Oligopolistic competition for the provision of hospital care

Transcription

1 Oligopolistic competition for the provision of hospital care Rosella Levaggi* and Laura Levaggi** * University of Brescia, Department of Economics and Management, Brescia, Italy ** Free University of Bolzano, Faculty of Science and Technology, Bolzano, Italy SIEP 2017 Catania, September, 2017 Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

2 Motivation Mixed markets where public hospitals compete with private ones for patients are quite common nowadays. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

3 Motivation Mixed markets where public hospitals compete with private ones for patients are quite common nowadays. Problems: Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

4 Motivation Mixed markets where public hospitals compete with private ones for patients are quite common nowadays. Problems: 1 mixed evidences on their being efficient Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

5 Motivation Mixed markets where public hospitals compete with private ones for patients are quite common nowadays. Problems: 1 mixed evidences on their being efficient 2 disagreement of the literature on their desirability Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

6 Motivation Mixed markets where public hospitals compete with private ones for patients are quite common nowadays. Problems: 1 mixed evidences on their being efficient 2 disagreement of the literature on their desirability Most literature models providers with asymmetric objectives, but on the same level as concerns patients evaluation. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

7 Motivation Mixed markets where public hospitals compete with private ones for patients are quite common nowadays. Problems: 1 mixed evidences on their being efficient 2 disagreement of the literature on their desirability Most literature models providers with asymmetric objectives, but on the same level as concerns patients evaluation. We argue that a more reasonable structure for competition in this market is to consider that private hospitals compete on the same level with a reference supply represented by the public hospital. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

8 Objectives Model a market for hospital care, where patients are located on the circumference of a Salop circle and may choose between: Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

9 Objectives Model a market for hospital care, where patients are located on the circumference of a Salop circle and may choose between: 1 being treated by a public hospital (located at the centre of the circle); Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

10 Objectives Model a market for hospital care, where patients are located on the circumference of a Salop circle and may choose between: 1 being treated by a public hospital (located at the centre of the circle); 2 N horizontally differentiated private suppliers located along the border. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

11 Objectives Model a market for hospital care, where patients are located on the circumference of a Salop circle and may choose between: 1 being treated by a public hospital (located at the centre of the circle); 2 N horizontally differentiated private suppliers located along the border. and providers have different objectives and constraints. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

12 Objectives Model a market for hospital care, where patients are located on the circumference of a Salop circle and may choose between: 1 being treated by a public hospital (located at the centre of the circle); 2 N horizontally differentiated private suppliers located along the border. and providers have different objectives and constraints. Welfare comparison between: benchmark (public provider at the centre), mixed market (public at the centre, private providers on the border) and private market (private providers on the border). Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

13 Main findings Depending on the entry cost and the relative efficiency of the private hospitals, monopolistic competition may be welfare improving. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

14 Main findings Depending on the entry cost and the relative efficiency of the private hospitals, monopolistic competition may be welfare improving. However, welfare composition should be closely monitored. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

15 Main findings Depending on the entry cost and the relative efficiency of the private hospitals, monopolistic competition may be welfare improving. However, welfare composition should be closely monitored. Pure public hospital run a deficit: soft budget may be the best solution. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

16 Main findings Depending on the entry cost and the relative efficiency of the private hospitals, monopolistic competition may be welfare improving. However, welfare composition should be closely monitored. Pure public hospital run a deficit: soft budget may be the best solution. Regulator has to decide how many providers in monopolistic competition. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

17 Main findings Depending on the entry cost and the relative efficiency of the private hospitals, monopolistic competition may be welfare improving. However, welfare composition should be closely monitored. Pure public hospital run a deficit: soft budget may be the best solution. Regulator has to decide how many providers in monopolistic competition. It could also extract a part of the surplus of private hospitals in this case. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

18 The environment N individuals, normalised to one: Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

19 The environment N individuals, normalised to one: 1 all in need of hospital care; Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

20 The environment N individuals, normalised to one: 1 all in need of hospital care; 2 distributed along a circumference of unit one. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

21 The environment N individuals, normalised to one: 1 all in need of hospital care; 2 distributed along a circumference of unit one. Costs and objectives of both providers are asymmetric. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

22 Consumers utility δ m x x U = v + { ϕqi m x ϕq δ ϕ: money equivalent utility of quality. v: sufficiently high to allow all the patient to ask for health care. Health care free at the point of use, but patients incur mobility costs. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

23 Consumers utility δ m x x U = v + { ϕqi m x ϕq δ ϕ: money equivalent utility of quality. v: sufficiently high to allow all the patient to ask for health care. Health care free at the point of use, but patients incur mobility costs. 1 at rate m x if they go to a private provider, where x is the distance; Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

24 Consumers utility δ m x x U = v + { ϕqi m x ϕq δ ϕ: money equivalent utility of quality. v: sufficiently high to allow all the patient to ask for health care. Health care free at the point of use, but patients incur mobility costs. 1 at rate m x if they go to a private provider, where x is the distance; 2 at rate δ if they choose to go to the centre. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

25 Hospital costs and objectives The cost to provide health care is made up of three components: Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

26 Hospital costs and objectives The cost to provide health care is made up of three components: 1 a fixed cost H : the fixed investment in technology necessary to run the hospital. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

27 Hospital costs and objectives The cost to provide health care is made up of three components: 1 a fixed cost H : the fixed investment in technology necessary to run the hospital. 2 a variable cost β. It may be reduced by a provider-dependent managerial effort θ. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

28 Hospital costs and objectives The cost to provide health care is made up of three components: 1 a fixed cost H : the fixed investment in technology necessary to run the hospital. 2 a variable cost β. It may be reduced by a provider-dependent managerial effort θ. 3 a quality related cost whose functional form depends on the type of provider. Private: C i = (β θ i +kq i )D i H Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

29 Hospital costs and objectives The cost to provide health care is made up of three components: 1 a fixed cost H : the fixed investment in technology necessary to run the hospital. 2 a variable cost β. It may be reduced by a provider-dependent managerial effort θ. 3 a quality related cost whose functional form depends on the type of provider. Private: C i = (β θ i +kq i )D i H Public : C = βd c + θ c 2 q2 H Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

30 Hospital objectives functions Private hospitals maximise their surplus: Π i = (S + θ i kq i )D i H D i : demand share of the private hospital S : S = T β (T=unit reimbursement) Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

31 Hospital objectives functions Private hospitals maximise their surplus: Public hospital maximises: Π i = (S + θ i kq i )D i H V = ϕq θ c 2 q2 H D i : demand share of the private hospital S : S = T β (T=unit reimbursement) Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

32 Benchmark (I) Benchmark: Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

33 Benchmark (II) Only public hospital at the centre; serves all the market (D c = 1). Chooses q to maximise: V = ϕq θ c 2 q2 H Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

34 Benchmark (II) Only public hospital at the centre; serves all the market (D c = 1). Chooses q to maximise: Solution: V = ϕq θ c 2 q2 H q c = ϕ θ c T = β+h S = H Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

35 Benchmark (II) Only public hospital at the centre; serves all the market (D c = 1). Chooses q to maximise: Solution: V = ϕq θ c 2 q2 H q c = ϕ θ c T = β+h S = H Welfare: v β H + ϕ2 θ c δ Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

36 Benchmark: Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

37 Monopolistic competition: Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

38 Private competitors: Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

39 Competition Benchmark Private market Mixed Market ϕ ϕ quality centre θ c θ c ( θ quality border i +H k ϕn m θ i +H P 2k ϕ δ θc ϕ) N N P = mk H ϕ N M < mk 2H ϕ - set by the regulator demand D P i = 1 N P existence H km 4ϕ θ i > mk ϕn P H D M i = ϕ m θ L i := k ( ϕ θ c δ ϕ θ i < k ( θi +H k + δ ϕ ϕ θ c ) D M c = 1 N M D M i H km 2ϕ ) + 2Hmk ϕ H θ i ( ϕ θc δ ϕ + m ϕn M ) H := θ U i (N M ) Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

40 Welfare analysis: viable alternatives (I) Viable alternatives depend on the parameters. θ i L θ i U θ NM =1 i U θ NM i =2 U θ NM =3 i U θ NM i =4 0 mk mk mk mk 32ϕ25ϕ18ϕ16ϕ mk mk 9ϕ 8ϕ mk 4ϕ H mk 2ϕ Figure: Feasibility areas Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

41 Welfare analysis: viable alternatives (II) H mk 2ϕ : only a public firm at the centre (benchmark) can be a viable solution. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

42 Welfare analysis: viable alternatives (II) H mk 2ϕ : only a public firm at the centre (benchmark) can be a viable solution. mk 4ϕ < H < mk 2ϕ : also mixed market with N M = 1 is viable, when θ i [θi L, θu i (1)). Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

43 Welfare analysis: viable alternatives (II) H mk 2ϕ : only a public firm at the centre (benchmark) can be a viable solution. mk 4ϕ < H < mk 2ϕ : also mixed market with N M = 1 is viable, when θ i [θi L, θu i (1)). mk 8ϕ H mk 4ϕ : in addition a private market with N P = 2 is feasible for any θ i. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

44 Welfare analysis: viable alternatives (II) H mk 2ϕ : only a public firm at the centre (benchmark) can be a viable solution. mk 4ϕ < H < mk 2ϕ : also mixed market with N M = 1 is viable, when θ i [θi L, θu i (1)). mk 8ϕ H mk 4ϕ : in addition a private market with N P = 2 is feasible for any θ i. mk 9ϕ H < mk 8ϕ : for the mixed market there are two choices of N M on the interval θ i [θi L, θu i (2)), i.e. N M = 1 or N M = 2. If θ i [θi U (2), θi U (1)) only N M = 1 is feasible. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

45 Welfare analysis: viable alternatives (II) H mk 2ϕ : only a public firm at the centre (benchmark) can be a viable solution. mk 4ϕ < H < mk 2ϕ : also mixed market with N M = 1 is viable, when θ i [θi L, θu i (1)). mk 8ϕ H mk 4ϕ : in addition a private market with N P = 2 is feasible for any θ i. mk 9ϕ H < mk 8ϕ : for the mixed market there are two choices of N M on the interval θ i [θi L, θu i (2)), i.e. N M = 1 or N M = 2. If θ i [θi U (2), θi U (1)) only N M = 1 is feasible.... Values of H and θ i determine which market organisations are feasible. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

46 Welfare analysis: mixed vs private markets The best level of W M is obtained for the maximum allowed number N M. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

47 Welfare analysis: mixed vs private markets The best level of W M is obtained for the maximum allowed number N M. In the comparison between W P and W M the ratio ϕ k plays a fundamental role and has a countervailing effect on three elements of welfare: Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

48 Welfare analysis: mixed vs private markets The best level of W M is obtained for the maximum allowed number N M. In the comparison between W P and W M the ratio ϕ k plays a fundamental role and has a countervailing effect on three elements of welfare: patients net utility (Φ P and Φ M ); Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

49 Welfare analysis: mixed vs private markets The best level of W M is obtained for the maximum allowed number N M. In the comparison between W P and W M the ratio ϕ k plays a fundamental role and has a countervailing effect on three elements of welfare: patients net utility (Φ P and Φ M ); profit of private hospitals in the private markets (Π P and Π M ); Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

50 Welfare analysis: mixed vs private markets The best level of W M is obtained for the maximum allowed number N M. In the comparison between W P and W M the ratio ϕ k plays a fundamental role and has a countervailing effect on three elements of welfare: patients net utility (Φ P and Φ M ); profit of private hospitals in the private markets (Π P and Π M ); profit of private hospitals net of deficit of public hospital in the mixed market ( ˆΠ M ). Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

51 Welfare analysis: mixed vs private markets The best level of W M is obtained for the maximum allowed number N M. In the comparison between W P and W M the ratio ϕ k plays a fundamental role and has a countervailing effect on three elements of welfare: patients net utility (Φ P and Φ M ); profit of private hospitals in the private markets (Π P and Π M ); profit of private hospitals net of deficit of public hospital in the mixed market ( ˆΠ M ). No necessary nor sufficient conditions on the superiority of the two market forms. Some conclusions can be drawn for alternative levels of ϕ k. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

52 Welfare analysis: mixed vs private - the role of ϕ k (I) ϕ = 2k ΦP ΠP ΦM ˆΠM L U θ i θ (2) U i θ NM = 2 (1) }{{} NM = 1 i }{{} Figure: Composition of the total welfare: case ϕ = 2k. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

53 Welfare analysis: mixed vs private - the role of ϕ k (II) ϕ = 1 2 k ΦP ΠP ΦM ˆΠM L U U θ θ (4) θ (3) U U θi i i i (2) θi (1) NM = 3 }{{} NM = 2 NM = 1 }{{}}{{} NM = 4 Figure: Composition of the total welfare: case ϕ = 1 2 k. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

54 Discussion Monopolistic competition can be a welfare improving solution. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

55 Discussion Monopolistic competition can be a welfare improving solution. Several countervailing effects determine this result. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

56 Discussion Monopolistic competition can be a welfare improving solution. Several countervailing effects determine this result. One of the key parameters is the ratio between patients evaluation of quality and its marginal cost in the private market. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

57 Discussion Monopolistic competition can be a welfare improving solution. Several countervailing effects determine this result. One of the key parameters is the ratio between patients evaluation of quality and its marginal cost in the private market. Profits in the private market depend on the rounding effect; on the mixed market exist because free entry is not viable. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

58 Discussion Monopolistic competition can be a welfare improving solution. Several countervailing effects determine this result. One of the key parameters is the ratio between patients evaluation of quality and its marginal cost in the private market. Profits in the private market depend on the rounding effect; on the mixed market exist because free entry is not viable. It may be advisable to determine entry in the mixed market through a monopoly franchise. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

59 Discussion Monopolistic competition can be a welfare improving solution. Several countervailing effects determine this result. One of the key parameters is the ratio between patients evaluation of quality and its marginal cost in the private market. Profits in the private market depend on the rounding effect; on the mixed market exist because free entry is not viable. It may be advisable to determine entry in the mixed market through a monopoly franchise. Soft budget constraints may be optimal in this context. Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21

60 Thank you for your attention! Rosella Levaggi and Laura Levaggi Competition in hospital care 21st September, / 21