Q1. Suppose the production function for average health (H) in Canada is H = f(C; L), where C is percentage of GDP devoted to health care and L is a measure of healthy lifestyle. Assume this function increases at a decreasing rate in both its arguments. Assume that the United States faces exactly the same production function.
(a) Sketch a diagram showing the relationship between H and C in Canada, for a given level of L, L = LC. Below this diagram, display the associated marginal product of health care in another diagram.
(b) Assume that in the U.S. lifestyle takes the level L = LUS where LC > LUS. Draw a relationship between health and health care in the U.S. on your diagram. Below this diagram, display the associated marginal product of health care in another diagram.
(c) Label points in your diagram consistent with the observation that Canada has higher average health but lower health care expenditures as a percentage of GDP than the U.S.
(d) In this model under these assumptions, is health care in Canada more efficient than health care in the U.S.? Briefly explain.
Q2. Assume that for every person, health (h) is determined by income (y) and by a genetic factor (g) through the production function: h = 0.5y + 2g.
(a) What is the causal effect of a one unit increase in income on health in this society?
(b) Sketch a diagram displaying production functions for health, with income on the horizontal and health on the vertical axis, for Fred who is endowed with g = 0, and for Bill, who is endowed with g =1.
(c) Suppose income is determined by the same genetic factors as health:
y = 3-2g
Label the health-income outcomes for Fred and for Bill on your diagram.
(d) Show that increases in income in this society are associated with decreases in health. Very briefly y reconcile your answers to (a) and (e). (Hint: why is it that correlation, does not always imply causation?)
Q3. Sam's preferences for income (Y) and leisure (TB) can be expressed as:
U(Y, TB) = 300 + 2Y TB - 67 Y - 100 TB
Out of the 365 days in the year, Sam devotes TH0=60 days to health production and spends TL0=15 days sick. The rest of the days are available to split between work and leisure. Sam earns $100 per day after taxes.
(a) Derive the equation for Sam's budget constraint and graph his budget line labeling as many points as you can.
(b) Derive the equation for Sam's marginal rate of substitution between income (Y) and leisure (TB).Does the property of diminishing marginal utility hold? Why?
Does the property of diminishing marginal rate of substitution hold? Why?
(c) Write the optimization problem for the consumer and find the optimal allocation of time to market work (Tw) and Leisure (TB), the optimal level of income, and the utility at the optimal point. Graph your result labeling as many points as you can.
(d) Suppose now that Sam's daily wage increases to $120. Show how his equilibrium level of income and leisure-work choice would change. Graph your result labeling as many points as you can.
(e) Go back to the baseline wage of $100. Suppose Sam increases the days to health production to TH1=70 and is able to lower the sick days to TL1=10 days. Show how his equilibrium level of income and leisure-work choice would change. Graph your result labeling as many points as you can. Is Sam better off or worse off, explain.
Q4. Sarah is an 18 year old high school graduate working at McDonalds. The depreciation rate of her health is given by δ18 , the interest rate at which he could save money is given by r, and her wage is Whs,
(a) Show graphically how Sarah's optimal health capital stock is determined in the Grossman model.
(b) Suppose Sarah decides to invest in university education, hoping to achieve a better job and higher salary. Show how her optimal health capital stock changes when she is 22 years old due to the higher salary.
(c) Now show how education could affect her optimal health stock if education also made her a more efficient producer of health.
(d) Suppose Sarah gets the new job, which in addition to the higher salary, has a healthier environment causing her health to depreciate more slowly. How would this affect Sarah's desired level of health capital? Explain
(e) Can the Grossman model explain the empirically observed positive correlation between education and health status? Explain. What are some other explanations?
(f) Suppose that from the age of 22 her salary does not change. Show what happens to Sarah's optimal health stock as she gets older, assuming that the depreciation rate of her health increases with age.