Question 201175: Free market. The equations S= 5000 + 200x and D= 9500-100x express the supply S and the demand D, respectively, for a popular compact disc brand in terms of its price x (in dollars).
a)Graph the equation on the same coordinate system
b) What happens to the supply as the price increases?
c) What happens to the demand as the price increases?
d) The price at which supply and demand are equal is called the equilibrium price. What is the equlibrium price?
help and thank you!
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! a) Using Algebra one can easily transform the two equations into the familiar slope-intercept form: y = mx + b
S = 200x + 5000
D = -100x + 9500
Therefore the graph of each will be a line. For S, the y-intercept will be 5000 and the slope will be 200. For D, the y-intercept will be 9500 and the slope will be -100.
b) Either from the graph or from the slope, you can tell that as the price goes up (in other words as you go from left to right on the graph) S, the supply, goes up, too.
c) Similarly D, the demand, goes down as the price goes up.
d) Since S = D at the equilibrium price, 200x + 5000 = -100x + 9500. To find the equilibrium price solve this equation:
200x + 5000 = -100x + 9500
Add 100x to both sides:
200x + 5000 + 100x = -100x + 9500 + 100x
300x + 5000 = 9500
Subtract 5000 from both sides:
300x + 5000 - 5000 = 9500 - 5000
300x = 4500
Divide both sides by 300
(300x)/300 = (4500)/300
x = 15
Therefore the equilibrium price is $15.00
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