Suppose that there is only one insurance company in an economy that provides health insur- ance...

 

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Suppose that there is only one insurance company in an economy that provides health insur- ance service. A higher quantity of health insurance indicates more comprehensive insurance coverage. Suppose that there are relatively unhealthy type 1 consumers and relatively healthy type 2 consumers. Suppose that we normalize the units of health insurance coverage such that the demand function for a representative consumer is " (p) = (On-p)/0n for type n. You can interpret x = 0 as no insurance and x = 1 as full insurance coverage. Let 0 = 20 and 02 10 for the two types of consumers. The marginal costs of providing additional insurance coverage for each types are MC = 8 and MC = 6 respectively, and there is no fixed cost. Assume the insurance company's profit maximizing choices are interior solutions for all of the below questions. (a) (3 pts) Calculate the socially efficient level of insurance for each representative consumer type. (b) (3 pts) If the insurance company cannot tell who is what type and can only charge a single per- unit price p for insurance to maximize her expected profit, how much will she charge assuming she knows that there are y shares of type 1 consumers and (1) shares of type 2 consumers, with <0.5? WLOG, normalize the total population to be 1. [Hint: if profits earned from a representative consumer of each types are and , the insurance company's expected profit is E(T) = + (1).] (c) (5 pts) What would the monopoly price be if y=0? What if y = 2/7? What is the highest that y can be and still result in type 2 consumers buying insurance? (d) (5 pts) Suppose that the insurance company can tell the health conditions of the two types of consumers, and for each type it uses a two-part pricing scheme involving a fixed fee to provide health service plus a unit price for the insurance coverage. How will the monopolist charge for the insurances? How much insurance will each consumer type purchase? How much will each type pay in total for her coverage? (e) (4 pts) How do your answers to (d) change if the monopolist third-degree price discriminates? (f) (4 pts) Suppose y = 0.5 i.e. half of the population is type 1 and half is type 2. Can you rank the three scenarios in (c), (d) and (e) from most efficient to least efficient? Explain. (g) (6 pts) Continue to assume that y=0.5. Can you rank (c), (d) and (e) in terms of their impact on consumer welfare for each type? What about in terms of population weighted average consumer welfare? Suppose that there is only one insurance company in an economy that provides health insur- ance service. A higher quantity of health insurance indicates more comprehensive insurance coverage. Suppose that there are relatively unhealthy type 1 consumers and relatively healthy type 2 consumers. Suppose that we normalize the units of health insurance coverage such that the demand function for a representative consumer is " (p) = (On-p)/0n for type n. You can interpret x = 0 as no insurance and x = 1 as full insurance coverage. Let 0 = 20 and 02 10 for the two types of consumers. The marginal costs of providing additional insurance coverage for each types are MC = 8 and MC = 6 respectively, and there is no fixed cost. Assume the insurance company's profit maximizing choices are interior solutions for all of the below questions. (a) (3 pts) Calculate the socially efficient level of insurance for each representative consumer type. (b) (3 pts) If the insurance company cannot tell who is what type and can only charge a single per- unit price p for insurance to maximize her expected profit, how much will she charge assuming she knows that there are y shares of type 1 consumers and (1) shares of type 2 consumers, with <0.5? WLOG, normalize the total population to be 1. [Hint: if profits earned from a representative consumer of each types are and , the insurance company's expected profit is E(T) = + (1).] (c) (5 pts) What would the monopoly price be if y=0? What if y = 2/7? What is the highest that y can be and still result in type 2 consumers buying insurance? (d) (5 pts) Suppose that the insurance company can tell the health conditions of the two types of consumers, and for each type it uses a two-part pricing scheme involving a fixed fee to provide health service plus a unit price for the insurance coverage. How will the monopolist charge for the insurances? How much insurance will each consumer type purchase? How much will each type pay in total for her coverage? (e) (4 pts) How do your answers to (d) change if the monopolist third-degree price discriminates? (f) (4 pts) Suppose y = 0.5 i.e. half of the population is type 1 and half is type 2. Can you rank the three scenarios in (c), (d) and (e) from most efficient to least efficient? Explain. (g) (6 pts) Continue to assume that y=0.5. Can you rank (c), (d) and (e) in terms of their impact on consumer welfare for each type? What about in terms of population weighted average consumer welfare?

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Answer a The socially efficient level of insurance for each type of consumer occurs where the margin... View the full answer