Health Economics – Homework 2 1. A clean water project in developing country… 1 answer below »

Health Economics – Homework 2 1. A clean water project in developing country would affect the health of a village of 500 people (100 children, 300 workers, and 100 elderly people). The project’s immediate implementation would cost $70, 000. It has been estimated that the project would improve the health of workers so that workers can work an extra 200 hours per year, starting next year, 2013. Five years down the road (in 2018) the central government will clean up all the water of the entire country for “free”. The village produces only one good: meat, which is sold in the world market for $4 per pound. The production function for annual meat output is: Y = 10 * Kˆ(1/2) * Lˆ(1/2), where Y is output of meat in pounds, K is capital and L is labor measured in worker hours. The village’s capital stock is constant at 1, 000 every year and a worker’s annual labor hours are 1, 500. The current interest rate is stable at 8% and is projected to increase to 10% in 3 years (in 2016). Use CBA and investigate whether to implement the clean water project or not. Carefully describe every step in your analysis. (a) HINTS: Calculate the current annual output of the village in $s (b) Calculate the annual output of the village if the water project would be installed in $s (c) Calculate the “extra” output due to the water project. Think carefully about the time horizon that extra benefits are realized and properly discount these benefit streams. Use the appropriate discount factors. (d) What is the present value of benefits and what is the present value of costs (all in $). (e) If you make assumptions, carefully describe them and explain why you make such an assumption! 2. Pritchett and Summers argue that income per capita is strongly and positively related to health status when viewed across the world. The following table presents data from the year 2000. Country GDP per capita Health Expenditure per capita Life expectancy Albania 3600 144 72 Bangladesh 1590 57 61 Brazil 7300 482 67 China 3920 176 70 Ethiopia 660 27 42 Germany 24920 2642 77 Nigeria 800 22 47 Russia 8010 368 66 USA 34100 4433 77 Plot a graph of GDP per capita against life expectancy for the countries shown. Does your plot confirm the Pritchett and Summers finding? 3. Suppose a firm has the following production technology for goods 1 and 2: Good 1 Good 2 Both Q1 Cost Q2 Cost Q1 Q2 Cost 10 $50 10 $60 10 10 $100 20 $100 20 $100 20 20 $180 30 $150 30 $130 30 30 $250 1 (a) Does Good 1 indicate economies of scale? Why? (b) Does Good 2 indicate economies of scale? Why? (c) Do the two goods indicate economies of scope? Why? 4. Consider the budget set of an individual who consumes health care (HC) and all other goods (OG). Set up the equation first. Then draw the budget set, clearly mark the intercept with the axes, and also draw an optimal point into this budget set using an indifference curve. Now assume that the same individual purchases a health insurance contract with a 30% coinsurance rate at a premium p. Set up the equation of the individuals new budget constraint. Draw this constraint into the old graph, then re-optimize using the indifference curve (this is only a graphical analysis). Determine what happens in the new equilibrium. Does the individual buy more or less of OG. Does the individual buy more or less of HC. Explain why. 5. Repeat exercise one and assume the income is $50, 000. The price of a unit of health care is $225 and the price of a unit of OG is $340. The insurance premium is $5, 000 and the coinsurance rate is still 30%. Draw all graphs again and be precise with the budget constraints. You know that in equilibrium the individual buys 120 units of HC. Find the optimal point and draw the indifference curve. Then draw the new budget constraint with the insurance and re-optimize. The re-optimization is just graphical, you do not have to calculate anything for that. 6. Budget Sets and Full Price Elasticity. (a) Suppose that Martha’s income is $40,000 per year. She can spend it on health care visits, which cost $80 per visit, or on groceries (standing for all other goods), which cost $100 per bag of groceries. Draw Martha’s budget constraint. Using indifference curves, show Martha’s optimum if she buys 300 bags of groceries per year. (b) Suppose that Martha’s income rises to $42, 000 per year, and that she increases her consumption of health care visits by five visits. Using the graphs for exercise 1, draw the new equilibrium. What is her income elasticity of demand for health care visits? 7. Health capital and healthy time (a) Suppose that John Smith gets promoted to a job that causes two changes to occur simultaneously: (i) John earns a higher wage, and (ii) a safer environment causes his health to depreciate less rapidly. How would these two changes together affect John’s desired health capital? (b) Suppose that John could work 365 days per year and could earn $200 per day for each day he worked. Draw his budget line with respect to his labor-leisure choice. (c) Suppose that John chooses to work 200 days per year. Draw the appropriate indifference curve, and note his equilibrium wage income and labor-leisure choices. (d) Suppose, as in exercise (c), that John’s wage rises from $200 to $210 per day. Show how his equilibrium level of income and labor-leisure will change. (e) Suppose that John is ill 10 days per year. Draw the impact of this illness on the equilibrium defined in exercise 5. How will it change his equilibrium allocation of earnings and labor-leisure? 8. Answer the following questions related to the Grossman model: 2 (a) Explain the difference between health being considered as (i) investment good and as (ii) consumption good. (b) One can derive a demand function for health and for medical services from the Grossman model. Explain the differences between the two demand functions. Why does demand for health and for medical services depend on age? (c) In richer countries, expenditure on medical services is higher. Explain this fact using the Grossman model. 9. Moral Hazard: Read the article by Pauly (1968) that is posted under reading assignments. Explain why on page 533 in Pauly (1968) the individual would have to pay 112.5 MC for the insurance policy. 10. Patient A buys 4 doctor visits at $20 a visit and 6 visits at $10 a visit. What is the price elasticity of his demand for visits? If in addition to the money price he has to spend $30 in waiting and commuting, what is the full price elasticity? The latter factors in the “total price” of a doctor visits. References: Pauly, Mark, V. (1968), “The Economics of Moral Hazard: Comment,” The American Economic Review, vol. 58, p. 531-537. 3

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