Lecture 10: Market Structure, Monopoly, Ordinary Price Discrimination (OPD), Isoprofit for Monopoly, and Tied Sales

Market Structure

Techniques - Isoprofit, short run, isoquant, long run

Functions - Codd-Douglas, quadratic & cubic, perfect sub & comp, hybrid

Markets - Perfect comp, monopoly, Oligopoly, monopolistic structures


a. definition

  1. Monopoly is a price maker
  2. One firm in industry
  3. There are no close subs

(U of T Business degree)

B. Types of Monopoly

  1. Natural-Large MES
  2. Franchise- created artificially government gives exclusion, geographic and time (patent)

C. Marginal Revenues

Marginal Revenues >> Marginal Cost & Marginal Revenue << Price

P=12QP= 12-Q, R=PQ=12QQ2R=PQ= 12Q-Q^{2}, MR=122QMR= 12-2Q

Why? MR << P because to sell an additional unit of output, you have to drop the price of all units.

The gap between P and MR depends on elasticity of demand. Why? If people are sensitive, E will be large, like -5.

00: P=P(Q)P= P\left ( Q \right ) ı=2Q2PPQ1N=212QQ\imath =\frac{2Q}{2P} \frac{P}{Q} \rightarrow \frac{1}{N}= \frac{21}{2Q}\cdot Q

R=P(Q)PR= P\left ( Q \right )-P

MR=P(Q)+P(Q)MR= P\left ( Q \right )+P\left ( Q \right )

=OPOQQ+P= \frac{OP}{OQ}-Q+P MR=P[1+12]MR=P\left [ 1+\frac{1}{2} \right ]

=P12+P=P\frac{1}{2}+P \therefore  if consumers are elastic (E=5)\left ( E=-5 \right ) ,

MR=0.8PMR= 0.8P (80% of price)

if consumers are less sensitive (E=12)\left ( E=-\frac{1}{2} \right )

MR=0.5PMR=0.5P  (50% of the price)

The gap is bigger when less elastic.

D. To MAx Profits

P=12QP=12-Q  C=Q2+4C=Q^{2}+4

i.) Q2:MR(Q2)=MC(Q2)Q^{2}: MR \left ( Q^{2} \right )=MC\left ( Q^{2} \right ) MR=122QMR=12-2Q MC=2QMC=2Q Q2=3Q^{2}=3

Why? Gap, last. If MR<MCMR< MC produce less. MR>MCMR>MC produce more

ii.) P2=P(Q2)P^{2}=P\left ( Q^{2} \right ) Max willing to pay P2=9P^{2}=9

iii) MCMC increasing or at win? Choose increasing part of MCMC

iv) Shut down LR:G<OLR: G< O SR:AVC SR: AVC

e. The efficiency loss


CS=(1282)4=S8CS=\left (\frac{12-8}{2} \right )4= S8 CS=(1292)3=S4.5CS= \left ( \frac{12-9}{2} \right )3= S4.5

PS=(82)4=S16PS= \left ( \frac{8}{2} \right )4=S16 PS=(96)3+(602)=S18PS=\left ( 9-6 \right )3+\left ( \frac{6-0}{2} \right )= S18

TS=24TS=24 TS=22.5TS=22.5

f. Per unit sub

a. Quota σ=4\sigma =4 won't work (regulation & info on MCMC

b. To calculate S2S^{2}  put QQ in demand,

get 8 (Q of comp) Put info MRMR ,

get 4, SOSO  S2=4S^{2}=4 SOSO  MC=2Q4=MRMC=2Q-4=MR

Problem: info about MCMC

cost of sub- Always bigger that E-loss

4x4=164x4=16  E-loss- 1.51.5

c. MCMC pricing law says PMC(Q)P\leq MC\left ( Q \right ) .Send to accountants. Works!

P=MLP=ML Q=4Q=4 Eloss=0E-loss=0

d. 2 part tariff- C & E. clubs, tuition


Total bill: 9.3+4.5=$31.59.3+4.5= \$ 31.5

CS=$832+8=40CS= \$ 8 32+8=40 Can increase revenue by ML=PML=P and Fee =CS=CS 

E-loss= 0, no info, no cost to government

Ordinary price discrimination: OPD (Third Degree)

Different prices for different groups of people.

  1. Exact same product
  2. No arbitrage
  3. Identification of group

C=Q2C=Q^{2} 1.) Aggregate Q=12PQ=12-P

Q1=712PQ_{1}=7-\frac{1}{2}P 2.) Invert P=12QP=12-Q

Q2=512PQ_{2}=5-\frac{1}{2}P MR=122QMR=12-2Q

3.) MR2MC=MRMR^{2} MC=MR  get Q2Q^{^{2}}

SOSO MR1=MR2MR_{1}=MR_{2}\Rightarrow  Key in OPD, must hold

4.) Plug MR2MR^{2} into each Market

MR1=P=10MR_{1}=P=10  Q=2Q=2 Π=19\Pi =19

MR2=8MR_{2}=8 Q=1Q=1

Isoprofit for Monopoly:

Previous: Slope is WP\frac{W}{P} , if the monopolist expands, they need to drop their price

SOSO slope is WMR\frac{W}{MR}

Tied Sales:

Increase price of ink till CS0CS_{0} CS1=36CS_{1}= 36 . Absorb the CSCS from Printer!

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