Suppose the demand equation is given by P=12-2Q and the supply equation is given by P=2+3Q. If the quota quantity is set at Q=1, what is the price that this unit will sell for?
To determine the price at which the unit will sell for with a quota quantity of Q=1, we need to find the intersection point of the demand and supply equations.
Given:
Demand equation: P = 12 - 2Q
Supply equation: P = 2 + 3Q
1. Substitute Q=1 into both equations to find the corresponding price:
For the demand equation: P = 12 - 2 * 1 = 12 - 2 = 10
For the supply equation: P = 2 + 3 * 1 = 2 + 3 = 5
So, the price at which the unit will sell for with a quota quantity of Q=1 is $5.
To find the price that this unit will sell for, we need to find the equilibrium price where the demand and supply curves intersect.
Setting the demand equation and the supply equation equal to each other, we have:
12-2Q = 2+3Q
Moving all the Q terms to one side and all the constant terms to the other side, we get:
12-2 = 3Q + 2Q
Simplifying the equation further, we have:
10 = 5Q
Dividing both sides of the equation by 5, we get:
Q = 2
Now, substitute this value of Q back into either the demand or supply equation to find the price. Using the supply equation:
P = 2 + 3Q
P = 2 + 3(2)
P = 2 + 6
P = 8
Therefore, the price at which this unit will sell for is 8.
To find the price at which the unit will sell for, we need to find the intersection point of the demand and supply curves.
Given:
Demand equation: P = 12 - 2Q
Supply equation: P = 2 + 3Q
Quota quantity: Q = 1
To find the equilibrium price, we need to set the quantity demanded equal to the quantity supplied and solve for the price.
Quantity demanded = Quantity supplied
12 - 2Q = 2 + 3Q
First, let's solve for Q:
12 - 2Q = 2 + 3Q
12 - 2 - 3Q = 2Q
10 = 5Q
Q = 2
Now that we have Q = 2, we can substitute this value back into either the demand or supply equation to find the corresponding price. Let's substitute it into the supply equation:
P = 2 + 3Q
P = 2 + 3(2)
P = 2 + 6
P = 8
Therefore, the price at which the unit with the quota quantity of Q = 1 will sell for is $8.