy: Output from Purchased by ChemicalsFuelsMachinery Chemicals Fuels Machinery 0.180.75 35 0.15 (0.1 0.45 0.47 0.15 (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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