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Using matrices to solve simultaneous equations

Maths with economic applications based matrices question. Stuck on how to do it!

(b) The demand and supply functions for two interdependent goods are given by:

QD1 = 50 – 2P1 + P2
QD2 = 10 + P1 – 4P2
QS1 = – 20 + P1
QS2 = – 10 + 5P2

Hence find the equilibrium price. (6 marks)

Cheers in advance!
Original post by Henry.Lister
Maths with economic applications based matrices question. Stuck on how to do it!

(b) The demand and supply functions for two interdependent goods are given by:

QD1 = 50 – 2P1 + P2
QD2 = 10 + P1 – 4P2
QS1 = – 20 + P1
QS2 = – 10 + 5P2

Hence find the equilibrium price. (6 marks)

Cheers in advance!


I don't know how you're meant to do it.

But assuuming Q1D=Q1SQ^D_1=Q^S_1 you can equate the two getting an equation of the form aP1+bP2=caP_1+bP_2=c where a,b,c are constants.

Similarly for the second commodity, and then slap both equations into an augmented matrix which you can reduce, giving you the prices.

But, not having studied this, I don't know if that's the way you're meant to do it.
Hmmnn... I didn't do much economics but am pretty good with maths.

What are the Q's? Are they constants?

If they are four different constants, then the system you have described is four equations in two unknowns: P1 and P2.

So the system won't have a unique solution. You have more equations than variables. The best you can do is try to fit the best line to the data.

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