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Economics/Demand and Supply Curves

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QUESTION: Hi there,

I am having trouble with the basics. Usually in numericals involving demand and supply, with equations like

QD=2800-4P  and  QS=250+2P;

why is Qs graphed so that its y-intercept is positive 125 and not -125. While solving numericals as well, I find solutions having used some sort of trick or changing sign or manipulating equations and getting equations in terms of P. Straight mathematics does not often provide right solution. Is it because there some sort of convention about signs? Or a method to tackle these problems?

For example, sometimes(the manipulation always goes with QS) QS above is changed as P=125+QS/2 which is mathematically incorrect.

Thank You.

ANSWER: Thanks for the question!

When you first start working with the mathematics of supply and demand curves, they're not really curves at all - they're linear.  That's the case with your equations as well; they're nothing more than linear algebra.  Let's break down your example a little bit and see if that doesn't help you understand it a bit better.

First, let's rearrange the equations a little bit.  Personally, I find them much easier to work with when arranged like a traditional equation of a line.
QD = -4P + 2800
QD means "Quantity Demanded".  -4P is the slope of the line.  It's a negative slope, which is shown by the negative value (-4) relative to P, which means that it moves downward.  The reason for this is that as price increases, people either can't afford as much, or they are unwilling to pay the price.  When price is 0 (i.e.: -4(0)), then demand is 2,800 units.  That is the Y-intercept; the last portion of the equation, then as price increases, demand goes down.

QS = 2P + 250
and QS means "Quantity Supplied".  Since the slope is positive (positive 2, in the 2P portion of the equation), that means as price increases the amount of supply increases.  This happens because producers are able to afford the increased production costs of producing additional units.  When price is 0 (i.e.: 2(0)), then supply will be 250.  250, then, is the Y-intercept, then as price increases, so does supply.

As for your calculation example:
Start: QS = 2P + 250
Subtract 2P from both sides: QS - 2P = 250
Subtract QS from both sides to get P by itself: -2P = -QS + 250
Divide the WHOLE THING by 2 to get P by itself: -P = -(QS/2) + 125
Divide the WHOLE THING by -1 to make P positive: P = (QS/2) - 125
End: Price is P = 0.5QS - 125

Hopefully that helps.

---------- FOLLOW-UP ----------

DemandNSupply
DemandNSupply  
QUESTION: Thank You for taking your valuable time in answering.

You did not get what I wanted to ask. Let me make it more clear with more robust example. The new example has very similar set of QS and QD Equations. You can disregard everything else on the attached image other than simply the demand and supply equations and their graph.

Following normal mathematics, we are expected to get a different graph as the one on right of image attached; one where the Supply line touches y-axis at (0,-125) but that is not true. Could you explain why is it done so?

Thank You.

Answer
Notice that if you use the exact same method I showed you and apply it to QD, that the price at Y in 700, as the graph shows.  For QS, it is different, however.  I think you have found an error in the problem, rather than in your answer.  They may come back and try to convince you that since price will never be negative, that you should use the absolute value of the price value.  You should tell them that they should edit their work better.

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