ECO101 Lecture 12

ECO101 - Week 12 Monopoly.pdf

Franchise Monopoly

This is when government gives access to one firm to sell
$P = 60 - 2 Q$
$C = Q^{2} + 100$
Last
- $M R$ has the same vertical intercept, but twice as steep as demand curve
- $R = P Q$
- $60 q - 2 q^{2}$
- $M R = \frac{\differential R}{\differential Q} = 60 - 4 q$
- $A C = q + 100 q^{- 1}$
- $M C = 2 q$
- $\begin{array}{l} q & p & m r \\ 2 & 56 & 56 \\ 3 & 54 & 48 \\ 4 & 52 \end{array}$
- $M R < P$
  - The reason why you incur more costs, is because it costs more to sell the $3^{rd}$ unit of output. You need to drop the price by 2 dollars, so you lose $3 (2) = 6$ dollars.
Profit maximization
- $q : M C (Q) = M R (Q)$
- why?
  - If $M C < M R$
    - You should increase your quantity
  - $M C > M R$
    - Decrease your quantity
  - When $M C = M R$
    - We maximize profit
  - Gap between $R, C$
    - $π = R - C$
- Charge a price based on demand curve
  - $P = P (Q)$
  - This dictates the maximum consumers are willing to pay
  - $M R = M C$
  - $2 q = 60 - 4 q$
  - $q = 10$
Efficiency Loss
- Because it's not profit maximizing to produce socially optimal output.
- See that consumer surplus goes down to just the area above profit
- Producer surplus is better because price is higher but quantity is lower
- The top half of eloss is consumer surplus loss, bottom is producer loss
- $\frac{b h}{2} = \frac{(20) (5)}{2} = 50$
Use a subsidy to fix the eloss
- $s^{*} : M C - S = M R \to Q^{*} = 15$
- We want to have a subsidy which shifts everything to the point where it's socially optimal.
- $2 q - s = 60 - 4 q$
- $s = 6 q - 60$
- At $q = 15$
- $s = 6 (15) - 60 = 30$
- Spending 450 dollars to fix a 50 dollar problem, isn't the best idea.
Two part tariff
- Example, tuition $P_{1}$ fee
- For tuition, you pay the price, and fee
- CNE
  - Price to get in, and price per ride
- Wonderland is a counterexample, you only pay a one time fee
- They want to drop the price as low as they can, to increase consumer surplus and charge a bigger fee
- Fee:
  - $\frac{b h}{2} = \frac{(15) (60 - 30)}{2} = 225$
- $π = (P - A C) q + Fee$
- $π = \frac{b h}{2} = \frac{(60) (15)}{2} = 450$
- This is efficient, because there is no eloss now. It's the socially optimal point.
- But $C S = 0$ , because now it's just fees.

Natural Monopoly

$P = 200 - Q$
$C = 6400$
This happens when there's only room for one firm
- Examples:
  - Basketball
  - Only room for one team in toronto
  - Raptors are natural monopoly
  - If there was another team, both teams would go bankrupt
  - $M E S$ is large
$A C = 6400 q^{- 1}$
- Minimum efficient scale is $\infty$
- $A C$ continue to decline
- $MR=MC$ - $MC=0$ - $0=200-2q$ - $q = 100$ - $p=200-q=100$ - $\frac{bh}{2}=\frac{(200-100)(100)}{2} = 5000$ - To eliminate the eloss - $MC$ pricing - The price charged by the firm, is not allowed to exceed $p\leq MC$ - So basically we have our demand is now $MC$
$P = M C$
- Most firms don't understand the idea of marginal cost
  - Example: Beaver Tails
  - You ask a business to not exceed $p \leq M C$ .
  - They won't know their $M C$
- Info
  - Example:
  - The only people who know $M C$ are the owners.
  - They can inflate their $M C$ to receive a big subsidy
- $π < 0$
  - If $p = M C$
  - then $p = 0$
  - Since $C > 0$
  - They're gonna shutdown
$A C$ pricing law
- $P \leq A C$
- You're not allowed to sell higher than average costs
- This is understandable,
  - The business knows their AC
- Info
  - They may still inflate their average costs
- $π = 0$
  - Fair, when economic profits are $0$
- Examples:
  - Parking
    - Total costs for parking services
    - Parking spaces available
    - This is the price

Ordinary Price Discrimination

$C = 0.025 q^{2}$
$D_{p} = 60 - 20 p$
$D_{s} = 100 - 20 p$
Ordinary Price Discrimination
- Charge different groups of customers different prices
- Example:
  - Country Doctor
  - Tuition International vs Domestic
    - International: Elasticity of demand is small, so they can't really switch easily.
      - Give these guys a big price increase, small reduction in quantity
      - Meaning more revenue
    - Local: Elasticity of demand is pretty big, so they'll switch
      - Drop the price, huge increase in quantity, more revenue.
  - Movie Theater cheap on tuesdays
- For Price Discrimination, we need the same product / service, identity the customer differently and rule out arbitrage.
  - Someone taking your cheap thing then selling it again expensively.
  - Arbitrage would collapse the arbitrage down to nothing.
- We get the $π = R - C$ is higher, since the costs are the same, but the revenues go higher.
- Can happens over time
To solve
- Agg ignore
  - Aggregate the demand curve, ignore which gorup they're from
  - $q = 160 - 40 p$
  - $p = 4 - \frac{1}{40} q$
  - $M R = 4 - \frac{1}{20} q$
  - $M C = \frac{1}{20} q$
  - $Q = 4 - \frac{1}{20} Q = \frac{1}{20} q$
  - $4 = \frac{2}{20} q$
  - $q = 40$
  - $M C (40) = 2$
- $M C = 2$ , allocate sales between the two demand curves
  - Profs
    - $P_{p} = 3 - \frac{1}{20} q$
    - $M R_{p} = 3 - \frac{1}{10} q$
    - $2 = 3 - \frac{1}{10} q$
    - $q = 10$
    - $P_{p} (10) = 3 - \frac{1}{20} (10) = \frac{5}{2} = 2.5$
  - Students
    - $P_{s} = 5 - \frac{1}{20} q$
    - $M R_{S} = 5 - \frac{1}{10} q$
    - $2 = 5 - \frac{1}{10} q$
    - $q = 30$
    - $P_{s} (30) = 5 - \frac{1}{30} (30) = 3.50$
- Profits will be higher?
  - without Price Discrimination
    - $q = 40$
    - $a c = 0.025 q$
    - $a c (40) = 0.025 (40) = 1.0$
    - Profits
      - $P (40) = 4 - \frac{1}{40} (40) = 3$
      - $π = (3 - 1) 40 = 80$
  - with Price Discrimination
    - $A C = 1$
    - profits
      - $π (2.50 - 1) (10) + (3.50 - 1) (30) = 10 π (1.5) + 75.0 = 122.123889803847$
- Key idea is that $M R_{1} = M C$ and $M R_{2} = M C$
  - This equalizes the curves for each market
  - If $M R_{B} = 10$ in brampton and $M R_{M} = 3$ in mississauga
  - Sell more in brampton and sell less in mississauga until $M R$ are the same for both
  - So $1$ unit sold will give the same revenues anyways

Perfect Price Discrimination

$P = 12 - q$
$C = q^{2}$
Not based on groups of people, but per person, charge their reservation price.
Example:
- Cellular Data
  - Literally everyone gets a different price based on credits, usage, etc.
  - Big price elasticity of demand will call their isp, and ask for a lower price, then switch.
  - This means $C S = 0$
- Producer surplus is total surplus
- No eloss
- Two part tariff and perfect Price Discrimination Equilibrium are the exact same.
- But the methods are different.
- Ideas
  - Types of customers
    - Homogeneous
      - Then perfect Price Discrimination will fail, when the customers have the exact same elasticity
    - Heterogeneous
      - Perfect Price Discrimination will be effective.
  - Sales
    - You require a lot of sales to find the best price for each person.
  - Number of customers
    - Trying to negotiate the best price for every single customer for a lot, won't work too much.
- Two part tariffs would work better
  - Price, then fee
- If you have less customers, then perfect Price Discrimination would work better.
Tied Sales
- Like a cross-sale.
- The consumer surplus is taken away with the secondary sale, by inflating price by cs.
- Walled garden

All or Nothing Demand

$p = 12 - q$
$C = q^{2}$
$\bar{p} = 8$
$\bar{q} = 6$
Tie in sales, because primary market gives you $C S = 8$ , but $C S = - 2$ in the secondary market.
We can have monopoly can be a sort of market imperfection / failure.