The Encyclopedia of Economic Principals

Chapter 38

Advertising, Differentiation, Quality, and Organizational Efficiency

Size the ad budget, pick the cheaper input mix, price status and sanctions, and find the quality distortion.

Four of the chapter's worked examples, made interactive: the Dorfman-Steiner advertising share, labor and compute mixes as expert labor gets dearer, status goods under a sumptuary ban, and Spence's quality distortion. Change one value at a time and watch the figure, the numbers and the hand calculation respond.

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 big should the ad budget be?

What share of sales should go to advertising, and what does the last ad dollar earn?

The price condition sets the margin (P - c)/P = 1/|e|; the advertising condition makes the last ad dollar return one dollar of contribution. Together they give A/PQ = eta_A / |e|: more responsive advertising raises the budget, more price-sensitive demand lowers it.

Equation, written in LaTeX: \frac{50-30}{50}=0.40,

Equation, written in LaTeX: \frac{A}{PQ}=\frac{0.20}{2.5}=0.08.

Equation, written in LaTeX: \frac{A}{PQ}=\frac{\eta_A}{|\varepsilon|}.

Scroll sideways for the whole equation

A is advertising spending, P price and Q quantity, so PQ is sales. eta_A is the advertising elasticity of quantity and |e| is the absolute price elasticity. Sales are held at $500,000 (price $50, 10,000 boxes) to read the share as a budget.

Predict first. If the advertising elasticity doubles from 0.10 to 0.20, does the indicated budget double?

Your prediction

Choose an example

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Figure: How big should the ad budget be? Two bars: the book's budget of $40,000 (8%) and this case's budget of $40,000 (8.0%) at illustrative sales of $500,000.
Advertising elasticity: 0.2, Price elasticity |e|: 2.5
Constructed example: the chapter's hypothetical meal kit (price $50, cost $30, 10,000 boxes, eta_A 0.20 and 0.10, |e| 2.5 and 4); an elasticity of 0.30 is added for comparison.

Calculated values

A/PQ = eta_A / |e|
8.0%
Budget at $500,000 sales
$40,000
Price-cost margin 1/|e|
0.40
Contribution per box P/|e|
$20.00
Extra boxes per ad dollar Q_A
0.050
Contribution per ad dollar
$1.00

A/PQ = 0.2 / 2.5 = 0.080, so the budget is 0.080 x 500,000 = $40,000. At that budget Q_A = 0.2 x 10,000 / 40,000 = 0.050 extra boxes per ad dollar, and each box contributes 50 / 2.5 = $20.00, so the last ad dollar returns 20.00 x 0.050 = $1.00, exactly its cost.

Worked steps

  1. A/PQ = 0.2 / 2.5 = 0.080
  2. A = 0.080 x 500,000 = $40,000
  3. Q_A = 0.2 x 10,000 / 40,000 = 0.050
  4. Contribution per box = 50 / 2.5 = $20.00
  5. Contribution per ad dollar = 20.00 x 0.050 = $1.00

Use the idea

Use the ratio as a check on an existing ad budget, then test the elasticity estimate, which carries most of the uncertainty.

Where the conclusion applies

Constant elasticities near the optimum, a single product, price set optimally and no rival response. Sales are held at $500,000 for the budget readout even where the elasticity changes.

Check your understanding: With eta_A = 0.30 and |e| = 2.5, what budget is indicated?
0.30 / 2.5 = 0.12, and 0.12 x 500,000 = $60,000.

Chapter 38 source: section "Dorfman-Steiner condition".

Demonstration 2 of 4

When expert labor gets expensive

Two mixes reach the same quality score. Which is cheaper as expert labor gets more expensive?

With the quality target fixed, the choice is pure cost minimization. The labor-heavy mix uses twice as much expert labor, so its cost line is steeper; once expert labor is expensive enough the compute-heavy mix wins.

Equation, written in LaTeX: C_L=8+7=\$15\text{ million}, C_K=4+14=\$18\text{ million}.

Equation, written in LaTeX: C_L'=4(8)+7=\$39\text{ million}, C_K'=4(4)+14=\$30\text{ million}.

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C_L is the cost of the labor-heavy mix (8 million of expert evaluation, 7 million of compute) and C_K the cost of the compute-heavy mix (4 and 14 million). w scales the price of expert labor; compute prices stay fixed. Both mixes reach a score of 76.

Predict first. At what labor price multiple does the cheaper mix switch?

Your prediction

Choose an example

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Figure: When expert labor gets expensive. Cost lines of the two mixes against the expert labor price multiple, crossing at 1.75. At a multiple of 1 the labor-heavy mix costs 15.00 million and the compute-heavy mix 18.00 million.
Expert labor price multiple: 1
Constructed example: the chapter's hypothetical digital service (mixes 8 + 7 and 4 + 14, labor price multiples 1 and 4); multiples of 1.5 and 2 are added for comparison.

Calculated values

C_L, labor-heavy ($ million)
15.00
C_K, compute-heavy ($ million)
18.00
Cheaper mix
Labor-heavy mix
Difference ($ million)
3.00

C_L = 8 x 1 + 7 = 15.00 and C_K = 4 x 1 + 14 = 18.00. The labor-heavy mix is cheaper by 3.00 million. The costs are equal where 8w + 7 = 4w + 14, that is w = 7 / 4 = 1.75.

Worked steps

  1. C_L = 8 x 1 + 7 = 15.00
  2. C_K = 4 x 1 + 14 = 18.00
  3. Difference = 15.00 - 18.00 = -3.00
  4. Switch: 8w + 7 = 4w + 14 gives 4w = 7, w = 1.75

Use the idea

Compare mixes only after confirming each one reaches the required quality on the failure modes that matter, then recompute costs at current input prices.

Where the conclusion applies

Both mixes reach the same verified score, input prices scale linearly and compute prices do not change. Compute cannot replace experts on failures that only experts can repair.

Check your understanding: At a multiple of 2, which mix is chosen and by how much?
C_L = 8(2) + 7 = 23 and C_K = 4(2) + 14 = 22, so the compute-heavy mix wins by 1 million.

Chapter 38 source: section "Quality-Adjusted Differentiation and Labor-Compute Substitution".

Demonstration 3 of 4

Status goods and the cost of evasion

Who buys a status garment, and when does a banned buyer evade the law?

For a buyer whose status value rises faster than price, a higher price raises net utility. A ban on display then works only through expected sanctions: lower detection makes evasion pay.

Equation, written in LaTeX: U_L=40+0.2(70)-70=-16,

Equation, written in LaTeX: U_M=40+1.2(70)-70=54, U_H=40+1.4(70)-70=68.

Equation, written in LaTeX: U_i^I=v_i+s_i(p,z)-p-\rho F-c_i^E,

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Each buyer gets use value 40 plus status value s p, where s is 0.2 for L, 1.2 for M and 1.4 for H, and pays the price p. rho is the detection probability, F = 100 the fine and the evasion cost c^E is taken as zero.

Predict first. With detection at 0.70, does a higher price raise or lower M's incentive to evade?

Your prediction

Choose an example

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Figure: Status goods and the cost of evasion. Bars for net utility at a price of 110: L -48, M 62, H 84, and M's illicit payoff -8 with detection probability 0.7.
Garment price ($): $110, Detection probability: 0.7
Constructed example: the chapter's hypothetical garment (use value $40, status 0.2p, 1.2p, 1.4p, prices $70 and $110, fine $100, detection 0.70 and 0.20); a price of $90 is added for comparison.

Calculated values

U_L
-$48
U_M
$62
U_H
$84
Expected sanction
$70
M's illicit payoff
-$8
M evades
No

At a price of 110: U_L = 40 + 0.2 x 110 - 110 = -48, U_M = 40 + 1.2 x 110 - 110 = 62 and U_H = 40 + 1.4 x 110 - 110 = 84. If only H may display the garment, M's expected sanction is 0.7 x 100 = 70, so its illicit payoff is 62 - 70 = -8: M does not evade.

Worked steps

  1. U_L = 40 + 22 - 110 = -48
  2. U_M = 40 + 132 - 110 = 62
  3. U_H = 40 + 154 - 110 = 84
  4. Expected sanction = 0.7 x 100 = 70
  5. M's illicit payoff = 62 - 70 = -8

Use the idea

When a restriction targets a status good, check enforcement odds against the payoff of illicit display rather than assuming demand simply falls.

Where the conclusion applies

Linear status values that are not credible at very high prices, a fixed fine, zero evasion cost and no change in status value from the restriction itself.

Check your understanding: At a price of 90 and detection 0.70, does M evade?
U_M = 40 + 1.2(90) - 90 = 58; the expected sanction is 0.70(100) = 70; 58 - 70 = -12, so no.

Chapter 38 source: section "Sumptuary Laws and Veblen Goods".

Demonstration 4 of 4

Does a monopolist under- or over-provide quality?

Whose valuation of quality does a uniform-price monopolist follow, and what does that cost users?

A uniform price lets the firm collect only the boundary buyer's gain from quality on every sale. Welfare counts the average gain. The firm under-provides quality when inframarginal buyers care more and over-provides when the boundary buyer cares more.

Equation, written in LaTeX: C(s)=20s^2, C_s(s)=40s.

Equation, written in LaTeX: 400=40s,

Equation, written in LaTeX: s_M=\frac{900}{40}=22.5,

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s is reliability and C(s) = 20 s^2 its cost, so one more unit costs 40s. There are 100 subscribers. vb is the boundary subscriber's value of one more unit and va the average subscriber's value; s_M is the monopoly choice and s_W the conditional welfare choice.

Predict first. If the boundary buyer values quality more than the average buyer, which way is the distortion?

Your prediction

Choose an example

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Figure: Does a monopolist under- or over-provide quality? Marginal cost line 40s crossing the firm's marginal revenue 400 at s_M = 10.0 and users' marginal benefit 700 at s_W = 17.5.
Boundary subscriber's value per unit ($): 4, Average subscriber's value per unit ($): 7
Constructed example: the chapter's hypothetical subscription service (100 subscribers, C(s) = 20s^2, vb 4 and 9, va 7); vb = 7 and va = 5 are added for comparison.

Calculated values

Firm's marginal revenue 100 vb
400
s_M (monopoly)
10.0
Users' marginal benefit 100 va
700
s_W (welfare)
17.5
Distortion
Under-provision

The firm sets 100 x 4 = 40s, so s_M = 400 / 40 = 10.0. Welfare sets 100 x 7 = 40s, so s_W = 700 / 40 = 17.5. The monopolist under-provides quality by 7.5 units. At s_M one more unit costs 400 and is worth 700 to users.

Worked steps

  1. Firm: 100 x 4 = 400 = 40s
  2. s_M = 400 / 40 = 10.0
  3. Welfare: 100 x 7 = 700 = 40s
  4. s_W = 700 / 40 = 17.5
  5. s_M - s_W = 10.0 - 17.5 = -7.5

Use the idea

Before calling a product's quality too low, ask whether the buyers at the margin value quality more or less than the typical buyer.

Where the conclusion applies

Quantity is fixed at 100 subscribers, valuations are linear in s and price is uniform. If quality changes who subscribes, both conditions must add those entrants.

Check your understanding: With vb = 7 and va = 5, what are s_M and s_W?
s_M = 700 / 40 = 17.5 and s_W = 500 / 40 = 12.5: over-provision by 5.

Chapter 38 source: section "Spence monopoly-quality distortion".