technology © allen c. goodman, 2013 introduction start with a typical production relationship of: q...

Technology

© Allen C. Goodman, 2013

Introduction

Start with a typical production relationship of:

Q = f (K, L)

Ignoring returns to scale, or anything of that type, we could conceive of technology as:

Qt+1 = ft+1 (K0, L0)

Qt = ft (K0, L0).

The difference in Q is often referred to as technological change.

Labor

Capital

L0

K0

Qt+1QtQt

More Technological ChangeAt a given factor price ratio, we

simply re-label the isoquant, so at the same total costs, the cost per unit has fallen.

Alternatively, for the same quantity, the total costs have fallen.

Labor

Capital

L0

K0

Qt+1

This might be considered to be "neutral" technological change; alternatively we might have "labor-saving" or "capital-saving" depending on what the new equilibrium is.

Typically, technology is measured as a residual. Once you've controlled for changes in labor and capital, what's left?

Health Care

Health care technology has some interesting twists.

For example, consider innovations that are considerably higher cost, but also are much higher quality.

For example, various major surgeries, or things like heart valves. They are more expensive, but they also allow people to live longer.

Plotting the cost of a unit of output, we see that technological change might lead to increases in costs. So we see curiously outward shifting (indexed on quality isoquants).

Weisbrod’s Examples

• Polio vaccines have decreased the demand for insurance by decreasing both the expected cost of treating the illness, and the cost variance. They have reduced the expected level of expenditures, as well as the variance around the mean. In the process, they have reduced the demand for health insurance.

• Organ transplants, on the other hand, have both increased the mean and the variance of desired individual expenditures, conditional on medical need. Before, a person with serious liver malfunction, simply died, with comparatively little health care expenditure.

• Here are some numbers!

Estimated US Average 2011 Transplant Costs Table 1 Estimated

Transplant Total Estimated Billed Chges

Single Organ/TissueBone Marrow-Allogenic 6,894 805,400Bone Marrow-Autologous 13,263 363,800Cornea 46,081 24,400Heart 2,161 997,700Intestine 74 1,206,800Kidney 16,571 262,900Liver 5,898 577,100Lung-Single 734 561,200Lung-Double 1,050 797,300Pancreas 286 289,400

Multiple OrganHeart-Lung 30 1,248,400Intestine w/ others 107 1,343,200Kidney-Heart 66 1,296,500Kidney-Pancreas 867 474,700Liver-Kidney 369 1,026,000Other Multi-Organ 42 1,707,500

Allogenic: Taken from others; Autologous – From Self

Milliman, 2011

Table 2 - Estimated Billed Charges Per Transplant30 Days Procure- 180 Days OP Immuno-

Transplant Pre- ment Hospital Physician Post-Op suppresants TotalSingle Organ/TissueBone Marrow 41,400 38,900 419,600 22,400 259,800 23,300 805,400 - Allogenic

Bone Marrow-Autologous 44,600 18,200 198,200 10,800 84,900 7,100 363,800 -Autologous

Cornea 0 0 16,500 7,900 0 0 24,400Heart 47,200 80,400 634,300 67,700 137,800 30,300 997,700Intestine 55,100 78,500 787,900 104,100 146,600 34,600 1,206,800Kidney 17,000 67,200 91,200 18,500 50,800 18,200 262,900Liver 25,400 71,000 316,900 46,600 93,900 23,300 577,100Lung-Single 10,300 73,100 302,900 33,500 117,700 23,700 561,200Lung-Double 21,400 90,300 458,500 56,300 142,600 28,200 797,300Pancreas 17,000 65,000 108,900 17,800 61,400 19,300 289,400

Table 3 Hospital Lengths of Stay (Days)

Transplant 2006 2008Single Organ/Tissue

Bone Marrow-Allogenic 33.9 33.1Bone Marrow-Autologous 20.7 20.4Heart 38.8 40.1Intestine 64.1 69.4Kidney 8.1 7.3Liver 22.2 20.9Lung-Single 19.6 18.9Lung-Double 29.9 28.1Pancreas 8.2 9.4

Multiple OrganHeart-Lung 44.0 44.7Kidney-Heart 60.4 46.0Kidney-Pancreas 12.6 12.4Liver-Kidney 30.9 27.5

Quality Adjusted Cost Indices

• If quality increases, then what may appear to be increase costs, may in fact decrease costs.

• Cutler et al recalculated costs for myocardial infarction (heart attack) treatment.

• Adjusted for gains in either life years or in QALYs.

Comparing Approaches

Unadjusted Indices Ave. Annual Price ChangeOfficial Medical Care CPI

Hospital Component 3.4%Room 6.2Other Inpatient Services 6.0

Heart Attack – unadjusted 2.8

Quality Adjusted IndicesQuality (extra years of life) -1.5%Quality (extra QALYs) -1.7%

Some Numbers

• Nominal health expenditures per capita were:$147 in 1960. Rose to $8,402 in 2010 -

a factor of 57!• Real health expenditures per capita ($1960)

were:$147 in 1960; $1,141 in 2010.

• $1,141/$147 = 7.76• Increase of about 676%. Are we 6-7 times as

healthy as in 1960?

Why do we care?

Newhouse (JEP, 1992) looks at:

Aging - Some impact but not much.

Increased Insurance - Coinsurance rates had fallen but not enough to explain the increase. Fell from about 67% in 1950 to 27% in 1980. With an elasticity of -0.2, with a linear demand function, and no technological change, 40% point drop in coinsurance rate should have caused about a 50% increase in demand, not 400%.

In addition, from 1980-90, there was basically a constant 5% coinsurance rate for hospital services and real hospital expenditure rose over 50%.

Why do we care?Increased income - Even using 1.0 as an income elasticity, you can account for a

little under a quarter of the overall increase.

Can also look at supplier-induced demand, and factor productivity.

It is clear that technological change must have something to do with it.

Technological change has got to be related to insurance. Weisbrod points out several aspects:

• Often procedures succeed or fail based on whether insurance will pay for them. Importance of mandated coverage.

• Compare current school with a school of 50 years ago; now do the same with a hospital. Schools have been funded by prospective payment. Hospitals have been funded with retrospective payment.

• Between 1960 and 2007, public school enrollment increased from 36M to about 50M) public school expenditures increased from 3.0% of GNP to about 5% of GDP. Health care expenditures rose from 4.6% to 18%, or more.

Goddeeris Model (Chapter 11)

Goddeeris - 1984 SEJ

He takes an interesting look at the interaction between insurance and incentives in medical care. He finds:

- If willingness to pay is not related to income, then insurance fundamentally biases innovation toward more expensive procedures.

In this model, the consumer pays a premium in return for coverage of a predetermined fraction of medical expenditures. Start with Utility Function (1):

V = (1-p)U1 (xo - ) + p U2 (xo - - zm, h(m)),

p = probability of illness

xo = endowment income

= insurance premium

z = coinsurance rate

m = medical expenditures if ill

h(m) = relation of health to m

1 = well; 2 = ill

Goddeeris Model

1 = well; 2 = ill

U1 and U2 are state-dependent (well, or ill) utility functions.

U1 and U2 are state-dependent (well, or ill) utility functions.

= pm - zpm = pm (1-z) (2)

Premium = expected payments - expected amount paid by coinsurance

m = m (xo - , z) (3)

medical expenditure, if ill, is a function of disposable income, and coinsurance rate.

Take a base period before innovation, and solve for m*, h*, *.

He then goes through a discussion of an innovation possibility curve. Ultimately, this falls out into a family of innovative techniques such that:

hI = hI (m)

hI refers to health innovations.

This gives the graph:

Goddeeris Model

Innovation Possibility Curve

Increased Health Expenditures, m

Improvements in Health, h

h (m)

Traditional Depiction of Technological Improvement

Cost-Reducing

Cost-Increasing

(0,0)




Dh (Dm)


Cost-Reducing

Cost-Increasing

Extra Profits (E) = h/z - m h =zE + z m

E1

E2

E3

E4

E5

Provider would like to makemoney by innovating with mand charging h.




Dh (Dm)


Cost-Reducing

Cost-Increasing

Equilibrium occurs at tangencyof Extra Profits curve and innovation curve.

Why there?

E1

E2

E3

E4

E5

m*

h*




Dh (Dm)


Cost-Reducing

Cost-Increasing

What happens if the coinsurancerate decreases?A> z decreases.

E1

E2





Dh (Dm)What happens if the coinsurancerate decreases?A> z decreases.

E1

E2


Increase in rate!

Increase in health!

Older Figures

Transplant 30 days pre- Procurement Hospital Physician 180 Days Post- OP Immuno- Totaltransplant Transplant During Transplant Suppressants

Admission Transplant Admission and Other RX

Single Organ Tissue

Bone-MarrowAllogeneic 30,400 29,400 380,700 19,600 197,100 19,600 676,800

Bone MarrowAutologous 31,300 21,200 169,900 10,600 62,100 5,300 300,400

Cornea 0 0 13,200 7,500 0 0 20,700

Heart 34,200 94,300 486,400 50,800 99,700 22,300 787,700

Intestine 48,400 77,200 743,800 100,600 124,300 27,500 1,121,800

Kidney 16,700 67,500 92,700 17,500 47,400 17,200 259,000

Liver 21,200 73,600 286,100 44,100 77,800 20,600 523,400

Lung - Single 7,500 53,600 256,600 27,900 84,300 20,500 450,400

Lung - Double 20,700 96,500 344,700 59,300 113,800 22,800 657,800

Pancreas 16,500 68,400 93,400 16,300 58,700 22,200 275,500

Multiple Organ

Heart-Lung 49,100 151,900 682,500 73,000 143,300 24,000 1,123,800

Intestine + Others 58,200 175,200 772,700 116,200 136,900 34,000 1,293,200

Kidney-Heart 34,400 145,600 608,800 66,000 129,600 21,300 1,005,700

Kidney-Pancreas 18,400 122,300 171,100 32,000 73,800 21,400 439,000

Liver-Kidney 31,300 127,000 403,400 65,000 114,700 22,100 763,500Source: 2008 US Organ and Tissue TransplantCost Estimates and Discussion, Milliman

Allogeneic: Taken from others. Autologous: Taken from self.

Hospital Lengths of Stay by Transplant

Single Organ Tissue2005 2006

Bone-MarrowAllogeneic 34 33.9

Bone MarrowAutologous 20.4 20.7

Heart 38 38.8

Intestine 56.1 64.1

Kidney 8.5 8.1

Liver 22.4 22.2

Lung - Single 20.6 19.6

Lung - Double 30.8 29.9

Pancreas 9.7 8.2

Multiple Organ

Heart-Lung 47.8 44

Kidney-Heart 64.6 60.4

Kidney-Pancreas 14.2 12.6

Liver-Kidney 25.9 30.9

Hospital Lengths of Stay by Transplant

by Year

Similar NumbersFor 2005-2008