4. (16 pts.) Consider an oligopoly in which firms choose quantities. The inverse market demand curve is given by P = 300 - (X + Y), where X is the quantity of Firm 1, and Y is the quantity of Firm 2. Firm I's marginal cost equals 40, and Firm 2's marginal cost equals 20. a) In a simultaneous Cournot duopoly, what are the best response functions of the firms? Graph them. (3 pts.) b) What is the Cournot equilibrium output for each firm? What is the market price at the Cournot equilibrium? What is the profit of each firm? (5 pts) c) What is the Stackelberg equilibrium output for each firm when Firm 1 decides its output first? What is the market price and each firm's profit? (5 pts) d) Between the above Cournot duopoly and Stackelberg duopoly from part c), which duopoly is preferred by the consumers and why? Which duopoly do firms prefer? (3 pts.)People who get angry easily tend to have more heart disease. That is the conclusion of a study that followed a random sample of 12,986 people from three locations for about four years. All subjects were free of heart disease at the beginning of the study. The subjects took the Spielberger Trait Anger Scale test, which measures how prone a person is to sudden anger. Displayed are data for the 8474 people in the sample who had normal blood pressure. CHD stands for "coronary heart disease," which includes people who had heart attacks and those who needed medical treatment for heart disease. Low anger Moderate anger High anger Total CHD 53 110 27 190 No CHD 3057 4621 606 8284 Total 3110 4731 633 8474 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV Crunchit! Does the data support the study's conclusion about the relationship between anger and heart disease? STATE: Is the level of anger associated with coronary heart disease (CHD)? PLAN: The chi-square tests the null hypothesis. "There is no relationship between anger level and coronary heart disease (CHD)." SOLVE: Are the conditions for using the chi-square test met? O Yes No Question Source: Baldi de - The Practice Of Statistics In The Life Sciences Publisher W.H. FrePART 3: Control Group - Data organization and Analysis DATA SET 2: CONTROL GROUP (Assume that q is unknown). 196 232 200 242 206 178 184 198 160 182 182 198 182 238 198 188 166 204 182 178 212 164 230 186 162 182 218 170 200 176 1) Construct a frequency distribution using 6 classes. 2) Construct a frequency histogram. 3) Describe the shape of the histogram. 4) Use your calculator to find the sample mean and sample standard deviation for the data set. 5) Determine the five number summary for the data set. 6) Find all of the outliers in the data set. Justify your answer. 7) Construct a box plot for the data set. 8) Determine the percentile of a person who is not a heart attack patient and who has a cholesterol level of 242 mg/dL. 9) Determine the z score of a person who is not a heart attack patient and who has a cholesterol level of 242 mg/dL. Is this level unusual? Explain your answer. PART 4: Control Group - Data Interpretation 1) Construct a 95% confidence interval for the population mean cholesterol level of people who have not had a heart attack. Show all work, and interpret the interval. 2) According to the Center for Disease Control (CDC), the normal cholesterol level for US adults is 199 mg/dL. At the .10 level of significance, test the claim that the mean cholesterol level of people who have not had a heart attack is normal. Show all work. 3) According to the Center for Disease Control (CDC), a high cholesterol level for US adults is greater than 240 mg/dL. At the . 10 level of significance, test the claim that the mean cholesterol level of people who have not had a heart attack is high. Show all work.5. Friedman and Rosenman (1974) have suggested that personality type is related to heart disease. Specifically, Type A people, who are competitive, driven, pressured, and impatient, are more prone to heart disease. On the other hand, Type B individuals, who are less competitive and more relaxed, are less likely to have heart disease. Suppose that an investigator would like to examine the relationship between personality type and disease. For a random sample of individuals, personality is assessed with a standardized test. These individuals are then examined and categorized as to whether they have a heart disorder. The observed frequencies are as follows. No heart disease Heart disease Type A 32 18 50 Type B 128 22 150 160 40 Is there a relationship between personality and heart disease? Test at the 05 level of significance.3 45 points I am considering opening up a smoothie stand in Walla Walla,* During this process I need help analyzing the inner workings of my firm as well as the Walla Walla labor market when making hiring decisions. (a) (5 points) Draw typical marginal cost and average total cost curves for a firm's output. Describe the shape of the average total cost curve. (b) (5 points) How does the market for inputs (e.g. labor, bananas, strawberries) differ from the market for outputs (e.g. smoothies)? Why do we treat the input market a bit differently? Briefly Explain. (c) (7 points) Assume the labor market is perfectly competitive. Provide the profit (or value) maximizing condition that my smoothie stand must satisfy when hiring labor. Describe each component. (d) (7 points) Describe how the supply of labor can potentially respond differently than the supply of other inputs as a result of an increase in the input price. (e) (7 points) Suppose that Walla Walla is considering an increase in the minimum wage (which I was going to pay the smoothie stand workers). Draw the supply and demand for a perfectly competitive labor market. Now describe why some may feel that an increase in the minimum wage may introduce inefficiencies. (f) (7 points) Given that I have yet to see another smoothie stand in Walla Walla it may be that my firm is the only one hiring this type of specialized smoothie labor. Depict this type of labor market on a graph. Describe why the relationship between what I spend on labor on average and my additional expenditure on labor is the way you have drawn it. (g) (7 points) Would a minimum wage have the same effect in part (f) as it did in part (e)? Why or Why not? Briefly Explain. 4 40 points