Please Answer Any Four Of The Five Exam Questions

Please Answer Any Four (4) Of The Five Exam Questions

Please answer any four (4) of the five exam questions. Each question requires a short essay response, consisting of complete sentences arranged in a logical order. The answer should provide a clear, concise explanation and not be merely an outline, bullet points, symbols, or abbreviations. While tables, graphs, or equations can be incorporated to support explanations, they should not replace the written response.

Paper For Above instruction

Question 1 involves evaluating whether J. Wellington Wimpy's current consumption of hamburgers and Zocor tablets maximizes his utility, considering his utility gains, income, and prices. To do this, one must analyze Wimpy's marginal utility per dollar spent on each good and determine if his chosen combination is optimal.

In question 2, the focus is on understanding why a dental clinic’s revenue declined after raising fees, despite aims to increase revenue through higher prices. The answer should explore factors such as consumer behavior, price sensitivity, and competitive market dynamics that may influence the observed outcome.

Question 3 explores the concept of moral hazard in health insurance, mechanisms for risk sharing in insurance design, and how the extent of risk sharing depends on the price elasticity of demand for insured services. The discussion should clarify the issues of moral hazard, delineate methods like deductibles and copayments, and explain the rationale behind increased risk sharing with higher demand elasticity.

Question 4 analyzes the decision of Stickum, Inc., whether to hire an additional worker based on marginal productivity and wage considerations. The response should incorporate cost-benefit analysis, including marginal cost and marginal revenue, and consider implications of wage increases on hiring decisions.

Question 5 concerns Maynard G. Krebs's expected utility regarding uncertain wealth and how insurance influences his utility. The response should compute his expected utility without insurance, determine the fair premium for a specified insurance policy, and assess the maximum premium he would be willing to pay, based on utility calculations.

Answer to the Selected Questions

Question 1: Utility Maximization for Wimpy

J. Wellington Wimpy consumes 30 hamburgers and 30 Zocor tablets each month, with his income at $150. The prices are $2 per hamburger and $3 per tablet. The marginal utility from the 30th hamburger is 45 units, and from the 30th Zocor tablet is 20 units. To evaluate whether Wimpy maximizes his utility, we compare the marginal utility per dollar spent on each good.

The marginal utility per dollar for the hamburger is 45 units divided by $2, which equals 22.5 units per dollar. For Zocor tablets, it is 20 units divided by $3, approximately 6.67 units per dollar. Since Wimpy spends equally on both goods (30 units of each), but the marginal utility per dollar is much higher for hamburgers, he could increase his overall utility by reallocating his expenditure towards hamburgers until the marginal utilities per dollar are equal for both goods.

Therefore, the current consumption does not maximize utility because the marginal utility per dollar is unequal. Wimpy should reduce his Zocor intake slightly and purchase more hamburgers until the marginal utility per dollar equates for both goods, satisfying the condition for utility maximization where MU per dollar for all goods consumed should be equal.

Additionally, considering his budget constraint, Wimpy's optimal point occurs where the last dollar spent on each good yields the same marginal utility, which suggests he needs to adjust his consumption bundle accordingly. His current combination indicates suboptimality because of the observed differences in marginal utility per dollar.

To increase his overall utility, Wimpy must reallocate spending such that the marginal utility per dollar is equalized across both goods. As he increases hamburger consumption and reduces Zocor intake, the marginal utility of additional hamburgers will decrease, while that of Zocor tablets will increase, until an equilibrium point is reached where MU per dollar is the same for both.

The point where Wimpy cannot further increase his utility is when the marginal utility per dollar for both goods aligns and his budget is exhausted — that is, at the bundle where MU per dollar is equalized, and the total expenditure equals his $150 income.

Question 2: Decline in Clinic Revenues After Fee Increase

The dental clinic's decision to increase fees by approximately 15% aimed to boost revenue; however, a substantial decline in patient care revenues occurred, contrasting with a slight increase in private dentists' revenues. Several factors could explain this unexpected outcome.

Firstly, in a market where most patients pay out-of-pocket without insurance, price sensitivity is high. Patients tend to be highly responsive to fee changes; even a modest increase might deter many from seeking care or prompt them to seek cheaper alternatives or delay treatment. This is consistent with the downward-sloping demand for dental services among uninsured patients.

Secondly, the clinic’s price increase may have exceeded the threshold of consumers' willingness to pay, leading to a significant reduction in patient volume. The perceived decrease in affordability could outweigh revenue gains per patient, causing overall revenue to fall. This is an example of demand elasticity — when demand is elastic, price increases lead to larger percentage reductions in quantity demanded.

Thirdly, patients’ perception of quality or value could have influenced the drop in visits. If patients viewed the fee increase as a decline in affordability or if they perceived the clinic as no longer offering competitive value, they might have shifted their patronage to alternative providers, including private dentists who perhaps maintained or lowered their fees.

Furthermore, for the private dentists, the slight revenue increase could be attributed to competitive advantages such as more flexible pricing, better marketing, or less perceived price sensitivity among their clientele. They might have capitalized on the reduced patient flow at the clinic by offering discounts or improved service offerings, attracting patients who avoided the pricier clinic.

In summary, the decline in clinic revenues primarily resulted from increased price sensitivity among the uninsured patient base, leading to reduced patient demand when fees rose. Other contributing factors include perceived value and competitive market dynamics, which caused patient reallocation toward private providers, ultimately undermining the clinic’s revenue objectives.

Question 3: Health Insurance: Moral Hazard and Risk Sharing

a. Moral hazard in health insurance refers to the tendency of insured individuals to alter their behavior after obtaining insurance coverage, often engaging in riskier activities or utilizing more services than they would without insurance, because they do not bear the full cost of their actions. This behavioral change can lead to over-utilization of medical services, raising overall costs for the insurer and the healthcare system. Moral hazard is significant because it can result in inefficient resource allocation, escalating healthcare costs, and challenges for insurers in designing sustainable benefit schemes.

b. Two mechanisms in traditional benefit design that promote risk sharing between the insured and the insurer are deductibles and copayments. Deductibles require the insured to pay a fixed amount before the insurer begins coverage, encouraging individuals to consider the necessity of each healthcare service and reduce unnecessary utilization. Copayments, a fixed fee paid per service, disincentivize excessive use by making the insured share some of the costs.

Risk sharing through these mechanisms helps mitigate moral hazard by aligning the incentives of the insured with cost-conscious behavior, thereby controlling over-utilization and helping contain costs. When individuals share in the costs, they are more likely to weigh the necessity of each visit or procedure, reducing unnecessary care consumption.

c. In optimal insurance design, the extent of risk sharing tends to increase with the price elasticity of demand for the insured service because when demand is highly elastic, consumers reduce their utilization substantially in response to price increases, which helps contain costs. Therefore, greater risk sharing (e.g., higher deductibles or copayments) is appropriate when demand is elastic, as it minimizes moral hazard and overuse. Conversely, services with inelastic demand (necessities) warrant less risk sharing, as consumers are less responsive to price changes. Aligning risk sharing with demand elasticity ensures that insurance incentives promote efficiency and cost containment without compromising access to essential care.

Question 4: Hiring Decision of Stickum, Inc.

Stickum, Inc. sells diabetes test strips at $3 per box. With current operations, the company employs 100 workers earning $50/day, and the non-labor variable costs are $0.10 per box. Each additional worker increases output by 20 boxes per day. To assess whether to hire the extra worker, the company must compare the marginal revenue product (MRP) of the worker with the wage.

In the current setup, the company sells as many boxes as it produces at $3 per box, translating to a marginal revenue (MR) of $3 for each additional box. The marginal product of labor (MP) is 20 boxes, so the marginal revenue product (MRP) is MR times MP: $3 * 20 = $60. Since the wage is $50 per day, and the MRP exceeds the wage, hiring the additional worker is profitable because the value of the increased output ($60) surpasses the cost ($50).

Therefore, Stickum should hire the additional worker at $50/day, as doing so enhances overall profit. The company gains net benefits of $10 per day from hiring this worker.

If the company has to raise wages to $55 per day to hire the worker, the comparison changes. Now, the wage exceeds the MRP of $60, which is still above $55—but this scenario requires precise calculation: since the MRP remains at $60, and the higher wage is $55, hiring the worker still has a net benefit of $5 ($60 - $55). Thus, even at $55 wages, hiring the worker remains profitable, although marginally so.

However, if wages increased beyond the MRP (for example, over $60), hiring would no longer be justified, as the additional labor would not generate enough revenue to cover wages. Ultimately, the decision hinges on the marginal revenue product and wage comparison, with the optimal choice favoring hiring as long as MRP exceeds wage.

Question 5: Expected Utility and Insurance Willingness

Maynard faces uncertain wealth outcomes: he will have $6,000 with a probability of 0.75, and $1,000 with a probability of 0.25. His utility function assigns specific utils to certain wealth levels: U($500)=200, U($1000)=600, U($1500)=900, U($2000)=1080, U($2500)=1210, U($3000)=1320, U($4000)=1415, U($5000)=1500, U($6000)=1560, and U($7000)=1600. To compute his expected utility without insurance, we multiply utilities by their probabilities and sum them:

EU = 0.75 U($6000) + 0.25 U($1000) = 0.75 1560 + 0.25 600 = 1170 + 150 = 1320 utils.

This value reflects his expected utility if he foregoes insurance. For an insurance policy paying $5,000 when wealth is $1,000, the insured wealth in that case becomes $6,000 (wealth plus payout), and in the other case, no payout occurs, leaving wealth at $6,000 or $1,000, respectively.

The actuarially fair premium equals the expected payout. Given the likelihood of the event, the fair premium is:

Premium = Probability of payout payout amount + (1 - probability) 0 = 0.25 $5,000 + 0.75 0 = $1,250.

This premium makes the insured indifferent between having or not having the insurance because the expected payout equals the premium, based on the probabilities.

Maynard's maximum willingness to pay for this insurance is the amount that keeps his expected utility unchanged, which involves comparing his utility with and without insurance, considering the premium. Since utility functions are given, he will pay up to the point where the expected utility of insuring equals or exceeds not insuring. Calculating this involves finding a premium that makes his expected utility with insurance at least equal to 1320 utils, which typically would be less than the fair premium ($1,250), depending on his risk preferences and utility curvature. Due to the diminishing marginal utility of wealth, he may be willing to pay less than the fair premium, prioritizing utility maximization over pure expected monetary gains.

References

• Barnhill, J. (2017). Principles of Microeconomics: Theory and Applications. Pearson.
• Culyer, A. J. (2017). Health Economics. In A. J. Culyer & J. P. Hansen (Eds.), Encyclopedia of Health Economics. Elsevier.
• Drummond, M. F., Sculpher, M. J., Claxton, K., Stoddart, G. L., & Torrance, G. W. (2015). Methods for economic evaluation of health care programmes. Oxford University Press.