d the questions are given below

12. (23 points) This question is about the choice of insurance for a risk-averse consumer. Suppose my utility function is U(w) = w, where w is my wealth in $1000. Suppose I face a risk p of getting sick, where p = 19/36. Suppose my initial wealth $100,000, but if I get sick, it falls to $64,000. This question will ask you to do some calculations (leaving numbers in fractions is fine). For partial credit, draw the graph and discuss what you find. a. What is my marginal utility of wealth when sick? When well? Am I risk averse? Risk loving? Risk neutral?

b. What is my expected wealth with no insurance? What is my expected utility with no insurance?

c. Cost-benefit analysis uses present discounted values to account for long run impacts of interventions while cost-utility analysis does not.

d. Cost-benefit analysis weights the utility of being sick and of being well differently while cost utility analysis does not.

9. (15 points) Which of the following are information problems that arise in the health care sector? Give an example of where they occur in health care.

10. (23 points) The following question is another screening/testing question, which will require you to use Bayes' rule. Remember, Bayes' rule says: P r(Ai |B) = P r(Ai) P r(B|Ai) Pk 1 P r(Aj ) P r(B|Aj ) . Suppose we have a test for breast cancer that is better at detecting who is not sick for people who are not sick than for telling who is sick. For someone with breast cancer, it will correctly identify them as having cancer 90% of the time (10% of the time they will be misdiagnosed as not having cancer). Someone without breast cancer will be identified as having cancer 5% of the time (95% of the time they will be correctly diagnosed as not having cancer, and 5% of the time they will be incorrectly diagnosed as having cancer).

a. Suppose there is a population of 1,000 women, and 20% (200) have breast cancer, and 80% do not (800 do not). Calculate the probability of getting a false positive (P(NC|+)), a true positive (P(C|+), a false negative (P(C|)), and a true negative (P(NC|)).

b. Now suppose we consider a population of 1,000 women whose mothers all have breast cancer. Suppose that 40% of them have the disease and 60% do not. So 400 have cancer, and 600 do not. Calculate the probability of getting a false positive (P(NC|+)), a true positive (P(C|+), a false negative (P(C|)), and a true negative (P(NC|)). Use Bayes' law.

c. Imagine we have the following costs and benefits of screening. Table 1: Benefits and costs of screening (per person per year) Dollar values (1000s) Screening costs 0.1 Treatment costs (if diagnosed positive) 5 Benefit of thinking you are negative 0.1 Benefit from early treatment (if sick only) 10 Cost of bad reaction to screen 0.02 Extra cost of false positive 5.5 What are the net benefits of this screen in the population described in part a.? What about in the population from part b.? Which population benefits more (on a per-person basis)

11. (23 points) Consider a market for elbow surgery where no one in the market has insurance. Let the demand curve for elbow surgery be P = 2000 4Q. Let the supply curve for elbow surgery be P = 1000 + Q. a. Graph the supply and demand curves and find the equilibrium price and quantity. Note on the graph the consumer and producer surplus created in the market.

b. Now assume everyone in the market buys an insurance policy that pays for 75% of any elbow surgery (so the coinsurance rate is 0.25). Redraw the graph from part a. above and add the effective demand curve now that everyone has insurance. What is the new equilibrium price and quantity? On the graph, illustrate consumer and producer surplus as well as any dead-weight loss that may result from moral hazard.

Fisher-Price Toys Company sells a variety of new and innovative children's toys. Management Learned that the preholiday season is the best time to introduce a new toy, because many families use this time to look for new ideas for December holiday gifts. When Fisher-Price discovers a new toy with good market potential, it chooses on October market entry date.

In order to get toys in its stores by October, Fisher-Price places one-time orders with its manufacturers in June or July of each year. Demand for children's toys can be highly volatile. If a new toy catches on, a sense of shortage in the marketplace often increases the demand to high levels and large profits can be realized. However, new toys can also flop, leaving Fisher-Price stuck with high levels of inventory that must be sold at reduced process. The most important question that company faces is deciding how many units of a new toy should be purchased to meet anticipated sales demand. If too few are purchased, sales will be lost; if too many are purchased, profits will be reduced because of low prices realized in clearance sales.

For the coming season, Fisher-Price plans to introduce a new product called Weather Teddy. This variation of a talking teddy bear is made by a company in Taiwan. When a child pressed Teddy's hand, the bear begins to talk. A built-in barometer selects one of five responses that predict the conditions. The responses range from "It looks to be a very nice day! Have Fun" to "I think it may rain today. Don't forget your umbrella." Tests with the product show that, even though it is not a perfect weather predictor, its predictions are surprisingly good. Several of Fisher-Price's managers claimed Teddy gave predictions of the weather that were as good as many local television weather forecasters.

As with other products, Fisher-Price faces the decision of how many Weather Teddy units to order for the coming holiday season. Members of the management team suggested order quantities of 15,000, 18,000, 24,000, or 28,000 units. The wide range of order quantities suggested indicates considerable disagreement concerning the market potential. The product management team asks you for an analysis of the stock-out probabilities for various order quantities, an estimate of the profit potential, and to help make an order quantity recommendation. Fisher-Price expects to sell Weather Teddy for $24 based on a cost of $16 per unit. If inventory remains after the holiday season, Fisher-Price will sell all surplus inventory for $5 per unit. After reviewing the sales history of similar products, Fisher-Price's senior sales forecaster predicted an expected demand of 20,000 units with a .95 probability that demand would be between 10,000 units and 30,000 units.

Question 1. Use the sales forecaster's prediction to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation.

I need to figure out how to calculate the Z-score using excel.

Let 'X' be the demand for the toy.

X has normal distribution with mean= 20000 and standard deviation

P(10000 < X < 30000) = 0.95

p((10000-20000) / < (X-20000)/ < (30000-20000)/) = 0.95

From tables of areas under the standard normal curve (30000-20000)/ = 1.96

How do i derive the below answer 1.96 via excel?