Review Questions X: Monopoly
1) For linear demand and a single price seller, find the total revenue function and graph that
function. Also, find the marginal revenue function and graph that function.
Inverse D
P = a-bQ
TR = P Q = Qa – bQ2
MR = dTR/dQ = a – 2bQ
MR
Q
TR
ED>1
ED = 1
slope = -2b
ED>1
ED<1
ED=1
Q
ED<1
2) For linear demand and a single price seller, what is the relationship between MR schedule
and the demand schedule?
Inverse D
MR
P = a-bQ
MR = a-2bQ
at each Q MR < P
and MR schedule declines at two times the rate of
the inverse demand schedule
3) For linear demand and a single price seller, what is the relationship between MR schedule
and the elasticity of demand?
MR = dTR/dQ
ED > 1
=
=P+Q
ED = 1
= P (1-
)
ED < 1
= P (1-
)
D
MR
Q
4) Using linear demand and standard u-shaped cost curves, illustrate the case of a single price
monopolist making zero economic profits. Is this the LR equilibrium prediction? Explain.
$
No. Zero economic profits is not
a LR prediction for a monopolist.
By definition, entry that would
lead to competition and zero profits
is not feasible.
MC
LRAC
P*
D
Q*
Q/t
MR
5) What is perfect price discrimination in a monopoly market? What information does it require
to be implemented? How does output with perfect price discrimination compare to the case
of a single price monopolist?
MC
Pricing each unit at limit price (or near the limit price).
Requires the firm to determine limit prices and prevent
resale.
in problem 4.
D=MR
6) What is meant by monopoly pricing with segmented markets? What conditions are necessary
for such pricing? How is optimal output and price determined in each market?
Model calls for segregating consumers into sub-markets based on ED.
Ex.
MC
P1
P2
D2
Market D
D1
MR1
horizontal
Mx = MR1+MR2
MR2
+
=