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Health Economics Analytic Problems

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  1. True/False Explain

Indicate whether each of the following statements in true or false and then explain why you think this. Include in your explanation any pertinent institutional details and economic reasoning (Including appropriate graphs and equations). Please provide concise, clear answers with minimum irrelevant detail. Explanation is required.

  1. An employer mandate forces all firms to provide health insurance for workers. This mandate will cause all firms to hire fewer workers. False

Not all employers will respond to employer mandate that forces all firms to provide health insurance for workers some are likely to find compliance less expensive or may opt for mandate avoidance. From an economics point of view, altering staff is generally costly and that such a move will push the unemployment tax higher and all firms will be required to pay higher rates. However, some firms mat respond to this mandate by scaling down the number of hours and hiring few employees in order to cut on the costs of hiring and training (Blavin et al., 2015).

  1. Proposed policies to change the definition of full time employment in the Affordable Care ACT to 40 hours a week would cause more people to gain employer provided insurance under ACA compared to the current law. True

Changing the definition of full time employment to 40 hours per week from the tradition 30 hours per week helps employers to mitigate on the mandate’s labor market costs by giving employers an incentive to opt for a range of options of absorbing these costs by choosing to reduce pay, employment, avoid the mandate and pay a fine (Moriya et al., 2016). The finding of employment survey shows that over 70 percent of employees worked 40 hours a week, meaning that more employers were ready to comply causing more people to gain employer provided insurance under ACA. The graph below:

 

  1. In the Rothschild-Stieglitz model, an individual who is offered a choice between full insurance and no insurance will always choose full insurance if they are risk averse. True

Whenever a consumer is presented with a choice between full insurance cover and no insurance, he/she will choose to pay up for ρmax = ω-ce because there exists a separating equilibrium (Salanié, 2017).


 

  1. Analytic Problems
  2. Individual Health Insurance Mandates and Adverse Selection

Consider a market for health insurance similar to the one depicted below that we discussed in class.

 

 

 

 

 

 

 

 

 

 

 

Suppose individuals have different health levels H, where H is distributed uniformly between 0 and 9. The marginal cost of medical care depends on an individual’s health H and is characterized by the function MC = 1000+1000*H (Notice that a higher value of H corresponds to a sicker person, with higher marginal costs, so the left edge of the graph corresponds to the sickest person with H=9, and the right edge of the graph corresponds to the healthiest person with H = 0. Individuals are risk averse, there is a single insurance plan available for purchase (As in Akerlof Model, NOT the R-S Model) and individuals have utility functions for this insurance plan that result in a risk premium equal to RP = 1000* H

  1. Write down the equation describing the demand function for this insurance plan. (Hint: The demand function should express willingness to pay for insurance as a function of H).

Marginal cost of Medicare can also be written as:

MC = (1000*H) + 1000

From the Equation, H represents the slope of the demand curve which is an individual’s health distributed uniformly between 0 and 9

Therefore from the equation above,

H can also be written as H = y2 – y1/x2-x1

= J-E/Qmax-Qe

Therefore;

Demand Function = 1000*(J – E/ Qmax – Qe) + 1000

  1. Write down the equations 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 of the line.

Average cost function of the insurer y = Mx + C

Where M = A-C/ Qmax-Qe + C

Therefore the Average cost function can also be written as;

AC = M* A-C/ Qmax-Qe + C

 

 

 

  1. 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=9) and right (H=0) sides of the graph.

 

 

Price P

Demand Curve

H0                                                                                                                                                                                                                                                                                                                                AC                                       H9

Quantity Q                Qeq       QMax

  1. What is the equilibrium price P* of the insurance plan in this market?

Equilibrium Price is Pe

                                                  = M * G – F/Qeq – Qmax + 1000

= H (G – F/Qeq – Qmax + 1000)

  1. Which consumers will purchase the insurance plan in equilibrium (Your Answer should depend on H)

Consumers with health levels between 4 and 5 will purchase the insurance plan in equilibrium.

 

 

 

 

 

  1. Calculate the size of the deadweight loss from adverse selection in the insurance market.

Deadweight loss = H* (Qmax – Qe) * Peq – F

Now suppose an individual insurance mandate is imposed that forces all consumers to purchase insurance or else pay a tax of $3000.

  1. What will the insurance mandate do to the equilibrium price of insurance?

An insurance mandate decreases the demand for the products because the equilibrium prices differ from the average costs causing the demand curve to shift downwards (Left) and the equilibrium price fall (Salanié, 2017).

  1. What is the effect of the mandate on the dead weight loss from adverse selection in the market?

Mandate on the deadweight loss from adverse selection leads to welfare loss as a result of downward sloping of the MC curve which causes underinsurance relative to social optimum.

 

 

 

 

 

 

 

From the graph above, Qeq < Qeff

  1. What is the smallest mandate tax penalty that will completely eliminate the dead weight loss from adverse selection in this market?

The smallest mandate tax penalty that will completely eliminate the deadweight loss from adverse selection in this market is determined at H = 0 health level, the least sick person.

Using the Risk Premium Formula, RP = 1000*H

= 1000*0

= 0

 

 

References:

Blavin, F., Shartzer, A., Long, S. K., & Holahan, J. (2015). An Early Look At Changes in Employer-Sponsored Insurance under the Affordable Care Act. Health Affairs34(1), 170-177.

Moriya, A. S., Selden, T. M., & Simon, K. I. (2016). Little Change Seen In Part-Time Employment As A Result Of the Affordable Care Act. Health Affairs35(1), 119-123.

Salanié, B. (2017). Equilibrium in Insurance Markets: An Empiricist’s View. The Geneva Risk and Insurance Review42(1), 1-14.

 

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