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

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

26 - 2P = -6 + 6P
32 = 8P
P = 4

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

Qd = 26 - 2(4)
Qd = 26 - 8
Qd = 18

Now we can calculate the consumer's surplus by finding the area of the triangle below the demand curve and above the price line:

Consumer's Surplus = (1/2) * (4) * (18)
Consumer's Surplus = 36

To find the producer's surplus, we calculate the area of the triangle above the supply curve and below the price line:

Producer's Surplus = (1/2) * (4) * (18)
Producer's Surplus = 36

Therefore, the equilibrium price is $4, the equilibrium quantity is 18 units, the consumer's surplus is $36, and the producer's surplus is $36.

1. Equilibrium Price and Quantity

To find the equilibrium price and quantity, we set Qd = Qs and solve for P:

```
26 - 2P = -6 + 6P
8P = 32
P = 4
```

Substituting P = 4 back into either equation:

```
Qd = 26 - 2(4) = 18
Qs = -6 + 6(4) = 18
```

Therefore, the equilibrium price is $4 and the equilibrium quantity is 18 units.

2. Consumer's Surplus

Consumer's surplus is the difference between the maximum price consumers are willing to pay (willingness to pay) and the equilibrium price:

```
Consumer's Surplus = ∫(WTP - P) dQ
```

Using the demand curve, WTP = 26 - 2Q:

```
Consumer's Surplus = ∫(26 - 2Q - 4) dQ
= ∫(22 - 2Q) dQ
= 22Q - Q^2 + C
```

Evaluating the integral from Q = 0 to Q = 18:

```
Consumer's Surplus = 22(18) - 18^2
= 396 - 324
= 72
```

3. Producer's Surplus

Producer's surplus is the difference between the equilibrium price and the minimum price producers are willing to accept (supply price):

```
Producer's Surplus = ∫(P - SP) dQ
```

Using the supply curve, SP = -6 + 6Q:

```
Producer's Surplus = ∫(4 - (-6 + 6Q)) dQ
= ∫(10 - 6Q) dQ
= 10Q - 3Q^2 + C
```

Evaluating the integral from Q = 0 to Q = 18:

```
Producer's Surplus = 10(18) - 3(18)^2
= 180 - 972
= -892
```

Note: The producer's surplus is negative, indicating that producers are making losses at the equilibrium price. This is because the supply curve is linear and slopes upward, implying increasing marginal costs.