1. The demand and supply curves for health care services are given by the following functions:
D=20000-2P, where D is the quantity of services demanded in a year and P is the price per unit of the services. The supply curve is S=-4000+ 4P.
(a) Find the equilibrium quantity and price. What is the total health expenditure on the services considered in the demand-supply functions?
(b) A new insurance plan has been introduced in the country. The insurance is provided free of cost (zero premium) but the individuals covered must pay 50% of health care cost at the point of delivery. Find the new equilibrium quantity and price after the introduction of the insurance plan. What happens to total health expenditures on these services after the introduction of the insurance plan?
(c)In this health care market, assume that there are 2000 consumers (demand curve for each is exactly identical). Derive the individual demand curve from the market demand curve given above (D=20000-2P). Rather than introducing coinsurance, assume that the health insurance was offered to all with a deductible of $12,000 and once the deductible is satisfied, all services are provided to the individual at zero coinsurance and copayments. Find the market equilibrium after the introduction of deductible compared to no-insurance situation.
2. The physician care market is often assumed as "monopolistic competition" market. Draw a hypothetical demand curve for a physician and the average cost and marginal cost of producing physician services (assume standard U-shaped average cost curve).
(a) In the diagram, show the market equilibrium fee and quantity of services sold by the physician when the physician is operating in a monopolistic competition environment. Show the income of the physician in the diagram.
(b) In another diagram, using the same average cost and marginal cost curves (same as the ones drawn for section (a) above), show the market equilibrium quantity if the physician is operating in a perfectly competitive market with market fee below the fee charged by the physician in the monopolistic competition market.
(c) Now, assume that the physician is a perfectly discriminating monopolist. Using the same curves used in section (a) above, find the market equilibrium quantity and fee for the physician. In the diagram, show the income earned by the physician and compare this income with the income earned if the physician was in a monopolistic competitive market.
3. Over the last 10 years, the price of hospital care (out-of-pocket expenses) has declined by 12%, income of the population has increased by 20%, and proportion of elderly in the population increased by 19%. Own price elasticity of hospital care is -0.17, income elasticity of hospital care is +0.29 and elasticity of hospital care with respect to changes in proportion of elderly is +0.8. If the hospital care cost per capita in 2003 was $1,900, predict the hospital cost in 2013 (in 2003 prices) because of changes in these three factors (use point elasticity formula). The CPI value in 2003 was 190 and the value of CPI in 2013 was 260. Find the hospital cost per capita in 2013 in terms of 2013 prices.
4. The population of five different areas of a country with the per-capita income levels are shown in the table below. If the physician location decision is based on income maximization, find the distribution of 700 physicians among these five areas. To find the physician distribution, assume that all physicians are identical and they share the whole market demand in the market with other physicians equally. The size of the market (expressed as an index of demand) is determined by two factors: number of population in the area and the per-capita income of the population. To distribute the physicians among these five areas, we have to develop an index of "demand" for each area. Since the index can be derived by using a specific area's income per capita as the "reference", define an area from these five areas as the reference. Calculate the percent deviation of income per capita of all areas from the income per capita of the reference area. If the income elasticity of demand of physician services is 0.6, calculate the percent increase in demand expected because of income factor (compared to the reference) and define total demand as: population of the area plus population of area multiplied by the fraction of demand increase expected due to income deviation from the reference area. Find the physician distribution among the five areas again if the number of physicians in the country increases to 1200. What is the minimum number of physician supply needed to ensure that at least two physicians will locate in the poorest area of the country? [Show all your calculations step by step including percent deviation of income from reference income, two components of demand index for each area, distribution of physicians among the five areas, etc. Describe the method of calculating geographic distribution of physicians].
|
Area
|
Pop
|
Income/cap
|
|
A
|
9,955,900
|
49500
|
|
B
|
3,150,500
|
40100
|
|
C
|
35210
|
18100
|
|
D
|
20700
|
17900
|
|
E
|
10300
|
17500
|
5. Draw the average and marginal cost functions of a hospital. Assume that the hospitals are operating in a competitive market so that they are "price-takers". Using the diagram, derive the supply curve of the hospital if the hospital's objective is "profit-maximization". Derive the supply curve for the hospital if the hospital's objective is "output maximization without incurring a loss". Show the derivation of the supply curves by assuming at least three different market prices of hospital services. After deriving the supply curves, describe the supply behavior of profit maximizing and not-for-profit hospital and their price sensitiveness in the market (i.e., how sensitive is supply to price changes).