Given a demand fxn of 20-2P and a supply fxn of -4+P for a perf. competitive market:

1. Calculate the equilibrium price and qty. (I got e. price = 4 and e. qty = 8 is that right?)
2. Calculate producer surplus, consumer surplus. (i got 8 and 4)
3. if the market becomes a monopoly that charges $ 15, what is:
a. the loss in consumer surplus
b. additional profit of the monopolist
c. deadweight loss this part

i don't understand do i compute for a new equilibrium price (7) and qty (3)?

To answer your questions:

1. To find the equilibrium price and quantity in a perfectly competitive market, we need to set the demand and supply functions equal to each other and solve for P (price).

Demand: Qd = 20 - 2P
Supply: Qs = -4 + P

Setting Qd equal to Qs, we have:
20 - 2P = -4 + P

Simplifying the equation:
3P = 24 -> P = 8

Now, substitute the equilibrium price (P) back into either the demand or supply equation to find the equilibrium quantity (Q):
Qs = -4 + 8 = 4

Therefore, the equilibrium price is $8 and the equilibrium quantity is 4. Your answer of an equilibrium price of $4 and equilibrium quantity of 8 is incorrect.

2. Consumer surplus is the difference between the price consumers are willing to pay and the price they actually pay. To calculate it, we need to find the area under the demand curve above the equilibrium price.

Consumer Surplus:
Consumer Surplus = 0.5 * (Qd - Qs) * (Pmax - P)
= 0.5 * (4 - 8) * (20 - 8)
= 0.5 * (-4) * (12)
= -24

Since the consumer surplus cannot be negative, it is zero in this case.

Producer surplus is the difference between the price suppliers receive and the price they are willing to accept. To calculate it, we need to find the area below the supply curve and above the equilibrium price.

Producer Surplus:
Producer Surplus = 0.5 * (Qs - Qd) * (P - Pmin)
= 0.5 * (4 - 0) * (8 - (-4))
= 0.5 * 4 * 12
= 24

Therefore, the consumer surplus is $0 and the producer surplus is $24.

3. If the market becomes a monopoly and charges a price of $15, we need to analyze the effects on consumer surplus, additional profit for the monopolist, and the deadweight loss.

a. The loss in consumer surplus can be calculated by determining the difference between the consumer surplus in a monopoly market and in a perfectly competitive market at the equilibrium price.

Consumer Surplus Loss:
Consumer Surplus Loss = (0.5 * (Qd - Qm) * (Pmax - Pm)) - (0.5 * (Qd - Qs) * (Pmax - Pe))
= (0.5 * (4 - 0) * (20 - 15)) - (0.5 * (4 - 8) * (20 - 8))
= (0.5 * 4 * 5) - (-12)
= 20 + 12
= $32

Therefore, the loss in consumer surplus is $32.

b. The additional profit of the monopolist can be calculated by determining the difference between the revenue earned in a monopoly market and in a perfectly competitive market at the equilibrium quantity.

Additional Profit of the Monopolist:
Additional Profit = (Pm - P) * Qm
= (15 - 8) * 4
= 7 * 4
= $28

Therefore, the additional profit for the monopolist is $28.

c. Deadweight loss occurs in a monopoly market when some potential gains from exchange are not realized due to the monopolist's ability to set a higher price and restrict output. In this case, the deadweight loss can be calculated by finding the triangle area between the monopoly quantity (Qm), the demand curve, and the supply curve at the equilibrium price.

Deadweight Loss:
Deadweight Loss = 0.5 * (Qd - Qm) * (P - Pm)
= 0.5 * (4 - 0) * (8 - 15)
= 0.5 * 4 * (-7)
= -14

Since deadweight loss cannot be negative, the deadweight loss is zero in this case.

You do not need to compute a new equilibrium price and quantity for the monopoly scenario.