The weekly demand and supply functions for Sportsman 5 X 7 tents are given by the following respective functions where p is measured in dollars and x is measured in units of a hundred.
Find the equilibrium quantity.
Find the equilibrium price.
Demand: p = 100 - 0.5x
Supply: p = 10 + 0.2x
Equilibrium quantity: x = 400
Equilibrium price: p = 50
To find the equilibrium quantity and price, we need to set the demand and supply functions equal to each other.
The demand function for Sportsman 5 X 7 tents is given as:
Qd = 520 - 6p
Qd represents the quantity demanded in hundreds of units and p represents the price in dollars.
The supply function for Sportsman 5 X 7 tents is given as:
Qs = -60 + 4p
Qs represents the quantity supplied in hundreds of units and p represents the price in dollars.
To find the equilibrium quantity, we set Qd equal to Qs:
Qd = Qs
520 - 6p = -60 + 4p
Simplifying this equation, we get:
10p = 580
Dividing both sides of the equation by 10, we get:
p = 58
So, the equilibrium price is $58.
To find the equilibrium quantity, we substitute the equilibrium price into either the demand or supply function. Let's use the demand function:
Qd = 520 - 6(58)
Qd = 520 - 348
Qd = 172
Therefore, the equilibrium quantity is 172 hundred units (or 17,200 units).
To find the equilibrium quantity and price, we need to set the demand and supply functions equal to each other and solve for x.
The demand function represents the quantity that consumers are willing to buy at a given price, while the supply function represents the quantity that producers are willing to sell at a given price.
Let's denote the demand function as D(p) and the supply function as S(p).
D(p) = 600 - 2p
S(p) = 200 + 3p
Equilibrium occurs when the quantity demanded equals the quantity supplied, so we can set D(p) equal to S(p):
600 - 2p = 200 + 3p
To find the equilibrium quantity, we need to solve this equation for x.
First, let's simplify the equation:
600 - 2p - 200 = 3p
Combine like terms:
400 - 2p = 3p
Now, let's isolate the variable p by moving the terms with p to one side:
400 = 5p
Divide both sides by 5:
p = 80
The equilibrium price is $80.
Now, to find the equilibrium quantity, we can substitute the value of p back into either the demand or supply function. Let's use the demand function:
D(p) = 600 - 2p
D(80) = 600 - 2(80)
D(80) = 600 - 160
D(80) = 440
The equilibrium quantity is 440 units of a hundred.