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omgzam August 7th, 2012 08:43 PM

Plotting Supply & Demand Curve
 
Hey everyone, I'm new here, would love some help on this problem.

*Note: At market equilibrium, we have Demand = Supply

Code:

The supply and demand functions for a good are given, respectively, by

q = 2p + 10    ,    p(q + 4) = 60,

where p is the price.

a) Determine the equilibrium price and quantity,
b) Sketch the supply and demand functions in the same graph for q?0.

I've managed to solve part (a) but am having problems with part (b).

(a)

q = 2p + 10 -----(1)
p(q + 4) = 60 ---(2)

substitute (1) into (2)

p ( (2p +10) + 4) = 60
2p^2 + 14p - 60 = 0
p^2 + 7p - 30 = 0
(p + 10) (p - 3) = 0
p = -10 or 3

But, price and quantity equilibrium can't be a negative, so p = 3.

That's part (a) solved. Now I have no idea how to transition to part (b), help would be appreciated, thanks!

MarkFL August 7th, 2012 08:52 PM

Re: Plotting Supply & Demand Curve
 
1 Attachment(s)
Since this does not involve the calculus, I have moved the topic to the appropriate forum.

Here is a plot of the two functions on the same graph:

[attachment=0:2jyfbf79]supplydemand.jpg[/attachment:2jyfbf79]

omgzam August 7th, 2012 08:59 PM

Re: Plotting Supply & Demand Curve
 
How do you derive the coordinates in relation to the supply and demand equation? Given that we know the market equilibrium falls on the (3,16) coordinates.

MarkFL August 7th, 2012 09:11 PM

Re: Plotting Supply & Demand Curve
 
If we let p be the independent variable, then the first equation:



is a line given in slope-intercept form. We know it will have the point (0,10) and since the slope is 2, it will also have the point (1,12). Then we just run a line through these two points.

If we solve the second equation for q, we find:



We see that this is a hyperbolic curve with vertical asymptote and horizontal asymptote .

We also know it contains the point (3,16). It also has the p-intercept at (15,0). This is enough information to sketch the curve.

omgzam August 7th, 2012 09:24 PM

Re: Plotting Supply & Demand Curve
 
Thanks Mark.

But what if I want p to be on the y-axis and q on the x-axis instead?

And wouldn't the supply curve be:

q = 2p +10
if q = 0,
0 = 2p+10
p = -5

(0 , -5) cutting through (16, 3) instead?

MarkFL August 7th, 2012 09:39 PM

Re: Plotting Supply & Demand Curve
 
1 Attachment(s)
Yes, you would find the point (-5,0) to be on the line if we extend it to the left.

If we wish for q to be the independent variable instead, then we solve both equations for p:

(1)

(2)

[attachment=0:5pfdprrb]supplydemand2.jpg[/attachment:5pfdprrb]

omgzam August 7th, 2012 09:51 PM

Re: Plotting Supply & Demand Curve
 
So, if I want to make a particular variable as the independent value, I'll just assume that it equals to 0?

*ps: What kind of software are you using to input the equations and graphs on your answers? I noticed that it's not text based when I tried to highlight it.

MarkFL August 7th, 2012 09:56 PM

Re: Plotting Supply & Demand Curve
 
If you want a particular variable to be independent, then solve for the other variable.

I am using the site http://www.wolframalpha.com/ to plot the graph.

For the second graph I used the command:

y=(x-10)/2,y=60/(x+4) for x = 0 to 20

Then, I hit [ALT][PRT SCRN] to save a screenshot to the clipboard, opened MS-Paint and copied, cropped and saved the image, then attached it.

omgzam August 7th, 2012 09:59 PM

Re: Plotting Supply & Demand Curve
 
Got it, thank you so much Mark! You've been a great help.

MarkFL August 7th, 2012 10:02 PM

Re: Plotting Supply & Demand Curve
 
Glad to help, and welcome to the forum! :mrgreen:


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