Chapter 10: Market Power – Monopoly & Monopsony (Microeconomics Study Notes)

Chapter 10: Market Power – Monopoly & Monopsony

10.1 Monopoly

A monopoly is a market structure in which a single firm is the sole supplier of a good or service with no close substitutes. This gives the firm significant control over price and output.

• Definition: A monopoly is the only supplier of a good for which there is no close substitute.

• Market Output: The monopolist's output is the market output, and the demand curve it faces is the market demand curve.

• Barriers to Entry: Entry is not possible; new firms cannot enter the market.

• Price Setting: Unlike a competitive firm, a monopolist can set its price.

• Profit Maximization: The monopolist chooses output (q) and price (P) to maximize profit.

Average Revenue and Marginal Revenue

Marginal revenue (MR) is the change in total revenue resulting from selling one additional unit of output.

• Relationship: For a linear demand curve, average revenue (AR) equals price, and marginal revenue is less than price for all positive quantities.

• Example Demand Curve: $P = 6 - Q$

Price (P)	Quantity (Q)	Total Revenue (R)	Marginal Revenue (MR)	Average Revenue (AR)
6	0	0	--	--
5	1	5	5	5
4	2	8	3	4
3	3	9	1	3
2	4	8	-1	2
1	5	5	-3	1

Marginal Revenue Curve and Demand Curve

• For all linear demand functions: $P(q) = a - bq$

• Total Revenue: $TR(q) = P imes q$

• Marginal Revenue: $MR(q) = a - 2bq$

• The MR curve starts at the same price as the demand curve but has twice the slope.

• The MR curve intersects the quantity axis at half the value of the demand curve.

Question 1 Example

• Market demand: $Q = 100 - 5P$

• Inverse demand: $P = 20 - 0.2Q$

• Marginal Revenue: $MR(Q) = 20 - 0.4Q$

The Monopolist’s Output Decision

The monopolist maximizes profit by producing the quantity where marginal revenue equals marginal cost ($MR = MC$).

• If $MR > MC$, increasing output increases profit.

• If $MR < MC$, decreasing output increases profit.

• Profit per unit is the difference between average revenue and average cost.

Example of Profit Maximization

• Given $TC(q) = 50 + q^2$, $MC(q) = 2q$, and $P = 40 - q$

• Set $MR = MC$: $40 - 2q = 2q$ $ightarrow$ $q^* = 10$

• Price: $P^* = 40 - 10 = 30$

• Economic profit: $TR - TC = 30 imes 10 - 50 - 100 = 150$

A Rule of Thumb for Pricing

• MR can be written in terms of elasticity of demand ($E_d$):

$MR = P + P \left( \frac{1}{E_d} \right)$

At profit maximization ($MR = MC$):

$P + P \left( \frac{1}{E_d} \right) = MC$

Rearranged:

$\frac{P - MC}{P} = -\frac{1}{E_d}$

Or, price as a markup over marginal cost:

$P = \frac{MC}{1 + (1/E_d)}$

Elasticity and Profit Maximization

• If demand is elastic, total revenue increases when price falls; MR is positive.

• If demand is inelastic, total revenue decreases when price falls; MR is negative.

• If demand is unitary elastic, MR is zero.

• Profit-maximizing price will never be in the inelastic part of the demand curve.

Shifts in Demand

• A monopolist has no supply curve; there is no one-to-one relationship between price and quantity produced.

• When demand shifts, the new MR curve may intersect MC at the same or a different point, affecting price and output.

The Effect of a Tax

• A specific tax per unit increases the firm's marginal cost by the amount of the tax.

• New profit-maximizing condition: $MR = MC + t$

• The increase in price may be larger than the tax itself.

The Multiplant Firm

When a firm operates multiple plants, it must allocate output to maximize profit.

• Let $Q_1$, $Q_2$ be outputs and $C_1(Q_1)$, $C_2(Q_2)$ be costs for each plant.

• Total output: $Q_T = Q_1 + Q_2$

• Profit: $\pi = P Q_T - C_1(Q_1) - C_2(Q_2)$

• Profit maximization requires: $MR = MC_1 = MC_2$

Question 3 Example

• Demand: $P = 120 - 3Q$

• Plant 1: $MC_1 = 10 + 20Q_1$

• Plant 2: $MC_2 = 60 + 5Q_2$

• Find $Q_T$ and $P^*$ where $MR = MC_T$

• Optimal total output: $Q_T^* = 7$, $P^* = 99$

• Optimal division: $Q_1^* = 3.4$, $Q_2^* = 3.6$

10.2 Monopoly Power

Monopoly power refers to a firm's ability to set prices above marginal cost.

• For a competitive firm: $P = MC$

• For a firm with monopoly power: $P > MC$

• Lerner Index: $L = \frac{P - MC}{P}$

• Expressed in terms of elasticity: $L = -\frac{1}{E_d}$

Elasticity of Demand and Price Markup

• If demand is elastic, markup is small and monopoly power is low.

• If demand is inelastic, markup is large and monopoly power is high.

10.3 Sources of Monopoly Power

• Elasticity of market demand: Less elastic demand increases monopoly power.

• Number of firms: Fewer firms increase monopoly power.

• Interaction among firms: Collusion or aggressive competition affects market power.

The Interaction Among Firms

• Firms may compete aggressively, driving prices down.

• Firms may collude, limiting output and raising prices, increasing monopoly power.

10.4 The Social Costs of Monopoly Power

Monopoly power leads to deadweight loss, reducing total welfare in the market.

• Competitive price and quantity: $P_c$, $Q_c$

• Monopolist's price and quantity: $P_m$, $Q_m$

• Consumers lose surplus; producers gain some surplus, but deadweight loss occurs.

• Deadweight loss: Area $B + C$ in the diagram.

Price Regulation

• Government may impose price ceilings to limit monopoly pricing.

• If price is regulated at $P_c$, output increases to competitive levels.

• Further lowering price causes shortages.

Natural Monopoly

• A natural monopoly occurs when a single firm can supply the entire market at lower cost than multiple firms due to economies of scale.

• Regulating price at competitive levels may cause losses; price is set to allow the firm to break even.

Regulation in Practice

• Rate-of-return regulation: Maximum price is set based on expected rate of return.

• Regulatory lag: Delays in adjusting regulated prices due to calculation and negotiation.

10.5 Monopsony

A monopsony is a market with a single buyer who has power over the price paid for goods or services.

• Oligopsony: Market with a few buyers.

• Monopsony power: Buyer's ability to affect price.

• Marginal value (MV): Additional benefit from purchasing one more unit.

• Total expenditure (TE): $TE = P \times Q_s$

• Marginal expenditure (ME): $ME = \Delta TE / \Delta Q_s$

• Average expenditure (AE): $AE = TE / Q_s$

Competitive Buyer vs. Competitive Seller

• Competitive buyer: Takes price as given; $ME = AE$; quantity purchased where price equals marginal value.

• Competitive seller: Takes price as given; $MR = AR$; quantity sold where price equals marginal cost.

Monopsonist Buyer

• Monopsonist faces an upward-sloping supply curve (AE).

• Marginal expenditure (ME) lies above AE.

• Profit maximization: $ME = MV$ (MV is also the demand curve).

• Price paid per unit is found from the AE curve at the profit-maximizing quantity.

Monopsony and Monopoly Compared

• Monopolist: Produces where $MR = MC$; $AR > MR$, so $P > MC$.

• Monopsonist: Purchases where $ME = MV$; $ME > AE$, so $MV > P$.

10.6 Monopsony Power

Monopsony power depends on the elasticity of supply.

• If supply is elastic, $ME$ and $AE$ are close; price is near competitive level.

• If supply is inelastic, $ME$ exceeds $AE$ by more; price is lower than competitive level.

Relationship between Supply and Marginal Expenditure

• If supply curve is $P = c + dQ$, then $ME = c + 2dQ$

Question 4 Example

• Inverse supply: $P = 4Q + 3$

• Marginal expenditure: $ME = 8Q + 3$

General Formula for Linear Supply

• For $P(q) = c + dq$:

• Total Expenditure: $TE(q) = P \times q$

• Marginal Expenditure: $ME = c + 2dq$

Elasticity and Monopsony Pricing

• At optimal $Q$, $MV = ME$

• $(MV - P)/P = 1/E_s$

• Since $E_s > 0$, $MV > P$

Question 5 Example

• Demand for nurses: $w = 30,000 - 125q$

• Supply for nurses: $w = 1000 + 75q$

• Marginal expenditure: $ME = 1000 + 150q$

• Profit max rule: $ME = MV$

• Set $1000 + 150q = 30,000 - 125q$ $ightarrow$ $q^* = 106$

• Wage: $w^* = 1000 + 75 \times 106 = 8950$

• If supply is perfectly elastic at $w = 10,000$, $ME = 10,000$; $MV = ME$ gives $q = 160$

Sources of Monopsony Power

• Elasticity of market supply

• Number of buyers

• Interaction among buyers

Social Costs of Monopsony Power

• Monopsony power can reduce total welfare, similar to monopoly power.

Bilateral Monopoly

• A market with one seller and one buyer.

• Monopsony and monopoly power counteract each other; outcome depends on bargaining.