Given the Demand function from Part 1: D(p) = 64 2p , The monopolist's cost is equal to C(Q) = Q2 + 2Q:

PART II. Now take the same demand function as in Part I but imagine that the market has two firms instead of 1. Also assume that the marginal cost of each firm is equal to 4. Market structure is therefore characterized as a duopoly. Suppose that firms compete by choosing their output levels simultaneously.

(14) (2 points) Write down the profit expressions of Firms 1 and 2.
(15) (4 points) Derive the best-response functions of Firms 1 and 2.
(16) (3 points) Plot the best-response functions of Firms 1 and 2.
(17) (2 points) Find the output choice of each firm. Show it on the graph you drew in (17). For 18-19, first state if the statement is True or False. Then, give a brief explanation.

(18) (3 points) Oligopolies create less deadweight loss than monopolies.
(19) (3 points) Consider a duopoly where firms compete by choosing quantities one after the other. The firm which makes its output choice first, enjoys more profits as it can set a higher price.

Types of data: are they nominal, ordinal, interval, or ratio? And are they categorical or continuous?

1. Gender (1=female/2=male)- my answers are nominal and categorical
2. Work status (1=part-time/2=full-time) - my answers are nominal and categorical
3. Hours worked per week (1 through 99 hours) - my answers are ratio and continuous
4. Region (1=Northwest/2=West/3=Southwest/4=Midwest) - my answers are nominal and categorical
5. Performance (1=below avg/2=avg/3=above avg) - my answers are ordinal and continuous
6. Organizational commitment (1=not at all through 7=very committed) - my answers are ordinal and continuous
7. Training program (1=new/2=old) - my answers are nominal and categorical
8. Turnover intentions (1=never through 7= frequently) - my answers are ordinal and continuous

1. Using the following table of relation between X & Y (Y is the independent Variable):

xi -2 2 4 5 4 6 7 8 11

yi -4 1 3 1 3 8 10 20 30

a. Find the estimated regression equation. Show ALL your calculations and the appropriate formula. WRITE Formula in all the questions below and substitute for the numbers, demonstrate your work.

b. Calculate R2. Comment on the Goodness of the Fit. Is it a good fit? Why?

c. Test the hypothesis regarding the significance of the slope β1. (Use α = 0.05) Show ALL the calculations necessary to get your answer. Hint: You need to calculate t by using all the formulas needed for it using t in the Formula Sheet.

d. Calculate the values of F, using formula for F statistics. e. Draw the scatter diagram and also your estimated regression line in a diagram.

Calculate the benefit, based on the forward rate agreements, that an investor can derive if his / her expectations of future interest rate movements are verified:

a. 3% after two months

b. 2.8% after three months

c. 2.5% after one month

d. 1% after five months

e. 2.9% after six months

1. A researcher wishes to see whether there is any difference in the weight gains of athletes following one of three special diets. Athletes are randomly assigned to three groups and placed on the diet for 6 weeks. The weight gains (in pounds) are shown here. At α = 0.05, can the researcher conclude that there is a difference in the diets?

Diet A             Diet B             Diet C             Total

                        3                      10                   8

6                      12                   3

7                      11                   2

4                      14                   5

                                    8

                                    6

the critical value = 3.98

Conclusion:

Analysis of Variance Summary Table

P-value

Source                             Sum of Squares       D.F.    Mean Square F ratio p-value

Between groups                      

Within                            

SSB                                                           SSW   

MSB = SSBk-1                                               MSW=SSWN-k

F = MSBMSW

ANOVA 1 TUKEY B

                                    ID         N

                                    ____________________________

                                    3           4       4.50

                                        ____________________________

                                    1          4          5.00             

                                    ____________________________

                                    2          6                                  10.17

                                    _____________________________

                                    Sig.                 .954               1.00

A statewide census examined the number of beds in households and reported a mean (μ) of 2.25 beds and standard deviation (σ) of 1.9 beds per household. But, since I live in a neighborhood with larger families, I have a hunch that the average number of beds in households will be higher in my neighborhood. To test this idea, I randomly picked 25 families in my neighborhood and surveyed them on the number of beds in their home. I would like to perform a Z test to see if the average number of beds in households in my neighborhood is significantly higher than the statewide average. The significance level for my Z test was set at α = .10.

a) What is the dependent variable in this study? b) What should be my null and alternative hypotheses? State each hypothesis using both words and statistical notation. Hint: I am interested in the idea of my neighbors having more beds per household than the state average, so the hypotheses would be directional. c) Calculate the sample mean. d) Calculate standard error (SE, which is the standard deviation of the sampling distribution) e) Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) f) Specify whether the hypothesis test should be a two-tailed or a one-tailed test, and explain the rationale for the choice. g) Determine the critical value for Z h) Compare obtained Z and critical Z and then make a decision about the result of the hypothesis test: Explicitly state “reject” or “fail to reject” the null hypothesis i) Write a 1-2 sentence conclusion interpreting the results (you can simply restate the accepted hypothesis or explain it in another way) j) Calculate the raw and standardized effect sizes k) If the test was done with α level of .05, using the same directional hypotheses, what would be the critical Z value from the Z table? What would be the result of the hypothesis test (in terms of rejecting or failing to reject the null hypothesis)? l) Compare the hypothesis tests result when α = .05 and when α = .10. Were the results the same? Why or why not?

Problem #2

1) Conduct an independent-measures t-test using the following data set:

Group 1: 12 10 15 12 4 16 6 10 8

Group 2: 8 5 9 0 6 5 0 1

-

2) Determine the critical values (for an alpha of .05) that you should use to evaluate this t-score.

Please be clear with your steps on how you solved. How did you get each number and whether or not the hypothesis is rejected.

Suppose the Fed is considering two different policy rules, shown in the following table. Graph the policy rules.

Inflation(0 2 4 6 8 ) Policy Rule 1 Interest Rate (1 3 5 7 9)Policy Rule 2 Interest Rate (3 5 7 9 11)

If the Fed currently is following Policy Rule 1 and then shifts to Policy Rule 2, which way will the aggregate demand curve shift? What reasons might the Fed have for changing its policy?

18. A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:

a. Find the sample regression equation for the model: Salary = β₀ + β₁Education + ε. (Round answers to 3 decimal places.)

Salaryˆ=Salary^=    +   Education

b. Interpret the coefficient for Education.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $5,991.

• As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $5,991.

• As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.

c. What is the predicted salary for an individual who completed 6 years of higher education? (Round answer to the nearest whole number.)

SalaryˆSalary^               $