Figure 4.11

Time Price

• p_f = cp_m + tw, where c = coinsurance rate; t = patient time per unit of service; w = value of patient time; p_m = money price of service
• Effects on pf of change in c; change in t; change in w; change in p_m
• High wage person will seek to reduce t

Time Price Example

• doctor 1 has long wait t=2, pm = $5 and doctor 2 has shorter wait t=1, pm = $40
• w = 100 high wage person; w=5 low wage person

Full Price (pf)

long wait MD $11 (low wage), $201 (high wage)

short wait MD $13 (low wage), $108 (high wage)

Insights from Full Price Formula

Demand is inelastic when insurance is complete

%change in quantity/%change in money price =

(%change in quantity/%change in full price)*

(%change in full price/%change in money price)

If c = 0, second term on right hand side = 0

Price elasticity is lower for person with high wage

 

Example c = .2, t = 1, pm goes from $10 to $5, w = $100

before: pf = $102

after:pf = $101

          say w = $5 before: pf = $7 after pf = $6
 

Empirical Studies of Demand

• Nonexperimental evidence: regression analysis--see Chapter 5 in Phelps
• Experimental evidence: What is is and its purpose

Special case of "natural experiments":  Mississippi Medicaid study; Canadian Insurance Plan Study; university (Stanford) changed clinic location; British National Health Service

Rationale for an Experiment
 

• Concept of reverse causality
• How experiment deals with reverese causality
• Problems with experiments:  cost; attrition bias; rare outcomes and long-range outcomes hard to study

Rand Health Insurance Study Design

• Conducted at 6 sites
• Participation for 3-5 years
• Excluded elderly
• Assigned randomly to plans: full coverage; 25%, 50% for all services; 50% copay for dental/mental and 25% for all other; individual deductible for ambulatory care only of $150/$450; 95% copay up to 5,10,15% of income up to max. of $1,000.
• Stop loss
• HMO plan
• Hold harmless clause
• Comparisons of mean values
• Regression analysis

Rand Results: Table 5.1 (p. 142)

• Some price responsiveness for face to face visits, especially for changes from 0 to 25% coinsurance
• Similar results for other services for comparable change in coinsurance rates
• Note that individual deductible plan behaves differently for ambulatory than for hospital care.

Other Key Results, Rand Study

• Arc elasticities in -.1 to -.2 range (Table 5.2, Phelps), but remember that percent changes in c to which elasticity applied can be high
• Arc elasticity for well ambulatory care (-.43) exceeds elasticity for chronic ambulatory care (-.23) (Table 5.3)
• Dental price elasticity about same as well ambulatory (Table 5.3)
• Hospital elasticity between -.1 and -.2 (Table 5.3)
• Simulations on effects of deductible reveal substantial effects although arc elasticities are very small (Table 5.6)

Implications: Cost-sharing is an effective instrument for achieving cost containment with some caveats: inappropriate care; distributional effects