health econ test 1

Who are the four key stakeholders in healthcare, and what are their roles?

• Individuals (Patients/Consumers)

• Medical Providers

• Insurance Companies

• Government

What are the three reasons why healthcare is special compared to goods and services in other markets?

• Extensive Government Intervention

• Uncertainty

• Huge Expenditure Share

How does the payment mechanism differ between healthcare and other markets?

In normal markets, consumers pay suppliers directly for goods/services.
In healthcare, a third party (insurance plan) usually pays providers on behalf of patients.The patient pays a premium to the insurer and possibly copayments, coinsurance, or deductibles.

How does the trend of healthcare expenditure in the U.S. compare to that in other high-income countries?

U.S. healthcare spending as a share of GDP has risen faster and higher than that of other OECD nations.
While most high-income countries spend around 10–12 % of GDP, the U.S. exceeds 17 %.
Growth has averaged 4–5 % per year, reflecting both higher prices and greater utilization intensity

What are the three key causes of higher healthcare spending in the U.S. compared to Canada?

• Higher administrative costs

• Higher prices for drugs and services

• Higher intensity of care

Why are the administrative costs higher in U.S. healthcare than in other high-income countries?

Because the U.S. uses a multi-payer system (many private insurers plus public programs) with different claim forms, billing rules, and provider networks.
Administrative functions such as marketing, eligibility verification, and claims processing are duplicated across insurers, unlike Canada’s single-payer system that centralizes administration

Why are drug prices higher in the U.S. than in other countries?

• The U.S. does not impose price controls or centralized negotiation on pharmaceuticals.

• Manufacturers can set launch prices freely.

• Public programs like Medicare are limited in their ability to bargain collectively, unlike national health systems elsewhere.
  

 What are two reasons for higher intensity of care among U.S. patients?

1. Greater use of advanced medical technology (MRI, CT scans, robotic surgeries).

2. Fee-for-service incentives that encourage more services per visit or episode rather than payment per outcome.
   

What measures indicate worse health outcomes in the U.S. compared to other high-income countries?

• Lower life expectancy at birth,

• Higher infant mortality,

• Higher rates of preventable chronic disease (e.g., diabetes, obesity).
  These outcomes illustrate inefficiency: more spending but comparatively poorer population health performance.
  

Why can health be considered a durable good? What is the key difference from other durable goods?

• Health provides utility over time — it’s a stock that produces a flow of healthy time or well-being.

• However, unlike other durables (like a car or house), health depreciates naturally with age or illness. You can invest in it (medical care, lifestyle), but it cannot be resold or fully repaired once lost

In the utility framework, does health have a positive marginal utility? Why do we assume diminishing marginal utility for health?

• Yes — as health improves, utility rises because good health increases productive and enjoyable time.

• But diminishing marginal utility applies because each additional improvement in health yields smaller increases in satisfaction once you are already healthy

What is the functional shape of the indifference curve for health (H) and all other commodities (X), and why?

• It is convex toward the origin.

• This shape reflects the trade-off: as you gain more health, you’re willing to give up fewer units of other goods for an extra unit of health.

• Convexity represents diminishing marginal rate of substitution (MRS) between health and other goods

Why is it not possible to consider a budget constraint for health and all other commodities?

• Health isn’t purchased directly — it’s produced using medical care and time.

• Because you can’t buy “health” in units, a budget constraint between H and X isn’t meaningful.

• Instead, you face a budget between medical care (m) and other goods (X), where H is an outcome of the production function H=g(m)H = g(m)H=g(m)

What is the typical shape of the health production function? What is the corresponding shape of the marginal product function? How are they related?

• Health production function (H = g(m)): concave — increases at a decreasing rate.

• Marginal product of medical care (MPₘ = g′(m)): positive but downward sloping.
  The MPₘ curve is the derivative (slope) of the health production curve, showing diminishing returns to medical care
  

Why do we focus on the region of the health production function where medical care increases health at a diminishing rate?

That’s the economically relevant region where additional medical care still improves health (g′(m) > 0), but the benefit declines. Beyond that, extra care can reduce health (negative returns) or waste resources

What is the relationship between medical care (m) and utility from health and all other commodities, U(X,H)?

• Medical care affects utility indirectly through health:
  UX>0,UH>0,U_X > 0, U_H > 0,UX​>0,UH​>0, and H=g(m)H = g(m)H=g(m).

• So utility increases with m only because m increases H.
  Mathematically: ∂U∂m=UH⋅g′(m)\frac{∂U}{∂m} = U_H · g′(m)∂m∂U​=UH​⋅g′(m).

• If g′(m) declines, the marginal utility of m also declines

How is the marginal utility of medical care defined, and how is it interpreted?

• MUm=UH⋅g′(m)MU_m = U_H · g′(m)MUm​=UH​⋅g′(m).

• It measures the additional utility gained from one more unit of medical care.

• Interpretation: it depends on how much extra health that unit produces (g′(m)) and how much utility health provides (U_H). If either falls, MUₘ decreases

 How do you interpret the (Marshallian) demand curve for medical care?

It shows the relationship between the price of medical care (pₘ) and the quantity demanded (m)*, holding income and preferences constant.
The curve slopes downward because of diminishing marginal utility and substitution between m and X

Between H and X, why do we use an Edgeworth box to characterize optimal levels? What is the typical shape, and under what condition does equilibrium occur?

• We use it to illustrate efficient trade-offs between health (H) and other goods (X).

• Indifference curves are convex; the health production isoquants show combinations of inputs yielding equal H.

• Equilibrium occurs when MRSₓₕ = MRTₓₕ, i.e., the rate at which a consumer is willing to trade X for H equals the rate at which H can be produced by giving up X.

Do we also use an Edgeworth box between m and X? Why or why not?

No — m is an input, not a direct source of utility.
We analyze m and X with a budget constraint (not an Edgeworth box) because m and X are purchased goods, not final goods jointly producing utility.

 In the model between H and X, what happens to equilibrium when the person becomes sick?

A decrease in health shifts the starting point along the H-axis leftward.
The person’s marginal utility of health rises (MU_H↑), leading to a new equilibrium with higher desired H relative to X — more resources are allocated toward regaining health

In the model between m and X, what happens to equilibrium when the person becomes sick?

Illness increases the marginal benefit of medical care (g′(m)↑), shifting the demand for m outward.
At the same price, the person demands more medical care to restore health.

 In the model between m and X, what happens when the person becomes sick and income decreases?

Illness effect: raises desired m (more care needed). 

 What does the expansion path represent?

The set of tangency points between budget lines and indifference curves as income changes.
It traces optimal combinations of m and X (or H and X) at different income levels, showing how consumption changes with income

What is the typical shape of the Engel curve for H and m?

• For H (health): concave — as income rises, additional income yields smaller health gains.

• For m (medical care): convex — health spending rises more than proportionally with income, as it is often a normal or luxury good

How do the sanitation effect, fast lane effect, and health spa effect shape the Engel curves?

• Sanitation effect: at higher income, people live in cleaner environments, needing less medical care → flattens Engel curve for m.

• Fast lane effect: rich people buy faster or higher-quality care, increasing m → steepens Engel curve.

• Health spa effect: high income allows healthier lifestyles, reducing m but increasing H

How do you derive the demand curve for medical care from the m–X model, and why do we focus on m rather than H?

• Hold preferences and income constant, vary pₘ, and record optimal m* for each price.

• Plot (pₘ, m*) to obtain the individual demand curve.

• We focus on m because it’s observable and purchasable, while H (health) is an unpriced, derived outcome

How does an increase in income affect the demand curve for medical care, and why?

An income rise shifts the demand curve for m to the right.
Medical care is a normal good — higher income allows more spending on it, increasing demand at each price

How do illnesses with different severity levels affect the demand curve for medical care?

• Mild illness: flatter (more elastic) demand — care is more price-sensitive.

• Severe illness: steeper (less elastic) demand — care becomes essential and less responsive to price

How is the aggregate demand curve derived?

By horizontally summing all individual demand curves — i.e., summing quantities demanded at each price level.
Aggregate demand shifts when population health, income, or illness distribution changes

What is the difference between simple linear regression and multiple linear regression?

• Simple linear regression explains the relationship between one dependent variable (y) and one independent variable (x):

• Multiple linear regression includes two or more explanatory variables to isolate partial effects:  Adding regressors helps control for confounding influences

What is the key assumption about the residual term (ε) required for linear regression estimation? What does the assumption imply?

The crucial assumption is exogeneity: It means the unobserved error is uncorrelated with every regressor.
Implication → OLS estimates are unbiased and consistent because deviations in y are driven only by X, not omitted factors

Does the estimate of βⱼ from linear regression always represent the causal effect of xⱼ on y?

No. βⱼ is causal only if the exogeneity assumption holds.
If any regressor is correlated with the error (e.g., omitted variables, reverse causality, measurement error), βⱼ captures both the true causal impact and bias.

How do you interpret the magnitude of βⱼ for a continuous independent variable xⱼ in

βⱼ = expected change in y from a one-unit increase in xⱼ, holding all other x’s constant.
Units: same as the dependent variable per unit of xⱼ.

 How do you interpret βⱼ for a binary independent variable xⱼ in the same model?

If xⱼ = 1 for a group and 0 otherwise, βⱼ represents the difference in the conditional mean of y between that group and the base group, holding other variables fixed.
Example: if xⱼ = 1 for insured and 0 for uninsured, βⱼ is the average difference in y (e.g., medical spending) between insured and uninsured.

When does the perfect collinearity problem occur?

Perfect collinearity arises when one regressor is an exact linear combination of others (e.g., x₃ = x₁ + x₂).
Then X′X is singular, OLS can’t compute unique estimates, and one variable must be dropped.

How do you interpret βⱼ when a binary xⱼ represents one of multiple categories?

It measures the difference from the omitted (reference) category.
Example: if race dummies include White, Black, Hispanic, and “White” is omitted, β_Black = mean difference (Black − White).

How do you interpret βⱼ when the dependent variable is logged and xⱼ is a binary variable?

 Then 100⋅βj100 · β_j100⋅βj​ ≈ the percent difference in y between the group with xⱼ = 1 and the baseline group (for small βⱼ).
Example: β_j = 0.05 → ≈ 5 % higher y on average.

How do you interpret βⱼ when both y and xⱼ are logged?

 βⱼ is an elasticity — the percent change in y from a 1 % change in xⱼ.
If βⱼ = 0.8, a 1 % increase in xⱼ raises y by 0.8 %.

 How is R-squared defined, and how is its value interpreted?

where SSR = sum of squared residuals, SST = total sum of squares.
It measures the proportion of variation in y explained by the model (values 0–1).
High R² ⇒ strong fit; low R² ⇒ most variation remains unexplained.

 What is health insurance, and what characteristics of healthcare services make people want to have it?

Health insurance is a contract between an individual and an insurer that covers part of the person’s medical expenses in exchange for a periodic payment (the premium).
People want it because:

• Medical needs are uncertain – illnesses and accidents occur unpredictably.

• Medical expenses are large – costs can exceed income.
  Insurance therefore spreads financial risk across many people and protects against catastrophic loss
  

What is the main reason for including cost-sharing for health insurance plans?

Cost-sharing (deductibles, copays, coinsurance) exists to reduce overuse of medical services that arises once care feels “free.”
It curbs moral hazard – the tendency to consume more care when someone else pays most of the bill

 What are the main types of cost-sharing, and how do they differ?

• Deductible: amount the insured must pay out-of-pocket before insurance begins to pay.

• Copayment: fixed dollar charge per service (e.g., $20 per visit).

• Coinsurance: the patient pays a fixed percentage of the cost after the deductible (e.g., 20 %).

• Indemnity payment: insurer pays a fixed cash benefit to the patient regardless of actual cost

How does non-zero coinsurance affect the demand curve for medical care, and why? What does this imply about elasticity under insurance coverage?

With coinsurance = C > 0, the consumer pays C · p while the insurer pays (1 − C) · p.
The demand curve rotates clockwise (becomes steeper) because the patient faces a lower effective price.
Elasticity falls – consumers become less price-sensitive since they no longer bear the full cost

What happens to the demand curve and elasticity when the coinsurance rate is zero?

If C = 0 (full insurance), the patient pays nothing out-of-pocket.
Demand becomes perfectly inelastic up to the level of maximum need—quantity is determined by health status rather than price. Elasticity ≈ 0.

How does an indemnity payment affect the demand curve for medical care?

An indemnity plan pays a fixed cash benefit per illness or service.
It shifts demand upward (patients have more income to spend) but does not change the slope, since the marginal price of care remains the same.

What is a deductible, and what is the motivation for using it?

A deductible (D) is the threshold of total spending that the insured must pay before coverage starts.
Motivation:

• Limits insurer payments to larger, less frequent claims.

• Reduces small, potentially unnecessary claims.

• Encourages price-sensitive behavior for minor illnesses
  

How does a deductible affect quantity demanded for people with illness severity below D?

They pay the full price for all care, so their demand behaves like uninsured consumers – lower quantity, more price-elastic.

How does a deductible affect quantity demanded for people with high severity (expenditure > D)?

Once spending passes D, the patient’s out-of-pocket price drops to the coinsurance rate (C · p).
Demand becomes less elastic and quantity rises sharply beyond that point.

How does a deductible affect those with moderate severity, whose expenses may or may not exceed D? Will they choose m* (where p · m* = D)?

Moderate-severity patients compare total consumer surplus below and above D:

• If the gain from extra covered care > extra cost to reach D, they’ll spend past m*.

• If not, they’ll stop short.
  They almost never stop exactly at m*; equilibrium lies just below or above depending on surplus comparison.
  

How does the utility function behave with respect to income for risk-averse individuals?

Utility of income is increasing and concave: Marginal utility of income declines as income rises, reflecting dislike of risk.

 Between an expected income of $40 000 and a guaranteed $40 000 with certainty, which does a risk-averse person prefer, and why?

They prefer the guaranteed $40 000, because certainty yields higher expected utility than a risky prospect with the same expected value.

 What is the risk premium? How is it related to the reservation price for insurance? How is it found using expected utility?

The risk premium is the maximum amount a person will pay above the actuarially fair premium to avoid risk.
Graphically, it’s the gap between expected income and the certainty-equivalent income that gives equal utility:

That extra payment equals the person’s reservation price for full insurance.

.What two factors determine the size of the risk premium, and how do they influence it?

1. Degree of risk aversion: More curvature (more concave U) → larger premium

2. Variance of loss: Greater potential loss → larger premium, since risk is costlier to bear.