Positive Externality

The market for jelly has a supply and demand given by the following:

Q_D=200-10p

Q_S=20p-100

The consumption of jelly creates a positive externality with marginal external benefit of:

MEB = 20-0.025Q

1. Find the competitive equilibrium price and quantity.
2. Find the CS, PS, and Total External Benefit.
3. What is the efficient output
4. What is the deadweight loss?
5. Suppose a subsidy is used to eliminate the inefficiency from the externality. What subsidy would lead to the efficient output?
6. With the subsidy, find the price consumers pay and price sellers get.
7. What is the PS, CS, Government expenditure, and Total external benefit with the subsidy?
8. Show that the deadweight loss matches the difference in welfare between (b) and (g).

PLEASE HELP ME EXPLAIN STEP BY STEP WHY THEY HAVE ANSWER LIKE THIS

a) P=10, Q=100 (b) CS=500, PS=250, TEB=1875 (c) First compute the inverse supply (PMC=SMC) and demand (PMB): PMB=20-0.05Q (inverse demand) PMC=SMC=5+0.2Q Add PMB+MEB=SMB: SMB = 40-0.075Q Efficiency is where SMB=SMC: Q=200 (d) DWL=875

(e) Sub=15 (f) Pc=0 Ps=15 (g) PS=1000, CS=2000, Govt spending = 3000, TEB=35009 (h) Before: CS+PS+TEB=2625 With sub: CS+PS-GE+TEB=3500 Difference = DWL = 875