CALCULATION 4 DEMAND AND SUPPLY FUNCTION FOR A COMMODITY ARE GIVEN QD=4P+30 AND QS=2P+6
To calculate the equilibrium price and quantity for a commodity, we need to determine the price at which the quantity demanded (QD) equals the quantity supplied (QS). In other words, we need to find the point where the demand and supply functions intersect.
Given:
QD = 4P + 30
QS = 2P + 6
To find the equilibrium price, we set QD equal to QS:
4P + 30 = 2P + 6
Simplifying the equation:
4P - 2P = 6 - 30
2P = -24
Dividing both sides by 2:
P = -24/2
P = -12
The equilibrium price is -12.
To find the equilibrium quantity, substitute the equilibrium price (-12) into either the demand or supply function:
QD = 4P + 30
QD = 4(-12) + 30
QD = -48 + 30
QD = -18
The equilibrium quantity is -18.
Please note that negative prices and quantities may not make practical sense in a real-world scenario, so this result should be interpreted with caution.
To analyze the demand and supply function for a commodity, we are given the following equations:
1. The demand function: QD = 4P + 30
2. The supply function: QS = 2P + 6
Here's how to interpret and calculate using these equations:
1. Demand Function (QD = 4P + 30):
The demand function represents the relationship between the price of a commodity (P) and the quantity demanded (QD). In this case, the equation suggests that for every unit increase in price, the quantity demanded will increase by 4 units. Additionally, there is a constant term of 30, which represents the quantity demanded when the price is zero.
2. Supply Function (QS = 2P + 6):
The supply function represents the relationship between the price of a commodity (P) and the quantity supplied (QS). Here, the equation indicates that for every unit increase in price, the quantity supplied will increase by 2 units. There is also a constant term of 6, which represents the quantity supplied when the price is zero.
To calculate specific values using these functions, here are a few examples:
Example 1: Determine the quantity demanded and supplied when the price is $10.
To find the quantity demanded (QD) at a price (P) of $10, we substitute P = 10 in the demand function:
QD = 4P + 30
QD = 4(10) + 30
QD = 40 + 30
QD = 70
Similarly, to find the quantity supplied (QS) at a price (P) of $10, we substitute P = 10 in the supply function:
QS = 2P + 6
QS = 2(10) + 6
QS = 20 + 6
QS = 26
Therefore, when the price is $10, the quantity demanded (QD) is 70 units, and the quantity supplied (QS) is 26 units.
Example 2: Find the equilibrium price and quantity.
In a market, equilibrium occurs when the quantity demanded (QD) matches the quantity supplied (QS).
To find the equilibrium price, we set QD equal to QS and solve for P:
QD = QS
4P + 30 = 2P + 6
4P - 2P = 6 - 30
2P = -24
P = -12
However, a negative price does not make sense in this context, so there is no equilibrium price in this case.
To find the equilibrium quantity, substitute the equilibrium price (P) into either the demand or supply function. Here, let's use the supply function:
QS = 2P + 6
QS = 2(-12) + 6
QS = -24 + 6
QS = -18
Again, a negative quantity does not make sense, so there is no equilibrium quantity in this case.
In conclusion, based on the given demand and supply functions, there is no equilibrium price and quantity for this commodity.