Market Structures & Industrial Organization
Industrial organization (IO) studies how firm behavior and market outcomes depend on the structure of the industry. Market structure ranges from perfect competition — where price equals marginal cost and economic profit is zero in the long run — to pure monopoly, where a single firm faces the entire market demand and maximizes profit by restricting output. Between these extremes lie monopolistic competition (differentiated products, free entry) and oligopoly (few firms, strategic interdependence). Game theory, particularly the Nash equilibrium concept, provides the toolkit for analyzing oligopolistic behavior, from Cournot quantity competition to Bertrand price competition.
Market Structures
All firms — regardless of market structure — maximize profit at $MR = MC$.
- Perfect competition: $P = MR$, so $P = MC$ in equilibrium.
- Monopoly: $MR = P\left(1 - \frac{1}{|E_d|}\right) < P$, so $P > MC$.
With demand $P = a - bQ$, the monopolist's $MR = a - 2bQ$. Optimal output: $a - 2bQ = MC \implies Q^M$. The Lerner index measures market power:
$$L = \frac{P - MC}{P} = \frac{1}{|E_d|}$$
$L = 0$ (perfect competition); $L \to 1$ (high market power).
Measures market concentration using each firm's market share $s_i$ (as a percentage):
$$HHI = \sum_{i=1}^{n} s_i^2$$
HHI $< 1{,}500$: competitive; $1{,}500$–$2{,}500$: moderate concentration; $> 2{,}500$: highly concentrated. US antitrust guidelines flag mergers that raise HHI by $> 200$ in concentrated markets.
Two firms set quantities simultaneously. Firm 1's reaction function:
$$q_1 = \frac{a - c_1}{2b} - \frac{q_2}{2}$$
Symmetric equilibrium ($c_1 = c_2 = c$): $q^C = \frac{a-c}{3b}$, total $Q^C = \frac{2(a-c)}{3b}$, $P^C = \frac{a+2c}{3}$. Output is between monopoly and perfect competition.
Two firms competing in prices (identical goods) drive price to marginal cost — the competitive outcome — even with only two firms. Price competition is more intense than quantity competition.
A Nash Equilibrium is a strategy profile $(s_1^*, s_2^*, \ldots)$ where no player can improve their payoff by unilaterally deviating. In the Prisoner's Dilemma, both players defect — the unique Nash equilibrium — even though mutual cooperation gives higher joint payoffs.
Demand: $P = 100 - Q$. $MC = 20$. Find the monopoly price, quantity, and deadweight loss.
- $MR = 100 - 2Q$.
- Set $MR = MC$: $100-2Q=20 \implies Q^M=40$, $P^M=60$. Competitive $Q^C = 80$, $P^C=20$.
- $DWL = \frac{1}{2}(60-20)(80-40) = \$800$.
$P = 100 - Q$, $c_1 = c_2 = 20$. Find Cournot quantities and price.
- $q^C = (100-20)/(3\cdot 1) = 80/3 \approx 26.7$ each.
- $Q^C = 160/3 \approx 53.3$.
- $P^C = 100 - 160/3 = 140/3 \approx \$46.67$.
Practice Problems
Show Answer Key
1. $MR=200-4Q$; $200-4Q=40 \Rightarrow Q=40$; $P=120$. Profit $= (120-40)(40)-500=\$2{,}700$.
2. $L=(50-30)/50=0.40$.
3. $HHI = 50^2+30^2+20^2=2500+900+400=3{,}800$ (highly concentrated).
4. Pre-merger: $50^2+50^2=5{,}000$. Post-merger: $100^2=10{,}000$. $\Delta HHI = +5{,}000$. Strongly flagged for antitrust review.
5. $q^C=(90-10)/3=80/3\approx 26.7$ each; $Q^C=160/3\approx 53.3$; $P^C=90-160/3=110/3\approx\$36.67$; profit $= (36.67-10)(26.7)\approx\$711.5$ per firm.
6. $P=\$15=MC$ (Bertrand paradox: price competition drives to MC with just two firms).
7. Product differentiation allows positive short-run profit, attracting entry. New firms capture demand from incumbents, shifting each firm's demand curve leftward until tangency with ATC (zero profit) in the long run.
8. (Defect, Defect) is the Nash equilibrium. Defecting is a dominant strategy for both players regardless of the opponent's choice.
9. $L = 1/2 = 0.50$. If $MC=\$20$, then $P = MC/(1-L) = 20/0.5 = \$40$; markup $= 100\%$ over MC.
10. Charging each consumer their maximum willingness to pay. Requires: ability to identify each consumer's WTP, prevent resale, and segment the market. In theory this eliminates deadweight loss but transfers all consumer surplus to the firm.