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: Q t+1 = f t+1 (K 0, L 0 ) Q t = f t (K 0, L 0 ). The difference in Q is often referred to as technological change. Labor Capital L0L0 K0K0 Q t+1 QtQt QtQt

More Technological Change At 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 L0L0 K0K0 Q t+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!

Allogenic: Taken from others; Autologous – From Self Milliman, 2011

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 IndicesAve. Annual Price Change Official Medical Care CPI Hospital Component3.4% Room6.2 Other Inpatient Services6.0 Heart Attack – unadjusted2.8 Quality Adjusted Indices Quality (extra years of life)-1.5% Quality (extra QALYs)-1.7%

Some Numbers Nominal health expenditures per capita were: $147 in Rose to $8,402 in a factor of 57! Real health expenditures per capita ($1960) were: $147 in 1960; $1,141 in $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 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 , 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 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)U 1 (x o -  ) + p U 2 (x o -  - zm, h(m)), p = probability of illness x o = 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 U 1 and U 2 are state-dependent (well, or ill) utility functions.

 = pm - zpm = pm (1-z)(2) Premium = expected payments - expected amount paid by coinsurance m = m (x o - , 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: h I = h I (m) h I 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)

Innovation Possibility Curve Increased Health Expenditures,  m Improvements in Health,  h Dh (Dm) Traditional Depiction of Technological Improvement Cost- Reducing Cost- Increasing Extra Profits (E) =  h/z -  m   h =zE + z  m E1E1 E2E2 E3E3 E4E4 E5E5 Provider would like to make money by innovating with  m and charging  h.

Innovation Possibility Curve Increased Health Expenditures,  m Improvements in Health,  h Dh (Dm) Traditional Depiction of Technological Improvement Cost- Reducing Cost- Increasing Equilibrium occurs at tangency of Extra Profits curve and innovation curve. Why there? E1E1 E2E2 E3E3 E4E4 E5E5  m*  h*

Innovation Possibility Curve Increased Health Expenditures,  m Improvements in Health,  h Dh (Dm) Traditional Depiction of Technological Improvement Cost- Reducing Cost- Increasing What happens if the coinsurance rate decreases? A> z decreases. E1E1 E2E2 Extra Profits (E) =  h/z -  m  h =zE + z  m

Innovation Possibility Curve Increased Health Expenditures,  m Improvements in Health,  h Dh (Dm) What happens if the coinsurance rate decreases? A> z decreases. E1E1 E2E2 Extra Profits (E) =  h/z -  m  h =zE + z  m Increase in rate! Increase in health!

Older Figures

Source: 2008 US Organ and Tissue Transplant Cost Estimates and Discussion, MillimanMilliman Allogeneic: Taken from others.Autologous: Taken from self.

Hospital Lengths of Stay by Transplant by Year

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