The competitive market for bicycles has a demand function given by Qd = 444 - 2P and a supply function given by Qs = 2P. What is the quantity of bicycles traded in the market equilibrium?[Round your answer to 2 decimals (e.g. 24.03)]
Question
The competitive market for bicycles has a demand function given by Qd = 444 - 2P and a supply function given by Qs = 2P. What is the quantity of bicycles traded in the market equilibrium?[Round your answer to 2 decimals (e.g. 24.03)]
Solution
To find the quantity of bicycles traded in the market equilibrium, we need to set the demand function equal to the supply function and solve for P (price).
The demand function is Qd = 444 - 2P and the supply function is Qs = 2P.
Setting these two equal to each other gives us:
444 - 2P = 2P
Solving for P, we add 2P to both sides to get:
444 = 4P
Then, divide both sides by 4 to isolate P:
P = 444 / 4 = 111
Now that we have the equilibrium price, we can substitute P = 111 into either the demand or supply function to find the equilibrium quantity (Q).
Using the supply function Qs = 2P:
Q = 2 * 111 = 222
So, the quantity of bicycles traded in the market equilibrium is 222.
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