lectures in microeconomics-charles w. upton the monopolist’s demand curve

Lectures in Microeconomics-Charles W. Upton

The Monopolist’s Demand Curve



• Want to develop some key propositions about the demand curve




• Many of these center on elasticities




• Many of these center on elasticities

• Then some applications


Marginal Revenue and Elasticity

• Recall our definition of point elasticity

Q

PSlope




• In the case of a linear demand function

Q = a – bP

Q

PSlope




• In the case of a linear demand function

Q = a – bP

Q

PSlope

Slope = -b



• A more general definition

Q

P

dP

dQ


Restating the Elasticity

Q

P

dP

dQ



P

Q

dPdQ11

Q

P

dP

dQ



PP

Q

dPdQ

P

11

P

Q

dPdQ11



PP

Q

dPdQ

P

11

QdQ

dPP

1



• The Monopolist cares about MR.

• There is a relation between MR and elasticity.

R = PQ

PQdQ

dP

dQ

dR



• The Monopolist cares about MR.

• There is a relation between MR and elasticity.

R = PQPQ

dQ

dP

dQ

dR

PMRQdQ

dP



PQdQ

dPMR

PMRQdQ

dP



PP

Q

dQ

dPPMR

PQdQ

dPMR

PMRQdQ

dP



1P

Q

dQ

dPPMR

PP

Q

dQ

dPPMR

PQdQ

dPMRPMRQ

dQ

dP



PMRQdQ

dP

1P

Q

dQ

dPPMR

PP

Q

dQ

dPPMR

PQdQ

dPMR

)1

1()11

(

PPMR


First Elasticity Relation

11PMR


Second Elasticity Relation

11PMR



11PMR

MCMR



11PMR

MCMR

11PMC



MCP 11



11

MCP


Third Elasticity Relation

MCP 11



MCP 11

MCPP 1



MCPP 1

1PMCP



1PMCP

1

P

MCP



1

P

MCP


A Summary

11PMR

11

MCP

1

P

MCP

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