Problem Set #2: Health InsuranceEcon 445: Health Economics: Professor Martin HackmannDue Date: March 3rd in class1Moral HazardStudents at Penn State need to see primary care physicians during the...

Problem Set #2: Health InsuranceEcon 445: Health Economics: Professor Martin HackmannDue Date: March 3rd in class1Moral HazardStudents at Penn State need to see primary care physicians during the academic year, at least some.Suppose for now that no student has access to health insurance and suppose that the demand forprimary care physician visits in the academic year ( fore each of the 40,000 students), Q, is givenby1∗PQ=3−1000which depends on the price per primary care visit, P . Let’s assume the price per visit equals themarginal cost per visit of $2000.1. In equilibrium, how often do Penn State students see the primary care physician per year?2. Draw the demand curve in a diagram with quantity on the x-axis and price on the y-axis,and illustrate equilibrium demand. Is there a welfare loss, if so show it graphically?3. No suppose students have access to the Nittany Club insurance plan that has a coinsurancerate of 40%. Show graphically how the demand for primary care physician visits changes ifevery student enrolls in the Nittany Club insurance plan. Suppose prices remain unchanged,what’s the new equilibrium demand? How much does the Nittany insurance club pay perstudent? How much does a Penn State student pay? Is there a welfare loss, if so show itgraphically?4. The Nittany Club figured that the current insurance plan isn’t all that great for them. Sothey decided to change the plan policy. In the new plan, they introduce a deductible of $5000and has a coinsurance rate of 40% for additional charges. Suppose every student enrolls inthis plan.• a) Describe the relationship between health care charges and out-of-pocket spending underthis insurance plan graphically.2Risk ProtectionKarl-Heinz runs the BBQ place “Fette Sau” in Williamsburg. His place is going reasonably wellbut he is worried about a fire that could ruin his inventory including the high-end sausages and thepork belly that he is selling. His wealth equals $1,000,000 and he figures that with 56.25 percentprobability he loses inventory worth $640,000. His utility over wealth is given by√U (W ) = W1with, for example,U (1, 000, 000)=U (810, 000)=900U (680, 625)=825U (640, 000)=800U (600, 625)=775U (490, 000)=700U (422, 500)=650U (360, 000)=600U (302, 500)=550U (250, 000)=500(1, 000, 000) = 1, 0001. What is Karl-Heinz’s expected wealth? What is Karl-Heinz’s expected utility?2. Draw Karl-Heinz’s utility function in a diagram that has his wealth on the x-axis and hisutility on the y-axis. Indicate his utilities in case of a fire and in the absence of a fire. Alsoindicate his expected utility and his expected wealth. Show graphically how the expectedutility and the expected wealth depend on the loss probability.3. Karl-Heinz is considering buying an insurance that would cover his losses in the event of thefire against a fixed premium. What would be the “fair” premium?4. How much would Karl-Heinz be willing to pay for the insurance? Does it exceed the “fair”premium and if so why? Display Karl-Heinz’s willingness to pay for insurance graphically.3Selection and the Demand for InsuranceMany people in Texas are not offered health insurance through their employers and considerbuying health insurance individually. Suppose there is one insurance plan that has a 10%coinsurance rate and suppose only the following 10 people consider buying it. These people differin their willingness-to-pay and their expected out-of-spending on health care services if theyremained uninsuredPerson#1#2#3#4#5#6#7#8#9#10Willingness-to-pay for insurance$10,000$9,000$8,000$7,000$6,000$5,000$4,000$3,000$2,000$1,000Table 1:Expected Out-of-pocket payments without insurance$6,000$5,500$5,000$4,500$4,000$3,500$3,000$2,500$2,000$1,50021. Draw the demand curve for health insurance in a diagram that has the insurance premiumon the y-axis and quantity on the x-axis. Please interpolate the points linearly to get to aderive a continuous demand curve.2. Now derive the average cost (average expense) curve of the health insurer per enrollee. Weassume that health expenses are the only expense for the insurer. Notice that the averageexpense per enrollee will depend on the premium that the insurer charges. Please interpolatethe points linearly to get to a continuous average cost curve.3. Now add the marginal cost (marginal expense) curve to the diagram. Please interpolate thepoints linearly to get to a continuous marginal cost curve.4. Describe the equilibrium outcome (premium and quantity) under perfect competition. Displaythe outcome in the diagram and quantify premium and quantity.5. Is there a welfare loss? If so describe it graphically and explain.6. Let’s consider imposing a tax penalty of $1,000 for the uninsured. How does that change thedemand curve? Show it graphically. Does the tax penalty increase social welfare?7. What is the minimal tax penalty that is necessary to achieve the social optimum?3