The demand function is given as QD = 40 – 2P

Question

The producer of a cosmetic product needs to decide the optimal price to charge and the optimal quantity to supply in the market. The demand function of the cosmetic product is given as QD = 40 – 2P, while the supply function of the cosmetic product is given as QS = 2P where P is price, QD is quantity demanded, and QS is quantity supplied.

Task: Solve the following:The demand function is given as QD = 40 – 2P
The supply function is given as QS = 2P
Calculate the equilibrium price and quantity.

Answer 1

First of all, you need to know what the equilibrium price and the equilibrium quantity are. The equilibrium price is the price at which the quantity demanded equals the quantity supplied. The equilibrium quantity is the quantity bought and sold at the equilibrium price.

 

Now looking at this problem, you are given the demand function Q^D=40 - 2P and the supply function Q^S=2P. In order to find the equilibrium price (P_e ), we need: quantity demanded = quantity supplied, namely, Q^D=Q^S ;

so we have the following : 40 - 2P = 2P, and solve for P, we get P_e = 10 (units), then we plug P_e=10 into either Q^D or Q^S to find the equilibrium quantity (Q_e) : Q_e=40 - 2x10=20 (units). 

Done. Hope it helps.