Question

Assume a private supply curve is given by P = 20+5Q. The corresponding demand curve is given by P = 200 -Q. As it turns out the supply is associated w/ an external cost of $20 per Q. What is the resulting Deadweight Loss??

Work please very confused!!!

Answer 1

We know that the Deadweigjt loss is the loss of the consumer surplus and the producer surplus due to increase in price or inclusion of external cost or imposition of tax, which is the area of triangle as shown below.

Deadweight loss = ar. triangle abe =1/2×ab×QQ1

At equilibrium, demand =supply or 20+5Q=200-Q or 6Q=180 or Q=180/6 =30

When Q=30, P= 20+5×30 =20+150 = 170.

When external cost is included P = 170+20 =190

When P = 190, Q1(from demand) will be 190=200-Q or Q= 200-190=10

When Q= 10, P2(from Supply) = 20 +5Q = 20+5×10 =20+50 =70

Dead weight loss = 1/2 × (P1-P2) × (Q-Q1) =1/2×120×20 =$1,200.