Chapter 94: Health Capital, Medical Uncertainty, and Provider Incentives. 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

Review before treatment

When does paying an independent reviewer save money?

Patients cannot judge whether treatment is needed, so who screens and how they are paid matters. A review is worth its fee when the procedures it prevents cost more than the reviews.

$Equation, written in LaTeX: 28(20{,}000)=560{,}000\text{ units}.$

$Equation, written in LaTeX: 28(1{,}000)+16(20{,}000)=348{,}000\text{ units},$

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A diagnostic signal is positive for 28 patients, 10 sick and 18 healthy. A procedure costs 20,000. Review costs a fee per positive case and removes some false positives without missing a sick patient.

Predict first. Does an expensive review (3,000 per case) that removes 12 false positives still save money?

Your prediction Yes No

Review cost per positive

False positives removed

Figure: Review before treatment. Two bars: treating all positives costs 560,000; reviewing first costs 348,000, of which 28,000 is review. — Review cost per positive: 1,000, False positives removed: 12
Constructed example: the book's hypothetical values are 28 positives, procedure 20,000, review 1,000 or 100 and 12 false positives removed; a review cost of 3,000 and 6 or 18 removals are added.

Automatic treatment: 560,000
Review cost: 28,000
Procedures after review: 16
Reviewed total: 348,000
Saving: 212,000

Hypothetical teaching values, not clinical or market data. Reviewing each of the 28 positives at 1,000 removes 12 false positives, leaving 16 procedures. The reviewed rule costs 28,000 + 16 x 20,000 = 348,000 against 560,000, so review saves 212,000. The review addresses hidden clinical quality, not the pooling of expenditure.

Worked steps

Automatic: 28 x 20,000 = 560,000
Review: 28 x 1,000 = 28,000; procedures 28 - 12 = 16
Reviewed: 28,000 + 16 x 20,000 = 348,000
Saving = 560,000 - 348,000 = 212,000

Use the idea

Value a second opinion by the procedures it removes times their cost, minus its fee on every case reviewed, and check the reviewer's own incentives.

Where the conclusion applies

Review removes false positives only and never misses a sick patient; the reviewer is not paid per procedure.

Check your understanding: At a review cost of 3,000 removing 6 false positives, what is the total cost?

28 x 3,000 + 22 x 20,000 = 84,000 + 440,000 = 524,000, a saving of 36,000.

Chapter 94 source: section "Arrow medical-care uncertainty principle".

Demonstration 2 of 4

The premium spiral

When does losing low-risk members drive the premium up again, and can reinsurance stop it?

A premium priced to the average attracts those who expect to claim more. If low-risk members leave, the average rises and more leave. Lowering the cost of high-risk members can hold the price below the renewal threshold.

$Equation, written in LaTeX: p_{t+1}=k+E[c_i\mid v_i-p_t\geq o_i].$

$Equation, written in LaTeX: \frac{600(2{,}000)+400(8{,}000)}{1{,}000}=4{,}400\text{ units}.$

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The plan has 400 high-risk members with expected claims of 8,000 and low-risk members with 2,000. The premium covers average claims of those who renew. Reinsurance lowers the plan's effective high-risk cost. As in the chapter's robustness check, the low-risk members who remain after the first exit are assumed to renew only below 4,500.

Predict first. With 300 low-risk renewals, does reinsurance that cuts the high-risk cost to 6,000 stop the spiral?

Your prediction Yes No

Low-risk members renewing

Effective high-risk cost (reinsurance)

Figure: The premium spiral. Two bars: the starting premium 4,400 and the next premium 5,429, with a line at 4,500. — Low-risk members renewing: 300, Effective high-risk cost (reinsurance): 8,000
Constructed example: the book's hypothetical values are 400 high-risk members at 8,000 or 6,000, low-risk claims 2,000, renewals 600, 300 and 100 and the 4,500 threshold; a cost of 7,000 is added.

Members: 700
Next premium: 5,429
Change from 4,400: +1,029
Spiral: Continues

Hypothetical teaching values, not clinical or market data. With 300 low-risk members renewing and a high-risk cost of 8,000, the break-even premium is (300 x 2,000 + 400 x 8,000) / 700 = 5,429, above the 4,500 renewal threshold, so further low-risk exit is predicted. Each price change alters who stays, which sets the next price.

Worked steps

Claims = 300 x 2,000 + 400 x 8,000 = 600,000 + 3,200,000 = 3,800,000
Premium = 3,800,000 / 700 = 5,429
5,429 against 4,500: above

Use the idea

Judge a stabilization policy by the premium it produces relative to actual renewal thresholds, not by its effect on average claims alone.

Where the conclusion applies

No loading, all high-risk members renew, and a single renewal threshold of 4,500 for the low-risk members who remain after the first exit.

Check your understanding: With 300 renewals and a high-risk cost of 7,000, is the premium below 4,500?

(600,000 + 2,800,000) / 700 = 4,857, above 4,500, so further exit is predicted.

Chapter 94 source: section "Health-insurance adverse-selection death spiral".

Demonstration 3 of 4

Depreciation, technology, and health spending

Why can unchanged medical spending go with falling health?

Health is a stock that depreciates. Spending buys investment through a technology, so the same spending can maintain, raise or lower health depending on depreciation and technology.

$Equation, written in LaTeX: I=4\sqrt{M},$

$Equation, written in LaTeX: H_{t+1}=0.8(80)+8=72.$

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H is the health stock (80 now), delta its depreciation rate, M medical input in hundreds of units, and I = A sqrt(M) health investment with technology coefficient A.

Predict first. If depreciation rises to 0.20 and spending stays at 4, where does health go?

Your prediction It stays at 80 It falls to 72 It rises

Depreciation

Technology coefficient

Medical input (hundreds)

Figure: Depreciation, technology, and health spending. Two bars: health 80 now and 80.00 next period, with a line at 80. — Depreciation: 0.1, Technology coefficient: 4, Medical input (hundreds): 4
Constructed example: the book's hypothetical values are H = 80, delta 0.10 and 0.20, A = 4 and 8 and M = 4, 9 and 16; combinations not worked in the chapter are added.

Investment I: 8.00
Next-period health: 80.00
Required investment: 8.00
Maintenance M: 4.00

Hypothetical teaching values, not clinical or market data. With depreciation delta = 0.10, technology I = 4 sqrt(M) and medical input 4 hundred, investment is 8.00 and next-period health is 0.90 x 80 + 8.00 = 80.00: health is maintained exactly. Holding health at 80 needs M = 4.00.

Worked steps

I = 4 x sqrt(4) = 8.00
H_t+1 = 0.90 x 80 + 8.00 = 72.00 + 8.00 = 80.00
Maintenance: 4 sqrt(M) = 0.10 x 80 = 8.00, so M = (8.00 / 4)^2 = 4.00

Use the idea

Measure spending, investment, depreciation and health separately before calling rising spending wasteful or flat spending adequate.

Where the conclusion applies

A square-root investment technology and a constant depreciation rate within the year.

Check your understanding: With delta = 0.20, A = 4 and M = 9, what is next-period health?

I = 4 x 3 = 12, so H = 0.8 x 80 + 12 = 76.

Chapter 94 source: section "Grossman health-capital model".

Demonstration 4 of 4

Coinsurance and extra visits

How many low-value visits does insurance add, and what do they cost in resources?

Insurance lowers the price the patient sees below the resource cost, so patients use visits worth less than they cost. Higher coinsurance trims those visits but shifts financial risk back to the patient.

Equation, written in LaTeX: B_q(q;s)=cp.

Equation, written in LaTeX: q=6-0.02P_o,

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q is follow-up visits, P_o the out-of-pocket price (coinsurance rate times the 200 resource cost). The six visits have marginal benefits 300, 240, 180, 120, 60 and 20.

Predict first. Moving from 25 to 50 percent coinsurance removes how many visits?

Your prediction One Two None

Coinsurance rate

Figure: Coinsurance and extra visits. Six bars of marginal benefit (300 down to 20) with a line at the resource cost 200 and the out-of-pocket price 50; 5 visits are used. — Coinsurance rate: 25%
Constructed example: the book's hypothetical values are demand q = 6 - 0.02 P_o, cost 200, benefits 300 to 20 and coinsurance of 25, 50 and 100 percent; zero coinsurance is added.

Out-of-pocket price P_o: 50
Visits q: 5
Visits beyond efficient: 3
Resource gap: 240

Hypothetical teaching values, not clinical or market data. At 25 percent coinsurance the patient pays 50 per visit and demand is 6 - 0.02 x 50 = 5 visits. Only the first 2 are worth their 200 resource cost, so 3 extra visits cost 600 and yield 360, a gap of 240. The gap is not the whole welfare effect, because insurance also protects against an uncertain bill.

Worked steps

P_o = 0.25 x 200 = 50
q = 6 - 0.02 x 50 = 5
Extra visits cost 3 x 200 = 600 and yield 180 + 120 + 60 = 360
Gap = 600 - 360 = 240

Use the idea

Estimate the utilization response to cost sharing, value the extra care against its resource cost, and weigh that against the risk protection lost.

Where the conclusion applies

Linear demand fixed by illness, a fixed provider price and stated marginal benefits.

Check your understanding: With full insurance (zero coinsurance), how many visits and what resource gap?

q = 6; visits 3 to 6 cost 800 and yield 380, a gap of 420.

Chapter 94 source: section "Ex-post moral hazard in health insurance".

Review before treatment

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

The premium spiral

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Depreciation, technology, and health spending

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies

Coinsurance and extra visits

Choose an example

Calculated values

Worked steps

Use the idea

Where the conclusion applies