Term 2 Week 9: Monopoly and Competitive Markets

Question 1

When does a firm have market power, and what are some extreme cases (1,2)

Answer 1

-A firm has market power when they have the ability to affect market price

Extreme cases include:
-A monopoly (single seller in a market)
-A monopsony (single buyer in a market)

Question 2

What is the traditional image of a monopolist, and does it apply in real life (3,1)

Answer 2

-The traditional image of a monopolist is a firm in an industry with large fixed costs
-Large infrastructure costs, such as power and telecoms, give way to natural monopolies, where only a large-scale producer can drive average costs down enough where LRAC<price
-It is more efficient in these industries to only have one producer

-However, the most valuable firms in the world don’t neccessarily align with this picture (5 of the biggest 6 firms are tech)

Question 3

What is a platform (3)

Answer 3

-A platform brings together different parties (buyers and sellers)
-Such platforms experience strong network effects (where new users increase the surplus for current users(more people on youtube = more views = more money = more people who want to make videos)
-Platforms like facebook, uber and airbnb also encounter lock-in (an arrangement where a person/company is obliged to deal only with a specific company)

Question 4

Why do monopolies exist (2)

Answer 4

-Monopolies exist due to barriers to entry
-This is because positive profits would draw the attention of competitors

Question 5

What are different types of barriers to entry (4,2)

Answer 5

Technical barriers:
-Strong increasing returns to scale
-Network effects
-Access to specific raw materials
-Tacit expertise/learning-by-doing

Legal Barriers:
-Patents and trademarks
-Government licences

Question 6

How may monopolists create extra barriers to entry (3)

Answer 6

-Maintaining company secrecy
-Buying unique resources
-Engaging in lobbying

Question 7

How can we represent revenue maximisation on a diagram (3)

Answer 7

-Draw a D=AR curve, with Q on the x axis and P on the y axis
-Then draw an MR curve, where the slope is twice as steep as linear demand
-Revenue is maximised where MR = 0

Question 8

How can we diagramatically represent profit maximisation (3)

Answer 8

-Draw a diagram with the AR, MR, MC and AC curve (classic a level)
-Profit maximisation is the q* where MR = MC
-From this q* , profit is the area between this quantity and 0, and AR and AC and this quantity level

Question 9

How can we represent profit maximisation with the FOC’s (4)

Answer 9

-Remember π(Q) = Qp(Q) - c(Q)
-dπ(Q)/dQ = p(Q) + Q(dp/dQ) - dc/dQ = 0
-p(Q) + Q(dp/dQ) = MR, dc/dq = marginal cost
-We want to find Q* such that MR = MC

Question 10

How can we work out elasticities from the profit max FOC’s (3,3)

Answer 10

-Remember p(Q) + Q(dp/dQ) - dc/dQ = 0
-p - c’ = -Q(dp/dQ)
-(p-c’)/p = -(Q/p)(dp/dQ) = 1/|ε|

-c’ is sometimes called the monopolist markup
-Price cost margin (markup) at the optimum is the inverse of the price elasticity of demand
-If demand is elastic, there wil be a very small profit margin

Question 11

How to diagramatically represent how monopolists lead to DWL (1,4,2)

Answer 11

-Draw a diagram with Q on the x axis, P on the y axis, both AR and MR, and then graph c’(Q), upward linear sloping from the origin

-Marginal social benefit of an extra unit of output is p(Q) = AR
-Marginal social cost of an extra unit = c’(Q)
-Social optimum is at Q** , where p(Q) = c’(Q)
-However, production occurs at Q* < Q**, as this is where MR = c’(Q)

-This leads to producer surplus of the area above c’(Q) below price and to the left of Q* , CS of the area below p(Q), above price and to the left of Q*
-This created DWL of the triangle trapped by p(Q) and c’(Q), in the distance from Q* to Q**

Question 12

How does elasticity impact DWL in a monopoly (1)

Answer 12

The more inelastic the market, the higher the DWL (output reduced by more)

Question 13

How does first degree price discrimination impact surplus in a monopoly (2)

Answer 13

-If a monopoly is able to price differently for every consumer, they can eliminate consumer surplus
-Picturing this on a MC = AR diagram, PS takes the whole area inside the diagram as opposed to only below the price

Question 14

What is a coase conjecture + diagram (3,3)

Answer 14

-A coase conjecture explores durable goods (lasts over time), where a monopolist has a large number (𝑞ത) of identical plots of land, where price p* maximises revenue
-Having sold q* , the monopolist faces the problem where 𝑞ത - q* plots remain, and more could be sold at price p’ < p* , but then earlier buyers could delay purchase, knowing the price will later be reduced
-Coase’s conjecture is as t -> ∞, a durable goods monopolist will price at p^c = 0 = MC, as buyers know future prices will fall

-Draw a diagram with q on the x axis, P on the y axis
-Have a downward sloping linear AR curve, and MR curve, and MC horizontal at p = 0 = p^c
-At q* , draw a new MR curve starting at that point of the AR curve, then where this = 0 is the p’

Question 15

What is a zero price monopolist + diagram (3,3)

Answer 15

-A zero price monopolist is where they do not charge a price for their product (google, youtube)
-These products often have a very low, or even 0 MC, where the firms may benefit per user gained (any costs offset by adverts)
-They typically want the largest Q possible to leverage EOS, hence p* = 0, and there is maximum CS

-q on the x axis, p on the y axis, and a normal AR and MR curve
-Draw MC constantly horizontal below p* = 0
-Draw AC starting on a positive y intercept and convexly decreasing, tending to AC = MC

Question 16

What are the 4 main assumptions of perfect competition (4)

Answer 16

-Many small buyers and sellers (no price setting power)
-Undifferentiated products (perfect substitutes)
-Perfect information about prices
-Equal access to resources and production technology

Question 17

Why can perfect competition be an important theory, and what are the main features of this theory (2,3)

Answer 17

Despite not being realistic, perfect competition can be an important theory as:
-It can be an approximation to some markets
-It can be a benchmark case

The main features are:
-Firms are price takers
-Transactions occur at a single market price
-There is free entry

Question 18

What is the slope of a demand function related to (1,3)

Answer 18

-The slope of a demand function is related to the elasticity of demand for a product at price p and output Q

The elasticity of demand depends on a number of factors:
-Preferences
-Necessity
-Availability

Question 19

How can we draw a firms demand and market supply/demand in perfect competition (1,2,2)

Answer 19

-Draw 2 diagrams next to eachother, with Q on the x axis and P on the y axis

-On the first diagram, draw a horizontal line for the firms demand
-This is because firms are price takers, and any price above competitors receives 0 demand

-On the second diagram, just draw a normal market supply and demand diagram
-The firms demand is the same price as market equilibrium

Question 20

How can we diagramatically represent how firms make 0 long term profit in perfect competition (3)

Answer 20

-Draw a diagram, with Q on the x axis, P on the y axis, A linear upward sloping MC curve, an AC curve, and a horizontal P = AR = MR curve
-Profit is the gap between AC and AR at q* (MR = MC), if there is profit new firms will enter the market
-This shifts each firms AR curve down, until the P = AR = MR curve is tangential to MC = AC, and hence profit is 0

Question 21

What do we assume in monopolistic competition (5)

Answer 21

-Firms can control prices
-Perfect information
-Large number of buyers and sellers
-No technological barriers to entry
-Imperfect substitutes exist

Question 22

What is the Dixit-Stiglitz model (3)

Answer 22

-It is a mathematical model of monopolistic competition
-It is a non-strategic model, widely used in trade, urban, industrial and growth economics
-This determines how much product variety is provided in equilibrium, looking at what determines the number of products in monopolistic competition

Question 23

What is the constant elasticity of substitution utility function in the Dixit-Stiglitz model (1,4)

Answer 23

-u = (∑^vx_i^(σ-1/σ))^(σ/σ-1)

-v is the number of possible varieties in the market (different types of toothpaste)
-There are N consumers, each with income m and CES utility function u
-x_i is the demand for good x with variety i
-σ measures how substitutable the goods are in the market, the elasticity of substitution (how does the % change in p_i/p_j impact the % change in q_i/q_j)

Question 24

What are some different σ values in the DS model (3,1)

Answer 24

-Perfect complements: σ -> 0
-Cobb-Douglas: σ -> 1
-Perfect substitutes: σ -> ∞

-DS assumes σ > 1 (elastic products)

Question 25

How can we rearrange the utility function in the DS model (5)

Answer 25

-u = (∑^vx_i^(σ-1/σ))^(σ/σ-1) -We want to maximise the utility function for each of the consumers -u^(σ-1)/σ = (∑^vx_i^(σ-1/σ)) -L = (∑^vx_i^(σ-1/σ)) - λ(∑^vp_ix_i - m) -This lagrangian represents the sum of all the expenditures - income

Question 26

How can we find the FOC's from the lagrangian in the DS model (1,2,2,2)

Answer 26

-L = (∑^vx_i^(σ-1/σ)) - λ(∑^vp_ix_i - m) -∂L/∂x_i = (σ-1/σ)_i^-1/σ - λp_i = 0 -∂L/∂x_j = (σ-1/σ)_j^-1/σ - λp_j = 0 Rearrange the two equations: -(σ-1/σ)_i^-1/σ = λp_i -(σ-1/σ)_j^-1/σ = λp_j Take the ratio: -(x_i/x_j)^-1/σ = p_i/p_j -x_j = x_i(p_i/p_j)^σ

Question 27

What can we take from the ratio of demands for goods in the DS model (1,3,1)

Answer 27

-Ratio: x_j = x_i(p_i/p_j)^σ -The demand for good j exceeds demand for good i if p_i > p_j -The extent of the difference in demand is scaled by σ (substitutability) -If these goods were close to perfect, a difference in price would make more of a difference -Note by rearranging, dln(x_i/x_j)/dln(p_i/p_j) = -σ -Hence, the constant elasticity of substitution

Question 28

How can we sub the ratio of goods in the DS model into the budget constraint, to get our demand for product i ()

Answer 28

-x_j = x_i(p_i/p_j)^σ -p_jx_j = p^σ_ix_ip^1-σ_j The budget constraint says that: -m = Σ^v_k=1 p_kx_k = p^σ_ix_iΣ^v_k=1p^1-σ_k Solving this equation for x_i then gives us the demand function: -x_i(p_i) = demand for product i = (m/(Σ^v_k=1p^-(σ-1)_k))p^-σ_i -Here, (Σ^v_k=1p^-(σ-1)_k) is a weighted average of prices -It measures the cost of the composite good in this market, and hence can be thought as an index of prices Therefore, -x_i = (m/p)(1/p^σ_i)

Question 29

What are the features of the demand function in the DS model (1, 4)

Answer 29

-Demand = -x_i = (m/p)(1/p^σ_i) -Demand decreases with p_i, moreso if products are close substitutes -Hence, 1/p^σ_i is a decreasing function -As σ -> 1, our expenditure is equal across all goods (cobb-douglas) -m/p is like a measure of real income

Question 30

What shifts curves outwards in the DS model (1,2)

Answer 30

-Draw convex curves with x_i on the x axis, and p_i on the y axis -If we increase income, our curves shift outwards -If there is an increase in other prices, these curves shift outwards

Question 31

How can we set up our profit function in the DS model, then maximise profit in regards to a price p_i (5,1)

Answer 31

-π_i = p_iQ(p_i) - cQ(p_i) - F -π_i = (p_i - c)(N((m/p)(1/p^σ_i)) - F -dπ_i/dp_i = N((m/p)(p^-σ_i) + (N(m/p)(-σ)(p^-σ-1_i))(p_i-c) = 0 -We ignore the effect of p_i on overall P, as each firm is small relative to the market -(1-σ)(1-(c/p_i)) = 0 -p_i = (σ/(σ-1))c

Question 32

What is the equation for the price of good i (p_i) which maximises profit in the DS model, and what can we tell from this (3)

Answer 32

-Since all goods have the same price p, P = Σ^v_i=1 p_i^1-σ = vp^1-σ -Subbing this into our optimal quantity for good x_i gives us: x_i = m(1/p)(p^1-σ/vp^1-σ) = m/vp -Plugging this into our indirect utility function gives us u(x* (p, m)) = (m/p)(1/(vσ - 1))

Question 33

What can we tell from our indirect utility function in the DS model (1,2)

Answer 33

-u(x* (p, m)) = (m/p)(1/(vσ - 1)) -Utility is increasing in v (consumers benefit the more variety there is) -The 'love of variety' decreases as σ gets large (the products become more similar and substitutable)

Question 34

How can we find the optimal variety of goods in the DS model (1,4,2)

Answer 34

-New firms will enter if positive profit is being made, but no more if the zero profit condition holds -D(p* )(p* - c) = F -(Nm/P)p^-σ(c/(σ-1)) = F -(Nm/vp^1-σ)p^-σ(c/(σ-1)) = F -(Nm/F)p^-σ = demand, (c/(σ-1) = price Solving for v: -v = (Nm/F)(c/p)(1/(σ-1)) -v = (Nm/F)(1/σ)

Question 35

How can we interpret the formula for optimal variety in the DS model (1,3)

Answer 35

-v = (Nm/F)(1/σ) There is more variety (high v) when: -Low fixed cost (F low) -Market is valuable (Nm high) -Products are weak substitutes (σ low)

Question 36

How to draw equilibrium in the DS model (3)

Answer 36

-Draw a graph with Q on the x axis, P on the y axis -Draw 2 convexly decreasing curves, one AC and one D = AR -Equilibrium is where the 2 are tangential to one another (D = AR above AC for all else)