3. Given the following market model, determine the equilibrium price, equilibrium quantity, consumer's surplus, and producer's surplus. Qd=26-2P Qs6+6P?

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied:

26-2P = 6+6P
20 = 8P
P = 2.5

Now that we have the equilibrium price, we can plug it back into either the demand or supply equation to find the equilibrium quantity:

Qd = 26-2(2.5)
Qd = 26-5
Qd = 21

Now that we have the equilibrium price and quantity, we can calculate the consumer's surplus and producer's surplus.

Consumer's Surplus:
Consumer's surplus is the area between the demand curve and the price line up to the equilibrium quantity. To calculate it, we need to find the area of the triangle formed by the demand curve, the price line, and the quantity axis.

Consumer's Surplus = (1/2) * (2.5) * (21)
Consumer's Surplus = 26.25

Producer's Surplus:
Producer's surplus is the area between the supply curve and the price line down to the equilibrium quantity. To calculate it, we need to find the area of the triangle formed by the supply curve, the price line, and the quantity axis.

Producer's Surplus = (1/2) * (2.5) * (21)
Producer's Surplus = 26.25

Therefore, the equilibrium price is $2.5, the equilibrium quantity is 21 units, the consumer's surplus is $26.25, and the producer's surplus is $26.25.

Equilibrium Price and Quantity:

To find the equilibrium price and quantity, we set Qd (quantity demanded) equal to Qs (quantity supplied) and solve for P:

26 - 2P = 6 + 6P
8P = 20
P = 2.5

Substituting P = 2.5 back into either Qd or Qs gives us the equilibrium quantity:

Qd = 26 - 2(2.5) = 21
Q = 21

Consumer's Surplus:

Consumer's surplus is the difference between the maximum price consumers are willing to pay (willingness to pay) and the actual price they pay. To calculate consumer's surplus, we create a demand curve by plotting Qd against P.

P | Qd
------- | -------
0 | 26
1 | 24
2 | 22
2.5 | 21
3 | 20
4 | 18

Consumer's surplus is the area below the demand curve and above the equilibrium price. It is a triangle with a base of 2.5 and a height of 21 - 2.5 = 18.5.

Consumer's Surplus = 1/2 - 2.5 - 18.5 = 22.875

Producer's Surplus:

Producer's surplus is the difference between the minimum price producers are willing to accept (willingness to accept) and the actual price they receive. To calculate producer's surplus, we create a supply curve by plotting Qs against P.

P | Qs
------- | -------
0 | 6
1 | 12
2 | 18
2.5 | 21
3 | 24
4 | 30

Producer's surplus is the area above the supply curve and below the equilibrium price. It is a triangle with a base of 2.5 and a height of 21 - 6 = 15.

Producer's Surplus = 1/2 - 2.5 - 15 = 18.75