Chapter 32: Market Structure, Competition, and Price Dispersion. The Encyclopedia of Economic Principals, interactive companion

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

How comparison shoppers set the price floor

Two labs sell the same test. How do comparing buyers spread prices and cut profit?

Each seller mixes over prices so that every price in the support earns the same profit: a high price earns a wide margin from captive buyers, a low price wins the comparers. The profit level is pinned by charging v to captive buyers only.

$Equation, written in LaTeX: p_L=15+60(\frac{0.60}{1.40})=\frac{285}{7}\approx\$40.71.$

$Equation, written in LaTeX: \bar\pi=\frac{(75-15)(0.60)}{2}=\$18.$

$Equation, written in LaTeX: q(51)=\frac{0.60}{2}+0.40(\frac{1}{2})=0.50,$

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c = 15 is marginal cost and v = 75 is the buyers' value, in dollars per test. lambda is the share of buyers who compare both labs; the rest see one lab at random. F(p) is the share of prices at or below p and p_L its lowest price.

Predict first. If the comparing share doubles from 0.40 to 0.80, does seller profit halve, fall by more, or fall by less?

Your prediction It halves It falls by more than half It falls by less than half

Share of buyers who compare

Figure: How comparison shoppers set the price floor. Equilibrium price distribution rising from 0 at 40.71 to 1 at 75 dollars when a share 0.40 of buyers compares prices. Seller profit is 18.00. — Share of buyers who compare: 0.4
Constructed example: the chapter's hypothetical labs (c = 15, v = 75, lambda 0.40 and 0.80, test price 51); comparing shares 0.20 and 0.60 are added for comparison.

Lower support p_L: $40.71
Profit per seller: $18.00
1 - F(51): 0.50
Expected quantity q(51): 0.50

With a comparing share of 0.40, the lower support is 15 + 60 x (0.60 / 1.40) = 40.71 and each seller earns 60 x 0.60 / 2 = 18.00. At 51 the rival is dearer with probability 0.5000, so q(51) = 0.30 + 0.40 x 0.5000 = 0.5000 and profit is 36 x 0.5000 = 18.00, the same as at every price in the support.

Worked steps

p_L = 15 + 60 x (0.60 / 1.40) = 40.71
Profit = 60 x 0.60 / 2 = 18.00
1 - F(51) = 0.60 / (2 x 0.40) x 24 / 36 = 0.5000
q(51) = 0.60 / 2 + 0.40 x 0.5000 = 0.5000
(51 - 15) x 0.5000 = 18.00

Use the idea

When a comparison tool raises the share of buyers who check every seller, expect both the floor of observed prices and seller margins to fall.

Where the conclusion applies

Two identical sellers, one unit per buyer, a common value and cost, and a fixed share of comparing buyers. The dispersion is a mixed strategy, not a difference in quality.

Check your understanding: With lambda = 0.60, what is the lowest price in the support, and the profit?

p_L = 15 + 60 x (0.40 / 1.60) = 15 + 15 = 30; profit = 60 x 0.40 / 2 = 12.

Chapter 32 source: section "Burdett-Judd price dispersion".

Demonstration 2 of 4

Zero profit, excess capacity

Why does a bakery that earns zero profit still price above marginal cost and below efficient scale?

The bakery prices on its own downward-sloping residual demand, so it stops where MR meets MC with price above MC. Entry shifts that demand until profit is zero, which happens where demand touches ATC on its falling part, left of minimum efficient scale.

Equation, written in LaTeX: p=20-0.5q,

Equation, written in LaTeX: VC(q)=5q+0.25q^2,

Equation, written in LaTeX: MR=20-q, MC=5+0.5q.

$Equation, written in LaTeX: ATC(q)=5+0.25q+\frac{75}{q},$

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q is thousands of specialty loaves and p dollars per loaf; money totals are thousands of dollars. The intercept is the height of the bakery's residual demand, F = 75 is fixed cost and ATC is average total cost.

Predict first. If entry lowers the demand intercept to 18, is profit about zero, slightly negative, or strongly negative?

Your prediction About zero Slightly negative Strongly negative

Residual demand intercept

Figure: Zero profit, excess capacity. Residual demand with intercept 20, marginal revenue, marginal cost and average total cost. The chosen output 10.00 thousand at price 15.00 lies left of minimum average cost at 17.32. — Residual demand intercept: 20
Constructed example: the chapter's hypothetical bakery (intercepts 20 and 18, F = 75); intercepts 19 and 21 are added for comparison.

Output q (thousand): 10.00
Price p: $15.00
Marginal cost: $10.00
Average total cost: $15.00
Profit ($ thousand): 0.00
Output at minimum ATC: 17.32

MR = MC gives 20 - q = 5 + 0.5q, so q = 10.00 thousand and p = 15.00. Revenue 150.00 less variable cost 75.00 and the fixed 75 leaves zero profit (0.00 thousand). Price 15.00 exceeds marginal cost 10.00, and output 10.00 is below the 17.32 that minimizes average cost.

Worked steps

20 - q = 5 + 0.5q, so q = 15 / 1.5 = 10.0000
p = 20 - 0.5 x 10.0000 = 15.0000
Revenue = 15.0000 x 10.0000 = 150.0000
VC = 5 x 10.0000 + 0.25 x 10.0000^2 = 75.0000
Profit = 150.0000 - 75.0000 - 75 = 0.00
MC = 5 + 0.5 x 10.0000 = 10.00, below the price 15.00

Use the idea

A firm with zero economic profit can still have a markup: check price against marginal cost and output against minimum efficient scale separately.

Where the conclusion applies

Linear residual demand, quadratic variable cost and a fixed cost that does not change with output. Entry is modeled only as a shift in the demand intercept.

Check your understanding: At intercept 21, what output and profit does the bakery reach?

21 - q = 5 + 0.5q gives q = 10.67, p = 15.67; revenue 167.11, VC 81.78, profit 167.11 - 81.78 - 75 = 10.33 thousand.

Chapter 32 source: section "Monopolistic competition".

Demonstration 3 of 4

Most-favored-customer clause flips a bid

When does a retroactive price guarantee make a profitable discount unprofitable?

A discount to one buyer triggers a refund to every protected earlier buyer, so the clause makes price cuts expensive for the seller. That is why such clauses can soften competition.

Equation, written in LaTeX: (42-30)(10)>(50-42)Q^P.

$Equation, written in LaTeX: Q^P<\frac{120}{8}=15$

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Quantities are thousands of cartons and payoffs thousands of dollars. Earlier buyers paid 50, marginal cost is 30 and the new order is 10. Q^P is the past volume protected by the clause, refunded the discount if the bid undercuts 50.

Predict first. Will coverage of 10 thousand past cartons still make the 42 bid profitable?

Your prediction Yes No

Protected past volume (thousand)

Bid price ($)

Figure: Most-favored-customer clause flips a bid. Bars: new-order contribution 120, refund 640 shown as a negative, and net payoff -520 thousand dollars for a bid of 42 with 80 thousand protected cartons. — Protected past volume (thousand): 80, Bid price ($): 42
Constructed example: the chapter's hypothetical carton producer (bid 42, protected volumes 80, 10 and 0, threshold 15); bids of 45 and 48 are added for comparison.

Contribution ($ thousand): 120
Refund ($ thousand): 640
Net payoff ($ thousand): -520
Threshold protected volume: 15.00
Decision: Do not bid

The new order adds (42 - 30) x 10 = 120 thousand. The clause refunds 8 on 80 thousand protected cartons, 640 thousand, so the net is -520 thousand and the order is not worth winning. Discounting pays only while protected volume is below 120 / 8 = 15.00 thousand.

Worked steps

Contribution = (42 - 30) x 10 = 120
Refund = (50 - 42) x 80 = 640
Net = 120 - 640 = -520
Threshold = 120 / 8 = 15.00

Use the idea

Before reading a most-favored-customer clause as buyer protection, measure how much past volume it covers and how that changes the seller's cost of discounting.

Where the conclusion applies

Full retroactive protection of the stated volume at the price gap, a fixed marginal cost and a bid that wins the order for sure.

Check your understanding: At a bid of 45 with 80 thousand protected cartons, what is the net payoff?

(45 - 30) x 10 = 150; refund (50 - 45) x 80 = 400; net = 150 - 400 = -250 thousand.

Chapter 32 source: section "Most-favored-customer effect".

Demonstration 4 of 4

The Diamond paradox and informed buyers

Why does a tiny search cost hold prices at the monopoly level, and what breaks it?

If no one searches, a price cut is invisible and only lowers the margin, so every seller charges the monopoly price. A positive informed share makes the cut visible to some buyers, and it pays.

$Equation, written in LaTeX: 24(\frac{1}{60})=\$0.40.$

$Equation, written in LaTeX: \frac{0.85}{60}+0.15=\frac{197}{1200}\approx0.1642.$

$Equation, written in LaTeX: (35-12)\frac{197}{1200}=\frac{4531}{1200}\approx\$3.78.$

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Sixty services have marginal cost 12 and customers value the task at 36. phi is the share of informed buyers who see every price; the rest stop at their first quote. Profit is per unit mass of customers.

Predict first. With no informed buyers (phi = 0), does cutting to 35 raise profit?

Your prediction Yes No

Informed share

Deviation price ($)

Figure: The Diamond paradox and informed buyers. Bars comparing profit at the common price 36, $0.40, with profit after cutting to 35, $3.78, when a share 0.15 of buyers sees every price. — Informed share: 0.15, Deviation price ($): 35
Constructed example: the chapter's hypothetical repair services (c = 12, v = 36, 60 sellers, phi 0 and 0.15, deviation to 35); phi 0.05 and 0.30 and deviation prices 24 and 30 are added.

Common-price profit: $0.40
Deviator demand: 0.1642
Deviator profit: $3.78
Undercutting: Profitable

At the common price each service earns 24 / 60 = 0.40. Cutting to 35 gives demand 0.85 / 60 + 0.15 = 0.164167 and profit (35 - 12) x 0.164167 = 3.776, so undercutting is profitable. The cut wins every informed buyer, a share 0.15, on top of its captive share.

Worked steps

Common profit = 24 x (1/60) = 0.40
Demand = 0.85 / 60 + 0.15 = 0.164167
Deviator profit = (35 - 12) x 0.164167 = 3.776

Use the idea

Small search frictions can sustain high prices; a tool that shows prices to even a few buyers can unravel them.

Where the conclusion applies

Identical services, a common value, ties split evenly and informed buyers who see all prices free.

Check your understanding: With phi = 0.05 and a deviation price of 30, is undercutting profitable?

Demand = 0.95/60 + 0.05 = 0.065833; profit = 18 x 0.065833 = 1.185 > 0.40, so yes.

Chapter 32 source: section "Diamond search paradox".

How comparison shoppers set the price floor

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Zero profit, excess capacity

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Most-favored-customer clause flips a bid

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

The Diamond paradox and informed buyers

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies