# 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

### Monopoly

#### a. definition

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

#### 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

﻿$P= 12-Q$﻿, ﻿$R=PQ= 12Q-Q^{2}$﻿, ﻿$MR= 12-2Q$﻿

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: ﻿$P= P\left ( Q \right )$﻿ ﻿$\imath =\frac{2Q}{2P} \frac{P}{Q} \rightarrow \frac{1}{N}= \frac{21}{2Q}\cdot Q$﻿

﻿$R= P\left ( Q \right )-P$﻿

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

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

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

﻿$MR= 0.8P$﻿ (80% of price)

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

﻿$MR=0.5P$﻿ (50% of the price)

The gap is bigger when less elastic.

### ﻿$P=12-Q$﻿﻿$C=Q^{2}+4$﻿

i.) ﻿$Q^{2}: MR \left ( Q^{2} \right )=MC\left ( Q^{2} \right )$﻿ ﻿$MR=12-2Q$﻿ ﻿$MC=2Q$﻿ ﻿$Q^{2}=3$﻿

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

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

iii) ﻿$MC$﻿ increasing or at win? Choose increasing part of ﻿$MC$﻿

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

#### e. The efficiency loss

At ﻿$MC =P AS=CS=PS$﻿ At ﻿$MC=MR$﻿

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

﻿$PS= \left ( \frac{8}{2} \right )4=S16$﻿ ﻿$PS=\left ( 9-6 \right )3+\left ( \frac{6-0}{2} \right )= S18$﻿

﻿$TS=24$﻿ ﻿$TS=22.5$﻿

#### f. Per unit sub

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

b. To calculate ﻿$S^{2}$﻿ put ﻿$Q$﻿ in demand,

get 8 (Q of comp) Put info ﻿$MR$﻿ ,

get 4, ﻿$SO$﻿ ﻿$S^{2}=4$﻿ ﻿$SO$﻿ ﻿$MC=2Q-4=MR$﻿

Problem: info about ﻿$MC$﻿

cost of sub- Always bigger that E-loss

﻿$4x4=16$﻿ E-loss- ﻿$1.5$﻿

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

﻿$P=ML$﻿ ﻿$Q=4$﻿ ﻿$E-loss=0$﻿

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

Fee﻿$=CS=4.5$﻿

Total bill: ﻿$9.3+4.5= \ 31.5$﻿

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

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

﻿$C=Q^{2}$﻿ 1.) Aggregate ﻿$Q=12-P$﻿

﻿$Q_{1}=7-\frac{1}{2}P$﻿ 2.) Invert ﻿$P=12-Q$﻿

﻿$Q_{2}=5-\frac{1}{2}P$﻿ ﻿$MR=12-2Q$﻿

3.) ﻿$MR^{2} MC=MR$﻿ get ﻿$Q^{^{2}}$﻿

﻿$SO$﻿ ﻿$MR_{1}=MR_{2}\Rightarrow$﻿ Key in OPD, must hold

4.) Plug ﻿$MR^{2}$﻿ into each Market

﻿$MR_{1}=P=10$﻿ ﻿$Q=2$﻿ ﻿$\Pi =19$﻿

﻿$MR_{2}=8$﻿ ﻿$Q=1$﻿

### Isoprofit for Monopoly:

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

﻿$SO$﻿ slope is ﻿$\frac{W}{MR}$﻿

#### Tied Sales:

Increase price of ink till ﻿$CS_{0}$﻿ ﻿$CS_{1}= 36$﻿ . Absorb the ﻿$CS$﻿ from Printer!