8B. The answer to question 8A is the outcome we expect in an unregulated market. What would happen if we were to regulate the market and require that all individuals must buy health insurance (individual mandate)?Opt = $260p*= $13O p* = $16.50 p* = $24
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- The unregulated market equilibrium price is given (likely $13 or $16.50 or $24, but we need to identify which corresponds to the unregulated market). - The outcome in an unregulated market is where supply equals demand without any external intervention. Show more…
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3. Obamacare with a faulty website. Health insurance markets are a classic example of adverse selection. One feature of the Affordable Care Act ("ACA", also known as Obamacare) is "Community Rating" on the health insurance exchanges, which says that a single price is offered to all consumers in a region and broad demographic group, without any medical tests. This question will examine the market for health insurance on the ACA for males in the 19-29 age range. In this age group, there are two types of individuals shopping on the ACA exchanges: "healthy" types, who are 90% of such individuals, and "chronic" types, who are 10%. The Healthy types have expected annual health expenses that are uniformly distributed between $0 and $1000 (math reminder: the mean of a uniform distribution between a and b is (a+b)/2, and the probability that a draw from such a distribution is at or above p is (b-p)/(b-a)). The Chronic types are guaranteed to have $1500 in annual expenses. All customers know their expected annual health expenses exactly, but insurers do not. a. First, suppose hypothetically that all individuals in this market (males age 19-29) will purchase insurance plans. Insurers negotiate rates with hospital networks so that the cost of providing care is 40% less than the true expense, so a $100 expense actually only costs the insurer $60. We will assume the market is competitive, so that premiums equal average costs. What will be the resulting policy premiums with all individuals covered? p = b. In reality, consumers will purchase an insurance plan only if the premium is less than their expected expenses (i.e. they are risk-neutral; making them risk-averse would complicate the math without changing the intuition). At the price you just found, what proportion of the Healthy types would choose to purchase health insurance if the requirement to purchase were lifted? Proportion of Healthy opting to buy insurance: Right away, we see the challenge with universal coverage: without some way of forcing individuals to buy insurance, the healthiest in a market would choose not to participate, which would increase the average cost, which would increase prices, and so on. We want to solve for what the market outcome would be if individuals can choose to be uninsured. We'll do this as a function of a general price for coverage, p. c. First, what is the fraction of Healthy types that would purchase insurance, given a price p. We will denote this fraction as f(p). f(p) =
Akash M.
Suppose individuals have different health levels H, where H is distributed uniformly between 0 and 1. Individuals are risk-averse. There is a single insurance plan available for purchase (as in the Akerlof model, NOT the R-S model). The marginal cost of medical care depends on an individual's health H and is characterized by the function MC = 2000 - 1000H (notice that a higher value of H corresponds to a healthier person, with lower marginal costs, so the left edge of the graph corresponds to the sickest person with H = 0, and the right edge of the graph corresponds to the healthiest person with H = 1). Individuals have utility functions for this insurance plan that result in a risk premium equal to RP = 750 - 500H. a) Write down the equation describing the demand function for this insurance plan. (Hint: the demand function is the sum of the marginal cost and risk premium and should express willingness to pay for insurance as a function of H). b) Write down the equation describing the average cost function of the insurer. (Hint: since the MC function is linear, the AC function is also linear. If you find any two points along the line, you can figure out the equation for the line.) c) Draw a graph similar to the one above containing the demand function, MC function, and AC functions. For each function, indicate the values of the vertical intercepts on the left (H = 0) and right (H = 1) sides of the graph. Clearly label the deadweight loss. d) What is the equilibrium price p* of the insurance plan in this market? e) Calculate the size of the deadweight loss from adverse selection in the insurance market. Now suppose an individual insurance mandate is imposed that forces all consumers to purchase insurance or else pay a tax of $250. f) What will the insurance mandate do to the equilibrium price of insurance? g) What is the effect of the mandate on the deadweight loss from adverse selection in the market? What is the gain in consumer surplus from lowered prices? What is the loss in consumer surplus from the mandate? h) Considering only the DWL from adverse selection and the consumer surplus components mentioned above, is the mandate welfare improving on average? For whom is the mandate most costly?
Shu N.
Let’s consider the health insurance market. Suppose there are two types of consumers: those with pre-existing conditions and those without. Those with pre-existing conditions make up 10% of consumers. All consumers are risk-averse with utility function, U left parenthesis X right parenthesis equals square root of X. Those with pre-existing conditions require medical care 50% of the time. Those without require medical care 5% of the time. Assume each consumer has an initial wealth of $1000 and medical care costs $500. If the insurance companies are allowed to sell insurance at different prices to the two types of consumers and competition forces them to charge the fair insurance premium, consumers without pre-existing conditions ___________ insurance at a price of $__________. Consumers with pre-existing conditions insurance ____________ at a price of $ _______________. Now suppose the government passes a law that bans discrimination on the basis of pre-existing conditions. In this case, the insurance companies can no longer offer insurance at two different prices (they can only charge a single price). In this case, in equilibrium, consumers without pre-existing conditions insurance _______________ at a price of $______________. Consumers with pre-existing conditions insurance ________________ at a price of $ ________________. Relative to before the law is passed, consumers without pre-existing conditions are _________________ off. Consumers with pre-existing conditions are ________________ off. DROP DOWN OPTIONS: 0 10 25 47.5 100 125 227.5 250 BUY DONT BUY INDIFFERENT BETWEEN BUYING AND NOT BUYING BETTER NEITHER BETTER OR WORSE WORSE
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