Question

A firm with market power faces the demand curve Q = 400 – P/4 and a marginal cost of MC = 2Q. Calculate the area of the deadweight loss triangle.

Answer #1

Answer

the firm produces at MR=MC

the inverse demand curve is

Q=400-P/4

Q+P/4=400

P/4=400-Q

P=1600-4Q

MR=1600-8Q ....... the MR curve is double sloped than the demand
curve

MC=2Q

equating both

1600-8Q=2Q

10Q=1600

Q=160

P=1600-4*160=960

MC=2*160=320

---

an efficient quantity is produced at MC=P

1600-4Q=2Q

6Q=1600

Q=1600/6=266.666667

---

DWL=0.5*(P-MC)*(efficient quantity-Q of monopoly)

=0.5*(960-320)*(266.666667-160)

=34133.3334

the DWL is $34133.3334

----

Part A
A demand curve is P = 10- Q. So its MR is
A)5-2Q
B)10- 4Q
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is
A)5-2Q
B)10- 4Q
C)10 - Q
D)5 - Q
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