The demand and supply functions of commodity x are given as follows: Qd = 20- 2p, Qs = 6p - 12 where p = price, Qd = quantity demanded and Qs = quantity sup...

The demand and supply functions of commodity x are given as follows: Qd = 20- 2p, Qs = 6p - 12 where p = price, Qd = quantity demanded and Qs = quantity supplied. Determine the equilibrium price

Answer Details

To find the equilibrium price, we need to find the price at which the quantity demanded (Qd) equals the quantity supplied (Qs). In other words, we need to find the price where the demand and supply curves intersect. The demand function is Qd = 20 - 2p, which means that as the price (p) increases, the quantity demanded (Qd) decreases. This is because consumers are generally willing to buy less of a product as its price goes up. On the other hand, the supply function is Qs = 6p - 12, which means that as the price (p) increases, the quantity supplied (Qs) also increases. This is because producers are generally willing to sell more of a product as its price goes up. Now, to find the equilibrium price, we need to set Qd equal to Qs and solve for p. That is: 20 - 2p = 6p - 12 Adding 2p to both sides, we get: 20 = 8p - 12 Adding 12 to both sides, we get: 32 = 8p Dividing both sides by 8, we get: p = 4 Therefore, the equilibrium price for commodity X is p = 4. At this price, the quantity demanded (Qd) equals the quantity supplied (Qs), which is: Qd = 20 - 2p = 20 - 2(4) = 12 Qs = 6p - 12 = 6(4) - 12 = 12 So, at the equilibrium price of 4, the quantity demanded and supplied for commodity X are both 12. In summary, the equilibrium price is the price at which the quantity demanded equals the quantity supplied. In this case, the equilibrium price for commodity X is 4, and at this price, the quantity demanded and supplied are both 12.