MATH LOVER- help! pretty plz?
1. In the small town of Negreanu, there is a competitive market for decks of playing cards.
Suppose that the demand curve is a straight line and is given by the following equation:
P = 9 – (2/3)QD, where P is the price per deck and QD is the quantity demanded per day.
The supply curve is also a straight line and is given by the following equation:
P = 2 + (1/2)QS, where P is the price per gallon and QS is the quantity supplied per day.
The equilibrium price per deck of cards equals ____, and the equilibrium quantity equals _____.
A. $7; 3 decks of playing cards
B. $5; 6 decks of playing cards
C. $6; 6 decks of playing cards
D. $5; 4 decks of playing cards
Favorite Answer
So:
P = 9 – (2/3)Q and P = 2 + (1/2)Q
Then:
9 – (2/3)Q = 2 + (1/2)Q
7 = (2/3 + 1/2)Q
7 = (7/6)Q
Q = 6
Plug this into either of the equations you gave us to get:
P = 2 + (1/2)*6
P = 2 + 3
P = 5
So B: $5; 6 decks of playing cards
I hope this is all clear!
Treat P like a Y, and treat QD and QS like an X.
Your equations become:
Y = 9 – (2/3)X
Y = 2 + (1/2)X
If you graph these lines, you can see they cross at about B. $5, 6 decks.
Also, you can confirm this by plugging these values into the equations. (Plug 6 in for QD and QS and see that they both work out to equal 5) Hope this helped. Good luck!
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