The demand and supply functions for different firms are given belowi) Qd = 200 – 2PQs= - 20 + 2Pii) Qd = 51 – 3PQs = -4 +8PDetermine the equilibrium price and equilibrium quantity for each firm
Question
The demand and supply functions for different firms are given belowi) Qd = 200 – 2PQs= - 20 + 2Pii) Qd = 51 – 3PQs = -4 +8PDetermine the equilibrium price and equilibrium quantity for each firm
Solution
Sure, let's solve these step by step.
i) Qd = 200 – 2P and Qs= - 20 + 2P
At equilibrium, quantity demanded (Qd) equals quantity supplied (Qs). So, we set the two equations equal to each other:
200 - 2P = -20 + 2P
Solving for P, we get:
4P = 220
P = 55
Substitute P = 55 into either the demand or supply equation to find the equilibrium quantity (Q). Let's use the demand equation:
Qd = 200 - 2*55 = 90
So, the equilibrium price is 55 and the equilibrium quantity is 90 for the first firm.
ii) Qd = 51 – 3P and Qs = -4 +8P
Again, at equilibrium, Qd = Qs. So, we set the two equations equal to each other:
51 - 3P = -4 + 8P
Solving for P, we get:
11P = 55
P = 5
Substitute P = 5 into either the demand or supply equation to find the equilibrium quantity (Q). Let's use the demand equation:
Qd = 51 - 3*5 = 36
So, the equilibrium price is 5 and the equilibrium quantity is 36 for the second firm.
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