Chapter 7: Medical Care Production and Costs   Health Economics
Assessing the Productivity of Medical Firms <ul><li>Economists often describe production of output as a function of labor ...
Assessing the Productivity of Medical Firms (cont.) <ul><li>Short run :  k   is fixed, while  n  is variable </li></ul>a) ...
Graphical Representation Total product =  q  =  f(n,k*) MP =   q   /   n <ul><li>MP is the slope of the TP curve . </li>...
Graphical Representation AP =  q   /   n <ul><li>AP is the slope of a ray from the origin to the TP curve. </li></ul>TP B ...
Numerical Example 60 10 3 30 10 2 10 10 1 --- --- 0 10 0 MP of n (  q/  n ) AP of n ( q/n ) Total output ( q ) Amount of...
<ul><li>People living in Boston are hospitalized about 1.5 times as often as those living in New Haven, However, the healt...
Substitutability in Production of Medical Care <ul><li>There may be more than one way to produce a given level of health c...
Substitutability in Production of Medical Care (cont.) <ul><ul><li>Elasticity of substitution : </li></ul></ul><ul><ul><li...
Production Function for Hospital Admissions <ul><li>Jensen and Morrisey (1986) </li></ul><ul><ul><li>Sample : 3,450 non-te...
Results <ul><li>Each additional physician generated 6.05 more  admits per year. </li></ul><ul><li>Nurses by far the most p...
Results (cont.) <ul><li>Each inputs is a substitute for other in production process. </li></ul><ul><li>If wages of nurses ...
Medical Care Cost <ul><li>Explicit costs of doing business. </li></ul><ul><ul><li>e.g. staff payroll, utility bills, medic...
Medical Care Cost (cost.) <ul><li>i.e. opportunity costs. </li></ul><ul><ul><li>e.g. opportunity cost of a facility being ...
Recall <ul><li>Given a production function : </li></ul><ul><li>q  =  f (n,k) </li></ul><ul><li>q  =  hospital services </l...
Short-Run Total Cost cost hospital service STC(  q  )   =  w n + r k* w  = wage rate for nurses  r  = rental price of capi...
Short-Run Total Cost  (cont.) STC(  q  )   =  w n + r k* <ul><li>In the short run,  k  is fixed. </li></ul><ul><ul><li>  ...
Short-Run Total Cost (cont.) <ul><li>Recall : Production function initially exhibits IRTS </li></ul><ul><ul><li>Total cost...
Marginal and Average Costs SMC =   STC  q =   ( wn + rk *)/  q =  w (  n /  q ) =  w (1/MP n ) =  w /MP n The short ...
Marginal and Average Costs  (cont). SAVC =  STVC q = ( wn) / q =  w (1/AP n ) =  w /AP n The short average variable cost o...
Graphing Marginal and Average Costs Costs q 0 q 0 SMC SATC SAVC SAVC 0 SATC 0 SMC 0
Graphing Marginal and Average Costs <ul><li>SATC and SAVC are u-shaped curves. </li></ul><ul><ul><li>Increasing returns to...
Relating Product and Cost Curves n q MP n AP n Cost n 1 n 3 0 MP n AP n SMC SAVC q 1 q 3
Average and Marginal Co (cont.) <ul><li>IRTS followed by DRTS in production leads to U  shaped AC curve.   </li></ul><ul><...
Determinants of Short-run Costs (cont.) <ul><li>5 different measures of q  inputs </li></ul><ul><li>ER care nursing labor ...
Findings <ul><li>Found short run economies of scale </li></ul><ul><ul><li>Hospitals operate to left of min. on AVC curve. ...
Findings (cont.) <ul><li>Definition : Economies of scope </li></ul><ul><ul><li>Cost of producing 2 outputs < sum of cost o...
Cost-minimizing input choice <ul><li>Example  </li></ul><ul><li>-  Health care providers’ choice of nursing staff mix.  </...
Cost Minimizing Input Choice <ul><li>Costs are minimized when: </li></ul><ul><li>Suppose that instead: </li></ul><ul><ul><...
Are physicians “costly” to hospitals?  <ul><li>Physicians bill insurers or their patients for care. </li></ul><ul><ul><li>...
Are physicians “costly” to hospitals? (cont.) <ul><li>Can solve for “shadow price” of doctors, if other variables known. <...
Does Higher Quality  Higher Costs? <ul><li>Reducing costs  without sacrificing quality.  </li></ul><ul><ul><li>Improved pr...
Does Higher Quality  Higher Costs? <ul><li>“  In an increasingly competitive environment, hospitals must take a critical l...
Business opportunities in costs <ul><li>Companies which can synthesize complex data to improve quality and restrain cost w...
Business opportunities in costs <ul><li>Express Scripts - </li></ul><ul><li>Practice Pattern Science (PPS)  </li></ul><ul>...
Business opportunities in costs <ul><li>Express Scripts - </li></ul><ul><li>Practice Pattern Science (PPS) (cont.)   </li>...
Business opportunities in costs (cont.) <ul><li>Practice Pattern Science (PPS) subsidiary.  </li></ul><ul><ul><li>Computer...
Long Run Costs of Production <ul><li>In the long run, all inputs are variable. </li></ul><ul><ul><li>k  is no longer fixed...
The Long Run Average Cost Curve Average Cost of Hospital Services # of patients LATC q 0 q 1 q 2
Long Run Costs of Production <ul><li>Just like the short run cost curve, the long run cost curve for a firm is also u-shap...
Long Run Costs of Production <ul><li>The u-shaped long run average cost curve is due to economies of scale and diseconomie...
Long Run Costs of Production <ul><li>Example of specialization and the resulting economies of scale. </li></ul><ul><ul><li...
Long Run Costs of Production <ul><li>Economies of scale  arise due to specialization of labor and/or capital. </li></ul><u...
Long Run Costs of Production <ul><li>Increasing returns to scale </li></ul><ul><ul><li>An increase in all inputs results i...
Long Run Costs of Production <ul><li>Diseconomies of scale  arise when a firm becomes too large. </li></ul><ul><ul><li>e.g...
The Long Run Average Cost Curve Average Cost of Hospital Services # of patients LATC q 0 q 1 q 2 Economies of scale Diseco...
Long Run Costs of Production <ul><li>Decreasing returns to scale </li></ul><ul><ul><li>An increase in all inputs results i...
The Long Run Average Cost Curve under Constant Returns to Scale Average Cost of Hospital Services # of patients
Long Run Costs of Production <ul><li>Like the short run cost curve, a number of factors can cause the short run cost curve...
Long Run Costs of Production <ul><li>Empirical evidence on HMOs and costs. </li></ul><ul><li>See handout. </li></ul>
Computing Profits <ul><li>Recall that the total costs of production for a firm are: </li></ul><ul><li>TC( q ) = w n  + r k...
Computing Profits (cont.) <ul><li>Thus, we can express profits for the firm as: </li></ul><ul><li> ( q ) = TR( q ) – TC( ...
Computing Profits (cont.) <ul><li>Assume that as output increases, total revenue rises at a diminishing rate. </li></ul><u...
Graphing Profits Total dollars Quantity of output ( q ) TC TR q 0 TR 0 TC 0  ( q 0 ) = TR 0  – TC 0 
Graphing Profits Total dollars Quantity of output ( q ) TC TR At what output level(s) does the firm make profits equal to ...
Graphing Profits Total dollars Quantity of output ( q ) TC TR q 0 TR 0 TC 0 Notice that I have plotted  q 0  where the TR ...
Computing Profits (cont.) <ul><li>I have plotted  q 0  at the point where the firm  maximizes  profits. </li></ul><ul><ul>...
Computing Profits (cont.) <ul><li>Recall that the slope of the total cost curve represents marginal costs. </li></ul><ul><...
Computing Profits (cont.) <ul><li>A firm maximizes profits where MR=MC.  Why? </li></ul><ul><li>Suppose the firm was inste...
Graphing Profits Total dollars Quantity of output ( q ) TC TR At  q 1 , the firm should raise output to increase profits. ...
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  1. 1. Chapter 7: Medical Care Production and Costs Health Economics
  2. 2. Assessing the Productivity of Medical Firms <ul><li>Economists often describe production of output as a function of labor and capital : </li></ul><ul><li>q = f(n,k) </li></ul><ul><li>In the case of health care : </li></ul><ul><li>q = hospital services </li></ul><ul><li>n = nurses </li></ul><ul><li>k = medical equipment, hospital building </li></ul>
  3. 3. Assessing the Productivity of Medical Firms (cont.) <ul><li>Short run : k is fixed, while n is variable </li></ul>a) At low level of n, k is abundant. Each in nurses when combined with capital greater in services. - potential synergy effect because nurses can work in teams. b) Further in nurses service, but a decreasing rate - law of diminishing marginal productivity. c) “Too many “ nurses can cause congestion, com- munication problems, hospital services
  4. 4. Graphical Representation Total product = q = f(n,k*) MP =  q /  n <ul><li>MP is the slope of the TP curve . </li></ul>n 1 n 2 hospital services (q) Nurses (n) marginal product nurses TP n 2 n 1
  5. 5. Graphical Representation AP = q / n <ul><li>AP is the slope of a ray from the origin to the TP curve. </li></ul>TP B C A hospital services average product B n 3
  6. 6. Numerical Example 60 10 3 30 10 2 10 10 1 --- --- 0 10 0 MP of n (  q/  n ) AP of n ( q/n ) Total output ( q ) Amount of k # of nurses ( n )
  7. 7. <ul><li>People living in Boston are hospitalized about 1.5 times as often as those living in New Haven, However, the health outcomes of patients in these 2 cities appear to be identical. Does this mean that hospital care has no ability to improve health? </li></ul>Practice Question health outcomes hospitalizations
  8. 8. Substitutability in Production of Medical Care <ul><li>There may be more than one way to produce a given level of health care. </li></ul><ul><ul><li>Licenced practical nurses (LPNs) vs Registered Nurses (RNs) in hospitals. </li></ul></ul><ul><ul><ul><li>LPNs have less training. </li></ul></ul></ul><ul><ul><ul><li>Maybe not as productive, but not as costly. </li></ul></ul></ul><ul><ul><li>Physician assistants vs physicians at ambulatory clinics. </li></ul></ul><ul><ul><ul><li>But physician assistants can’t prescribe meds in most states . </li></ul></ul></ul>
  9. 9. Substitutability in Production of Medical Care (cont.) <ul><ul><li>Elasticity of substitution : </li></ul></ul><ul><ul><li>  = [  (I 1 /I 2 ) / I 1 /I 2 ] : [  (MP 2 /MP 1 ) / MP 2 /MP 1 ] </li></ul></ul><ul><ul><li>% change in input ratio, divided by % change in ratio of inputs’ MPs. </li></ul></ul><ul><ul><li> = 0 no substitutability . </li></ul></ul><ul><ul><li> = perfect substitutability. </li></ul></ul>8 <ul><ul><li>Potential for substitutability If price of 1 input increases, can minimize impact on total costs by substituting away. </li></ul></ul>
  10. 10. Production Function for Hospital Admissions <ul><li>Jensen and Morrisey (1986) </li></ul><ul><ul><li>Sample : 3,450 non-teaching hospitals in 1983. </li></ul></ul><ul><li>q = hospital admissions </li></ul><ul><li>inputs : physicians, nurses, other staff, hospital beds . </li></ul><ul><li>q =  0 +  1 physicians +  2 nurses + …. +  </li></ul><ul><li>Coefficients in regression are MPs. </li></ul>
  11. 11. Results <ul><li>Each additional physician generated 6.05 more admits per year. </li></ul><ul><li>Nurses by far the most productive </li></ul>Annual Marginal Products for Admissions Physicians 6.05 Nurses 20.30 Other Staff 6.97 Beds 3.04 Input MP (at the means)
  12. 12. Results (cont.) <ul><li>Each inputs is a substitute for other in production process. </li></ul><ul><li>If wages of nurses rise, can substitute away by having more hospital beds. </li></ul>Elasticity of Substitution between Inputs Physicians with nurses 0.547 Physicians with beds 0.175 Nurses with beds 0.124 Input pair  Ex. for when  = 8
  13. 13. Medical Care Cost <ul><li>Explicit costs of doing business. </li></ul><ul><ul><li>e.g. staff payroll, utility bills, medical supply costs. </li></ul></ul><ul><li>Necessary for : </li></ul><ul><ul><li>Comparing performance evaluation across providers/depts. </li></ul></ul><ul><ul><li>Taxes </li></ul></ul><ul><ul><li>Government reimbursement/rate setting </li></ul></ul>Accounting Costs
  14. 14. Medical Care Cost (cost.) <ul><li>i.e. opportunity costs. </li></ul><ul><ul><li>e.g. opportunity cost of a facility being used as an outpatient clinic = rent it could earn otherwise. </li></ul></ul><ul><li>Necessary for : </li></ul><ul><ul><li>optimal business planning. </li></ul></ul><ul><ul><li>allows one to consider highest returns to assets anywhere, not just vs. direct competitors, or w/in health care industry. </li></ul></ul>Economic Costs = Accounting Costs
  15. 15. Recall <ul><li>Given a production function : </li></ul><ul><li>q = f (n,k) </li></ul><ul><li>q = hospital services </li></ul><ul><li>n = labor = nurse = n </li></ul><ul><li>k = c apital = medical equipment, hospital </li></ul><ul><li>building </li></ul>
  16. 16. Short-Run Total Cost cost hospital service STC( q ) = w n + r k* w = wage rate for nurses r = rental price of capital short run k fixed w n = variable cost r k = fixed cost . q 0 STC STC w n r k
  17. 17. Short-Run Total Cost (cont.) STC( q ) = w n + r k* <ul><li>In the short run, k is fixed. </li></ul><ul><ul><li> rk* is the same, regardless of the amount of hospital services ( q ) produced. </li></ul></ul><ul><li>As q rises, increases in STC are only due to increases in the number of nurses needed ( n ). </li></ul>
  18. 18. Short-Run Total Cost (cont.) <ul><li>Recall : Production function initially exhibits IRTS </li></ul><ul><ul><li>Total costs rise at decreasing rate up to q 0 </li></ul></ul>q 0 STC STC w n r k cost hospital service <ul><li>After q 0 , DTRS in production costs rise at increasing rate </li></ul>
  19. 19. Marginal and Average Costs SMC =  STC  q =  ( wn + rk *)/  q = w (  n /  q ) = w (1/MP n ) = w /MP n The short run marginal cost of nurses depends on their marginal productivity.
  20. 20. Marginal and Average Costs (cont). SAVC = STVC q = ( wn) / q = w (1/AP n ) = w /AP n The short average variable cost of nurses depends on their average productivity.
  21. 21. Graphing Marginal and Average Costs Costs q 0 q 0 SMC SATC SAVC SAVC 0 SATC 0 SMC 0
  22. 22. Graphing Marginal and Average Costs <ul><li>SATC and SAVC are u-shaped curves. </li></ul><ul><ul><li>Increasing returns to scale followed by decreasing returns to scale. </li></ul></ul><ul><li>SMC passes through the minimum of both SATC and SAVC. </li></ul><ul><ul><li>If marginal cost is greater than average cost, then the cost of one additional unit of output must cause the average to rise. </li></ul></ul>
  23. 23. Relating Product and Cost Curves n q MP n AP n Cost n 1 n 3 0 MP n AP n SMC SAVC q 1 q 3
  24. 24. Average and Marginal Co (cont.) <ul><li>IRTS followed by DRTS in production leads to U shaped AC curve. </li></ul><ul><li>Hospital doesn’t necessarily produce at q* (min. cost). </li></ul><ul><ul><li>Depends on hospital’s objectives. </li></ul></ul><ul><ul><li>Even so, will attempt to stay on the cost curve (not above it). </li></ul></ul>
  25. 25. Determinants of Short-run Costs (cont.) <ul><li>5 different measures of q inputs </li></ul><ul><li>ER care nursing labor </li></ul><ul><li>medical/surgical care auxiliary labor </li></ul><ul><li>pediatric care professional labor </li></ul><ul><li>maternity care administrative labor </li></ul><ul><li>other inpatient care general labor </li></ul><ul><li>materials and supplies </li></ul>Cowing and Holtmann 1981
  26. 26. Findings <ul><li>Found short run economies of scale </li></ul><ul><ul><li>Hospitals operate to left of min. on AVC curve. </li></ul></ul><ul><ul><li>i.e Larger hospitals producing at lower costs than smaller hospitals. </li></ul></ul><ul><li>Best way to reduce aggregate hospital costs? </li></ul><ul><ul><li>Reduce # of hospital beds by a fixed % in all hospitals. </li></ul></ul><ul><ul><li>Close the smallest hospitals in each region. </li></ul></ul>
  27. 27. Findings (cont.) <ul><li>Definition : Economies of scope </li></ul><ul><ul><li>Cost of producing 2 outputs < sum of cost of production 2 goods separately. </li></ul></ul><ul><li>Found Dis economies of scope with respect to ER and other services. </li></ul><ul><ul><li>Larger ER’s may bring in more complex mix of patients to the hospital. OR </li></ul></ul><ul><ul><li>Larger ER’s generate operating challenges for other services (e.g. communication, staffing scheduling). </li></ul></ul>
  28. 28. Cost-minimizing input choice <ul><li>Example </li></ul><ul><li>- Health care providers’ choice of nursing staff mix. </li></ul><ul><li>RN’s care for 6 patients per hour; hourly wage = $20 </li></ul><ul><li>LPN’s care for 4 patients per hour; hourly wage = $10 </li></ul><ul><li>TC( q 0 )=20 RN + 10 LPN </li></ul>If a hospital needs to hire nurses to care for growing patient volume, which should be hired?
  29. 29. Cost Minimizing Input Choice <ul><li>Costs are minimized when: </li></ul><ul><li>Suppose that instead: </li></ul><ul><ul><li>Then the last dollar spent on an LPN generates more output than the last dollar spent on a registered nurse. </li></ul></ul>MP RN w RN = MP LPN w LPN MP RN w RN < MP LPN w LPN
  30. 30. Are physicians “costly” to hospitals? <ul><li>Physicians bill insurers or their patients for care. </li></ul><ul><ul><li>In most cases, physician not paid a wage by a hospital. </li></ul></ul><ul><li>However, physicians generate other hospital costs. </li></ul><ul><ul><li>Review and process physician’s application. </li></ul></ul><ul><ul><li>Monitor physician’s performance. </li></ul></ul><ul><ul><li>Examining rooms and other supplies. </li></ul></ul>MP doc MP n w doc w n
  31. 31. Are physicians “costly” to hospitals? (cont.) <ul><li>Can solve for “shadow price” of doctors, if other variables known. </li></ul><ul><ul><li>w doc = $7,012 per year. </li></ul></ul>
  32. 32. Does Higher Quality Higher Costs? <ul><li>Reducing costs without sacrificing quality. </li></ul><ul><ul><li>Improved production line. </li></ul></ul><ul><ul><li>bedside access to computerized treatment guidelines. </li></ul></ul><ul><ul><li>computerized patient charts. </li></ul></ul><ul><ul><li>Motivated work force. </li></ul></ul><ul><ul><li>involving nurses in case management </li></ul></ul><ul><ul><li>reimburse physicians based on performance evaluations </li></ul></ul>
  33. 33. Does Higher Quality Higher Costs? <ul><li>“ In an increasingly competitive environment, hospitals must take a critical look at their product lines… Many institutions must decide between eliminating or investing in unprofitable product lines” </li></ul><ul><li>Juran Report </li></ul><ul><li>e.g. Hospital may have unprofitable, high quality heart surgery, but kidney surgery may be losing $, lower quality. </li></ul>
  34. 34. Business opportunities in costs <ul><li>Companies which can synthesize complex data to improve quality and restrain cost will survive. </li></ul><ul><li>Express Scripts - </li></ul><ul><li>Pharmacy Benefit Manager (PBM) </li></ul><ul><ul><li>Manages prescription claims on behalf of HMO’s, insurance companies, unions, etc. </li></ul></ul><ul><ul><li>Obtains drug cost savings through drug utilization review, generic substitution, mail-order pharmacy, volume discounts from retail pharmacy. </li></ul></ul>
  35. 35. Business opportunities in costs <ul><li>Express Scripts - </li></ul><ul><li>Practice Pattern Science (PPS) </li></ul><ul><ul><li>An information service company. </li></ul></ul><ul><ul><li>Offers practice variation analysis and disease management support service linking healthcare data from all points of care. </li></ul></ul><ul><ul><li>Complements PBM services </li></ul></ul><ul><ul><li>Be a leader in the development of disease management, provider profiling and outcomes assessment technologies. </li></ul></ul>
  36. 36. Business opportunities in costs <ul><li>Express Scripts - </li></ul><ul><li>Practice Pattern Science (PPS) (cont.) </li></ul><ul><ul><li>Diagnostic Cluster SM Methodology : </li></ul></ul><ul><ul><ul><li>links to a “global” pattern treatment through its patient treatment episodes (PTE TM ) </li></ul></ul></ul><ul><ul><li>Provider Profiling : </li></ul></ul><ul><ul><ul><li>reduce providers practice pattern variation </li></ul></ul></ul><ul><ul><li>Diseases Management Support Service : </li></ul></ul><ul><ul><ul><li>Gatekeeper of patient case mix. </li></ul></ul></ul><ul><ul><ul><li>Scorekeeper for patterns of treatment. </li></ul></ul></ul><ul><ul><li>Pharmaceutical Information : </li></ul></ul><ul><ul><ul><li>Benchmark prescription drug patterns </li></ul></ul></ul><ul><ul><ul><li>Track the composition of prescription drugs </li></ul></ul></ul><ul><ul><ul><li>Report the mean and median global treatment cost </li></ul></ul></ul>
  37. 37. Business opportunities in costs (cont.) <ul><li>Practice Pattern Science (PPS) subsidiary. </li></ul><ul><ul><li>Computerized patient profile database. </li></ul></ul><ul><ul><li>Bars claims if potential dangerous interactions identified. </li></ul></ul><ul><ul><li>Identifies people over-utilizing drugs by visiting multiple doctors. </li></ul></ul>
  38. 38. Long Run Costs of Production <ul><li>In the long run, all inputs are variable. </li></ul><ul><ul><li>k is no longer fixed. </li></ul></ul><ul><ul><li>e.g. A hospital can build a new facility or add extra floors to increase bedsize in the long run. </li></ul></ul><ul><li>If all inputs are variable, what does the long run average cost curve look like? </li></ul>
  39. 39. The Long Run Average Cost Curve Average Cost of Hospital Services # of patients LATC q 0 q 1 q 2
  40. 40. Long Run Costs of Production <ul><li>Just like the short run cost curve, the long run cost curve for a firm is also u-shaped. </li></ul><ul><ul><li>However, the short run cost curve is due to IRTS, then DRTS relative to a fixed input . </li></ul></ul><ul><ul><li>e.g. In the short run, the only way to increase the number of patients treated was to hire more nurses; but the # of beds (k) was fixed. </li></ul></ul><ul><ul><li>But in the long run, there are no fixed inputs. </li></ul></ul>
  41. 41. Long Run Costs of Production <ul><li>The u-shaped long run average cost curve is due to economies of scale and diseconomies of scale. </li></ul><ul><li>Economies of scale </li></ul><ul><ul><li>Average cost per unit of output falls as the firm increases output. </li></ul></ul><ul><ul><li>Due to specialization of labor and capital. </li></ul></ul>
  42. 42. Long Run Costs of Production <ul><li>Example of specialization and the resulting economies of scale. </li></ul><ul><ul><li>A large hospital can purchase a sophisticated computer system to manage its inpatient pharmaceutical needs. </li></ul></ul><ul><ul><li>Although the total cost of this system is more than a small hospital could afford, these costs can be spread over a larger number of patients. </li></ul></ul><ul><ul><li> The average cost per patient of dispensing drugs can be lower for the larger facility. </li></ul></ul>
  43. 43. Long Run Costs of Production <ul><li>Economies of scale arise due to specialization of labor and/or capital. </li></ul><ul><ul><li>That is, the long run relationship between average costs and output reflects the nature of the production process. </li></ul></ul><ul><ul><li>This is why economies of scale (in costs) are can also be referred to as increasing returns to scale (in production). </li></ul></ul>
  44. 44. Long Run Costs of Production <ul><li>Increasing returns to scale </li></ul><ul><ul><li>An increase in all inputs results in a more than proportionate increase in output. </li></ul></ul><ul><ul><li>e.g. If a hospital doubles its number of nurses and beds, it may be able to triple the number of patients it cares for. </li></ul></ul><ul><li>However, most economists believe that economies of scale are exhausted, and diseconomies of scale set in at some point. </li></ul>
  45. 45. Long Run Costs of Production <ul><li>Diseconomies of scale arise when a firm becomes too large. </li></ul><ul><ul><li>e.g. bureaucratic red tape, or breakdown in communication flows. </li></ul></ul><ul><ul><li>At this point, the average cost per unit of output rises, and the LATC takes on an upward slope. </li></ul></ul><ul><li>Diseconomies of scale (in costs) imply decreasing returns to scale in production. </li></ul>
  46. 46. The Long Run Average Cost Curve Average Cost of Hospital Services # of patients LATC q 0 q 1 q 2 Economies of scale Diseconomies of scale
  47. 47. Long Run Costs of Production <ul><li>Decreasing returns to scale </li></ul><ul><ul><li>An increase in all inputs results in a less than proportionate increase in output. </li></ul></ul><ul><ul><li>e.g. Doubling the number of patients cared for in a hospital may require 3 times as many beds and nurses. </li></ul></ul><ul><li>In some cases, the production process exhibits constant returns to scale . </li></ul><ul><ul><li>A doubling of inputs results in a doubling of output. </li></ul></ul>
  48. 48. The Long Run Average Cost Curve under Constant Returns to Scale Average Cost of Hospital Services # of patients
  49. 49. Long Run Costs of Production <ul><li>Like the short run cost curve, a number of factors can cause the short run cost curve to shift up or down. </li></ul><ul><ul><li>Input prices. </li></ul></ul><ul><ul><li>Quality. </li></ul></ul><ul><ul><li>Patient casemix. </li></ul></ul><ul><li>e.g. If the hourly wage of nurses increases, the average cost of caring for each patient will also rise. </li></ul><ul><ul><li> The average cost curve will shift _____ </li></ul></ul>
  50. 50. Long Run Costs of Production <ul><li>Empirical evidence on HMOs and costs. </li></ul><ul><li>See handout. </li></ul>
  51. 51. Computing Profits <ul><li>Recall that the total costs of production for a firm are: </li></ul><ul><li>TC( q ) = w n + r k </li></ul><ul><li>Sum of each input price times the # of inputs used. </li></ul><ul><li>We can express total revenues derived from producing and selling a given level of output (q) as: </li></ul><ul><li>TR( q ) = output price x q </li></ul>
  52. 52. Computing Profits (cont.) <ul><li>Thus, we can express profits for the firm as: </li></ul><ul><li> ( q ) = TR( q ) – TC( q ) </li></ul><ul><li> = Profits </li></ul><ul><li>TR = Total revenue </li></ul><ul><li>TC = Total costs </li></ul><ul><li>We assume that firms choose a level of output ( q ) to maximize profits. </li></ul>
  53. 53. Computing Profits (cont.) <ul><li>Assume that as output increases, total revenue rises at a diminishing rate. </li></ul><ul><li>Also, recall the shape of short run total cost curve derived previously. </li></ul><ul><li>Then we can graph the total revenue curve and the total cost curve, and use them to visualize profits. </li></ul><ul><ul><li>Profits will be the vertical distance between total revenues and total costs at any given quantity of output. </li></ul></ul>
  54. 54. Graphing Profits Total dollars Quantity of output ( q ) TC TR q 0 TR 0 TC 0  ( q 0 ) = TR 0 – TC 0 
  55. 55. Graphing Profits Total dollars Quantity of output ( q ) TC TR At what output level(s) does the firm make profits equal to 0? At what output levels could the firm make negative profits ?
  56. 56. Graphing Profits Total dollars Quantity of output ( q ) TC TR q 0 TR 0 TC 0 Notice that I have plotted q 0 where the TR curve is above the TC curve, and the 2 curves are the furthest apart (in vertical distance). 
  57. 57. Computing Profits (cont.) <ul><li>I have plotted q 0 at the point where the firm maximizes profits. </li></ul><ul><ul><li>At this point the difference between total revenues and total costs is the greatest, and TR>TC. </li></ul></ul><ul><li>Note that this is also the point where the slopes of the TR curve and the TC curve are equal. </li></ul>
  58. 58. Computing Profits (cont.) <ul><li>Recall that the slope of the total cost curve represents marginal costs. </li></ul><ul><li>MC =  TC/  q </li></ul><ul><li>The slope of the total revenue curve represents marginal revenue . </li></ul><ul><li>MR =  TR/  q </li></ul><ul><li> A firm maximizes profits where: </li></ul><ul><li>MR=MC </li></ul>
  59. 59. Computing Profits (cont.) <ul><li>A firm maximizes profits where MR=MC. Why? </li></ul><ul><li>Suppose the firm was instead producing at a point where MR>MC. </li></ul><ul><ul><li>Then additional units of output would generate more marginal revenues than marginal costs, and profits could be higher. </li></ul></ul><ul><li>Suppose the firm was instead producing at a point where MC>MR. </li></ul><ul><ul><li>Then the last unit of output generates economic losses. </li></ul></ul>
  60. 60. Graphing Profits Total dollars Quantity of output ( q ) TC TR At q 1 , the firm should raise output to increase profits. At q 2 , the firm should lower output to increase profits.  MC>MR  MR>MC q 1 q 2

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