Please answer with detailed math 7 If the demand curve for w

Please answer with detailed math

7. If the demand curve for wheat in the United States is P = 12.4-QD where P is the farm price of wheat (in dollars per bushel) and Qn is the quantity of wheat demanded (in billions of bushels), and the supply curve for wheat in the United States is P =-2.6 + 20, where Qsis the quantity of wheat supplied (in billions of bushels), what is the equilibrium price of wheat? What is the equilibrium quantity of wheat sold? Must the actual price equal the equilibrium price? Why or why not?

Solution

The equilibrium quantity and price is found where demand and supply equals,
So it is found by finding price where Qd = Qs
12.4-P = (P+2.6)/2
24.8-2P = P+2.6
22.2 = 3P
P = 7.4
So now the equilibrium quantity is found by replacing P in any of the equation,
Qd = 12.4-7.4 = 5
Qs = (7.4+2.6)/2 = 5
If the market is perfect competition the actual price would be equilibrium price but if it faces any imperfect competition then the actual price would differ from equilibrium.