Suppose a hospital is planning about how many patients to treat over the next two years. One key factor the hospital needs to consider in its planning is that hospitals that see many patients in one year have lower costs of care in subsequent years. Let p be the price of hospital care, let q₁ be the number of patients the hospital treats in year one, let q2 be the number of patients the hospital treats in year two, and let c₁ and c₂ be the hospital's per-patient cost in years one and two. The hospital's profits over the two year period are: II (pi-c1)q1+(p2-2)92 The hospital takes p1 and p2 as fixed and they choose q₁ and q2 to maximize profits, II. (1) 1. Suppose, as a warm up exercise, that there is no learning by doing, and that the unit cost functions are as follows: c₁ = 2 and c₂ = 22. Is the cost of caring for patients increasing or decreasing in the number of patients seen? Derive the supply function in periods one and two for the hospital. [Hint: Substitute the unit cost functions into the profit functions and take the derivative of II with respect to 91 and 92]. 2. Let us introduce learning-by-doing into the problem. Now, the unit costs in period two are lower if the hospital has a higher number of patients seen in period one. The unit cost function in period one is still c₁ = 21, but the unit cost function in period two now depends also on 2 6 the number of patients seen in period one: c₂ = Derive the supply function in periods 291' one and two for the hospital. [Hint: Solve first for the optimal 92 taking 91 as given. Then use your expression for q; in your expression for qj.] 3. Should the hospital see more or fewer patients in period one if there is learning-by-doing?
Suppose a hospital is planning about how many patients to treat over the next two years. One key factor the hospital needs to consider in its planning is that hospitals that see many patients in one year have lower costs of care in subsequent years. Let p be the price of hospital care, let q₁ be the number of patients the hospital treats in year one, let q2 be the number of patients the hospital treats in year two, and let c₁ and c₂ be the hospital's per-patient cost in years one and two. The hospital's profits over the two year period are: II (pi-c1)q1+(p2-2)92 The hospital takes p1 and p2 as fixed and they choose q₁ and q2 to maximize profits, II. (1) 1. Suppose, as a warm up exercise, that there is no learning by doing, and that the unit cost functions are as follows: c₁ = 2 and c₂ = 22. Is the cost of caring for patients increasing or decreasing in the number of patients seen? Derive the supply function in periods one and two for the hospital. [Hint: Substitute the unit cost functions into the profit functions and take the derivative of II with respect to 91 and 92]. 2. Let us introduce learning-by-doing into the problem. Now, the unit costs in period two are lower if the hospital has a higher number of patients seen in period one. The unit cost function in period one is still c₁ = 21, but the unit cost function in period two now depends also on 2 6 the number of patients seen in period one: c₂ = Derive the supply function in periods 291' one and two for the hospital. [Hint: Solve first for the optimal 92 taking 91 as given. Then use your expression for q; in your expression for qj.] 3. Should the hospital see more or fewer patients in period one if there is learning-by-doing?
Chapter17: Income, Poverty, And Health Care
Section: Chapter Questions
Problem 13P
Related questions
Question
![Suppose a hospital is planning about how many patients to treat over the next two years. One key
factor the hospital needs to consider in its planning is that hospitals that see many patients in one
year have lower costs of care in subsequent years. Let p be the price of hospital care, let q₁ be
the number of patients the hospital treats in year one, let q2 be the number of patients the hospital
treats in year two, and let c₁ and c₂ be the hospital's per-patient cost in years one and two. The
hospital's profits over the two year period are:
II (pi-c1)q1+(p2-2)92
The hospital takes p1 and p2 as fixed and they choose q₁ and q2 to maximize profits, II.
(1)
1. Suppose, as a warm up exercise, that there is no learning by doing, and that the unit cost
functions are as follows: c₁ = 2 and c₂ = 22. Is the cost of caring for patients increasing
or decreasing in the number of patients seen? Derive the supply function in periods one and
two for the hospital. [Hint: Substitute the unit cost functions into the profit functions and
take the derivative of II with respect to 91 and 92].
2. Let us introduce learning-by-doing into the problem. Now, the unit costs in period two are
lower if the hospital has a higher number of patients seen in period one. The unit cost function
in period one is still c₁ = 21, but the unit cost function in period two now depends also on
2
6
the number of patients seen in period one: c₂ = Derive the supply function in periods
291'
one and two for the hospital. [Hint: Solve first for the optimal 92 taking 91 as given. Then
use your expression for q; in your expression for qj.]
3. Should the hospital see more or fewer patients in period one if there is learning-by-doing?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10fa051a-d9bc-4043-b538-02be11dabc4b%2Fd7233e04-5852-48af-8f8b-43ddc688230b%2F5xq1jfd_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose a hospital is planning about how many patients to treat over the next two years. One key
factor the hospital needs to consider in its planning is that hospitals that see many patients in one
year have lower costs of care in subsequent years. Let p be the price of hospital care, let q₁ be
the number of patients the hospital treats in year one, let q2 be the number of patients the hospital
treats in year two, and let c₁ and c₂ be the hospital's per-patient cost in years one and two. The
hospital's profits over the two year period are:
II (pi-c1)q1+(p2-2)92
The hospital takes p1 and p2 as fixed and they choose q₁ and q2 to maximize profits, II.
(1)
1. Suppose, as a warm up exercise, that there is no learning by doing, and that the unit cost
functions are as follows: c₁ = 2 and c₂ = 22. Is the cost of caring for patients increasing
or decreasing in the number of patients seen? Derive the supply function in periods one and
two for the hospital. [Hint: Substitute the unit cost functions into the profit functions and
take the derivative of II with respect to 91 and 92].
2. Let us introduce learning-by-doing into the problem. Now, the unit costs in period two are
lower if the hospital has a higher number of patients seen in period one. The unit cost function
in period one is still c₁ = 21, but the unit cost function in period two now depends also on
2
6
the number of patients seen in period one: c₂ = Derive the supply function in periods
291'
one and two for the hospital. [Hint: Solve first for the optimal 92 taking 91 as given. Then
use your expression for q; in your expression for qj.]
3. Should the hospital see more or fewer patients in period one if there is learning-by-doing?
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