Jane has a budget of I dollars and is deciding how to invest over the three healthcare-related out-of- pocket spending categories: (1) preventive care, (2) dental care, and (3) chronic disease management. Denote the price of health investment in category 1, 2, and 3 as P1, P2, and P3 respectively; denote the quantity of health consumption in category 1, 2, and 3 as M1, M2, and M3, respectively. (a) Suppose the utility function of Jane is U(M₁, M₂, M³) = MM² Mr. Set up the Lagrange constrained optimization problem and write down the budget constraint. (b) Solve for Jane's optimal health investment quantity in category 1 (preventative care), 2 (dental care), and 3 (chronic disease management). (c) Provide an economic intuition of parameters a, ẞ, and y.

EBK HEALTH ECONOMICS AND POLICY
7th Edition
ISBN:9781337668279
Author:Henderson
Publisher:Henderson
Chapter4: Economic Evaluation In Health Care
Section: Chapter Questions
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Jane has a budget of I dollars and is deciding how to invest over the three healthcare-related out-of-
pocket spending categories: (1) preventive care, (2) dental care, and (3) chronic disease management.
Denote the price of health investment in category 1, 2, and 3 as P1, P2, and P3 respectively; denote the
quantity of health consumption in category 1, 2, and 3 as M1, M2, and M3, respectively.
(a) Suppose the utility function of Jane is U(M1, M2, M3) = M{ M, M. Set up the Lagrange
constrained optimization problem and write down the budget constraint.
(b) Solve for Jane's optimal health investment quantity in category 1 (preventative care), 2 (dental
care), and 3 (chronic disease management).
(c) Provide an economic intuition of parameters a, B, and y.
(d) Now suppose the government offers Mf unit of free annual teeth cleaning through public health
insurance coverage, where Mf > 0. The quantity of dental care consumption for Jane is now
Mrew = M2 + Mf. How much out-of-pocket spending quantity will Jane allocate to dental care
category, i.e., what is the M2 quantity with the provision of free annual teeth cleaning?
Transcribed Image Text:Jane has a budget of I dollars and is deciding how to invest over the three healthcare-related out-of- pocket spending categories: (1) preventive care, (2) dental care, and (3) chronic disease management. Denote the price of health investment in category 1, 2, and 3 as P1, P2, and P3 respectively; denote the quantity of health consumption in category 1, 2, and 3 as M1, M2, and M3, respectively. (a) Suppose the utility function of Jane is U(M1, M2, M3) = M{ M, M. Set up the Lagrange constrained optimization problem and write down the budget constraint. (b) Solve for Jane's optimal health investment quantity in category 1 (preventative care), 2 (dental care), and 3 (chronic disease management). (c) Provide an economic intuition of parameters a, B, and y. (d) Now suppose the government offers Mf unit of free annual teeth cleaning through public health insurance coverage, where Mf > 0. The quantity of dental care consumption for Jane is now Mrew = M2 + Mf. How much out-of-pocket spending quantity will Jane allocate to dental care category, i.e., what is the M2 quantity with the provision of free annual teeth cleaning?
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