In a competitive market the demand curve is given by P = 120–2q and supply by P = q. What are the equilibrium price and quantity traded?Group of answer choicesP* = 60, q* = 60P* = 40, q* = 80P* = 40, q* = 40P* = 20, q* = 40None of the above.
Question
In a competitive market the demand curve is given by P = 120–2q and supply by P = q. What are the equilibrium price and quantity traded?Group of answer choicesP* = 60, q* = 60P* = 40, q* = 80P* = 40, q* = 40P* = 20, q* = 40None of the above.
Solution
In a competitive market, the equilibrium occurs where the quantity demanded equals the quantity supplied. This is where the demand curve and supply curve intersect.
The demand curve is given by P = 120 - 2q and the supply curve is given by P = q.
To find the equilibrium price (P*) and quantity (q*), we set the two equations equal to each other and solve for q:
120 - 2q = q 120 = 3q q = 120 / 3 q = 40
Substitute q = 40 into the supply equation to find P:
P = q P = 40
So, the equilibrium price (P*) is 40 and the equilibrium quantity (q*) is 40. Therefore, the correct answer is P* = 40, q* = 40.
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