Suppose that the demand and supply functions for three related goods are: qf = 50 – 2p1 + 5P2 – 3P3, q = 8p1 -5 q = 22 + 7p1 – 2P2 +5p3, q3 = 12p2-5 qg = 17+ P1 +5p2- 3P3, q3 = 4p3 – 1 Use condition, equilibrium q° = qf = qj, i = 1, 2 ,3 and rewrite this system the of equations in the form Ap = b, where A is a P1 3x3 matrix of coefficients, p = | P2 and b is a P3 3x1 vector. (This should be done as rough work on a piece of paper). Use Cramer's rule to solve for p. Also calculate the equilibrium quantities.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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Suppose that the demand and supply functions
for three related goods are:
qf = 50 – 2p1 + 5P2 – 3P3, q = 8p1 -5
q = 22 + 7p1 – 2P2 +5p3, q3 = 12p2-5
qg = 17+ P1 +5p2- 3P3, q3 = 4p3 – 1
Use
condition,
equilibrium
q° = qf = qj, i = 1, 2 ,3 and rewrite this system
the
of equations in the form Ap = b, where A is a
P1
3x3 matrix of coefficients, p = | P2 and b is a
P3
3x1 vector. (This should be done as rough
work on a piece of paper).
Use Cramer's rule to solve for p. Also calculate
the equilibrium quantities.
Transcribed Image Text:Suppose that the demand and supply functions for three related goods are: qf = 50 – 2p1 + 5P2 – 3P3, q = 8p1 -5 q = 22 + 7p1 – 2P2 +5p3, q3 = 12p2-5 qg = 17+ P1 +5p2- 3P3, q3 = 4p3 – 1 Use condition, equilibrium q° = qf = qj, i = 1, 2 ,3 and rewrite this system the of equations in the form Ap = b, where A is a P1 3x3 matrix of coefficients, p = | P2 and b is a P3 3x1 vector. (This should be done as rough work on a piece of paper). Use Cramer's rule to solve for p. Also calculate the equilibrium quantities.
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